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An Infinitely Large Napkin RZP28ERRZV

URIm2://res/RZP28ERRZV
Kindtextbook
CreatorsEvan Chen
Date2026-10-23
MSC00-01
Scopein

Expressions

e1: edition

Languageen
Date2026-10-23
Contents
  • chapter 1: Group actions overkill AIME problems
  • section 1.1: Definition of a group action
  • section 1.2: Stabilizers and orbits
  • section 1.3: Burnside's lemma
  • section 1.4: Conjugation of elements
  • chapter 2: Groups
  • section 2.1: Definition and examples of groups
  • section 2.2: Properties of groups
  • section 2.3: Isomorphisms
  • section 2.4: Orders of groups, and Lagrange's theorem
  • section 2.5: Subgroups
  • section 2.6: Groups of small orders
  • section 2.7: Unimportant long digression
  • section 2.8: \problemhead
  • chapter 3: Homomorphisms and quotient groups
  • section 3.1: Generators and group presentations
  • section 3.2: Homomorphisms
  • section 3.3: Cosets and modding out
  • section 3.4: (Optional) Proof of Lagrange's theorem
  • section 3.5: Eliminating the homomorphism
  • section 3.6: (Digression) The first isomorphism theorem
  • chapter 4: Flavors of rings
  • section 4.1: Fields
  • section 4.2: Integral domains
  • section 4.3: Prime ideals
  • section 4.4: Maximal ideals
  • section 4.5: Field of fractions
  • section 4.6: Unique factorization domains (UFD's)
  • section 4.7: Extra: Euclidean domains
  • section 4.8: \problemhead
  • chapter 5: Rings and ideals
  • section 5.1: Some motivational metaphors about rings vs groups
  • section 5.2: (Optional) Pedagogical notes on motivation
  • section 5.3: Definition and examples of rings
  • section 5.4: Fields
  • section 5.5: Homomorphisms
  • section 5.6: Ideals
  • section 5.7: Generating ideals
  • section 5.8: Principal ideal domains
  • section 5.9: Noetherian rings
  • section 5.10: \problemhead
  • chapter 6: The PID structure theorem
  • section 6.1: Finitely generated abelian groups
  • section 6.2: Some ring theory prerequisites
  • section 6.3: The structure theorem
  • section 6.4: Reduction to maps of free $R$-modules
  • section 6.5: Uniqueness of primary form
  • section 6.6: Smith normal form
  • chapter 7: Find all groups
  • section 7.1: Sylow theorems
  • section 7.2: (Optional) Proving Sylow's theorem
  • subsection 7.2.1: Definitions
  • subsection 7.2.2: Step 1: Prove that a Sylow $p$-subgroup exists
  • subsection 7.2.3: Step 2: Any two Sylow $p$-subgroups are conjugate
  • subsection 7.2.4: Step 3: Showing $n_p \equiv 1 \pmod p$
  • subsection 7.2.5: Step 4: $n_p$ divides $m$
  • section 7.3: (Optional) Simple groups and Jordan-H\"older
  • chapter 8: Bonus: A Bit on Artin Reciprocity
  • section 8.1: Overview
  • section 8.2: Infinite primes
  • section 8.3: Modular arithmetic with infinite primes
  • section 8.4: Infinite primes in extensions
  • section 8.5: Frobenius element and Artin symbol
  • section 8.6: Artin reciprocity
  • section 8.7: Application: Generalization of sum of two squares
  • section 8.8: \problemhead
  • chapter 9: Minkowski bound and class groups
  • section 9.1: The class group
  • section 9.2: The discriminant of a number field
  • section 9.3: The signature of a number field
  • section 9.4: Minkowski's theorem
  • section 9.5: The trap box
  • section 9.6: The Minkowski bound
  • section 9.7: The class group is finite
  • section 9.8: Computation of class numbers
  • section 9.9: Optional: Proof that $\OO_K$ is a free $\ZZ$-module
  • subsection 9.9.1: First proof
  • subsection 9.9.2: Second proof
  • subsection 9.9.3: Third proof
  • chapter 10: Unique factorization (finally!)
  • section 10.1: Motivation
  • section 10.2: Ideal arithmetic
  • section 10.3: Dedekind domains
  • section 10.4: Unique factorization works
  • section 10.5: The factoring algorithm
  • section 10.6: Fractional ideals
  • section 10.7: The ideal norm
  • chapter 11: More properties of the discriminant
  • chapter 12: Finite fields
  • section 12.1: Example of a finite field
  • section 12.2: Finite fields have prime power order
  • section 12.3: All finite fields are isomorphic
  • section 12.4: The Galois theory of finite fields
  • section 12.5: Extra: The multiplicative group of a finite field
  • chapter 13: The Frobenius element
  • section 13.1: Frobenius elements
  • section 13.2: Conjugacy classes
  • section 13.3: Chebotarev density theorem
  • section 13.4: Example: Frobenius elements of cyclotomic fields
  • section 13.5: Frobenius elements behave well with restriction
  • section 13.6: Application: Quadratic reciprocity
  • subsection 13.6.1: Step 1: Setup
  • subsection 13.6.2: Step 2: Reformulation
  • subsection 13.6.3: Step 3: Introducing the Frobenius
  • subsection 13.6.4: Finishing up
  • section 13.7: Frobenius elements control factorization
  • section 13.8: Example application: IMO 2003 problem 6
  • chapter 14: Things Galois
  • section 14.1: Motivation
  • section 14.2: Field extensions, algebraic extension, and splitting fields
  • section 14.3: Embeddings into algebraic closures for number fields
  • section 14.4: Everyone hates characteristic 2: separable vs irreducible
  • section 14.5: Automorphism groups and Galois extensions
  • section 14.6: Fundamental theorem of Galois theory
  • section 14.7: (Optional) Proof that Galois extensions are splitting
  • chapter 15: The ring of integers
  • section 15.1: Norms and traces
  • section 15.2: The ring of integers
  • section 15.3: On monogenic extensions
  • section 15.4: \problemhead
  • chapter 16: Algebraic integers
  • section 16.1: Motivation from high school algebra
  • section 16.2: Algebraic numbers and algebraic integers
  • section 16.3: Number fields
  • section 16.4: Primitive element theorem, and monogenic extensions
  • section 16.5: \problemhead
  • chapter 17: Bonus: Let's solve Pell's equation!
  • section 17.1: Units
  • section 17.2: Dirichlet's unit theorem
  • section 17.3: Finding fundamental units
  • section 17.4: Pell's equation
  • chapter 18: Ramification theory
  • section 18.1: Ramified / inert / split primes
  • section 18.2: Primes ramify if and only if they divide $\Delta_K$
  • section 18.3: Inertial degrees
  • section 18.4: The magic of Galois extensions
  • section 18.5: (Optional) Decomposition and inertia groups
  • section 18.6: Tangential remark: more general Galois extensions
  • chapter 19: Affine varieties
  • section 19.1: Affine varieties
  • section 19.2: Naming affine varieties via ideals
  • section 19.3: Radical ideals and Hilbert's Nullstellensatz
  • section 19.4: Pictures of varieties in $\Aff^1$
  • section 19.5: Prime ideals correspond to irreducible affine varieties
  • section 19.6: Pictures in $\Aff^2$ and $\Aff^3$
  • section 19.7: Maximal ideals
  • section 19.8: Motivating schemes with non-radical ideals
  • chapter 20: Bonus: B\'ezout's theorem
  • section 20.1: Non-radical ideals
  • section 20.2: Hilbert functions of finitely many points
  • section 20.3: Hilbert polynomials
  • section 20.4: B\'ezout's theorem
  • section 20.5: Applications
  • chapter 21: Localization
  • section 21.1: Spoilers
  • section 21.2: The definition
  • section 21.3: Localization away from an element
  • section 21.4: Localization at a prime ideal
  • section 21.5: Prime ideals of localizations
  • section 21.6: Prime ideals of quotients
  • section 21.7: Localization commutes with quotients
  • section 21.8: \problemhead
  • chapter 22: Morphisms of locally ringed spaces
  • section 22.1: Morphisms of ringed spaces via sections
  • section 22.2: Morphisms of ringed spaces via stalks
  • section 22.3: Morphisms of locally ringed spaces
  • section 22.4: A few examples of morphisms between affine schemes
  • subsection 22.4.1: One-point schemes
  • subsection 22.4.2: Examples of constant maps
  • subsection 22.4.3: The map $t \mapsto t^2$
  • subsection 22.4.4: An arithmetic example
  • section 22.5: The big theorem
  • section 22.6: More examples of scheme morphisms
  • section 22.7: A little bit on non-affine schemes
  • section 22.8: Where to go from here
  • section 22.9: \problemhead
  • section 22.10: Projective scheme
  • section 22.11: Morphisms of sheaves
  • chapter 23: Projective varieties
  • section 23.1: Graded rings
  • section 23.2: The ambient space
  • section 23.3: Homogeneous ideals
  • section 23.4: As ringed spaces
  • section 23.5: Examples of regular functions
  • chapter 24: Morphisms of varieties
  • section 24.1: Defining morphisms of baby ringed spaces
  • section 24.2: Classifying the simplest examples
  • subsection 24.2.1: Affine classification
  • subsection 24.2.2: Projective classification
  • section 24.3: Some more applications and examples
  • section 24.4: The hyperbola effect
  • chapter 25: Sheaves and ringed spaces
  • section 25.1: Motivation and warnings
  • section 25.2: Pre-sheaves
  • subsection 25.2.1: Usual definition
  • subsection 25.2.2: Categorical definition
  • section 25.3: Stalks and germs
  • section 25.4: Sheaves
  • section 25.5: For sheaves, sections ``are'' sequences of germs
  • section 25.6: Sheafification (optional)
  • chapter 26: Interlude: eighteen examples of affine schemes
  • section 26.1: Example: $\Spec k$, a single point
  • section 26.2: $\Spec \CC[x]$, a one-dimensional line
  • section 26.3: $\Spec \RR[x]$, a one-dimensional line with complex conjugates glued (no fear nullstellensatz)
  • section 26.4: $\Spec k[x]$, over any ground field
  • section 26.5: $\Spec \ZZ$, a one-dimensional scheme
  • section 26.6: $\Spec k[x] / (x^2-7x+12)$, two points
  • section 26.7: $\Spec k[x]/(x^2)$, the double point
  • section 26.8: $\Spec k[x]/(x^3-5x^2)$, a double point and a single point
  • section 26.9: $\Spec \Zc{60}$, a scheme with three points
  • section 26.10: $\Spec k[x,y]$, the two-dimensional plane
  • section 26.11: $\Spec \ZZ[x]$, a two-dimensional scheme, and Mumford's picture
  • section 26.12: $\Spec k[x,y]/(y-x^2)$, the parabola
  • section 26.13: $\Spec \ZZ[i]$, the Gaussian integers (one-dimensional)
  • section 26.14: Long example: $\Spec k[x,y]/(xy)$, two axes
  • subsection 26.14.1: Picture
  • subsection 26.14.2: Throwing out the $y$-axis
  • subsection 26.14.3: Stalks above some points
  • subsection 26.14.4: Stalk above the origin (tricky)
  • section 26.15: $\Spec k[x,x\inv]$, the punctured line (or hyperbola)
  • section 26.16: $\Spec k[x]_{(x)}$, zooming in to the origin of the line
  • section 26.17: $\Spec k[x,y]_{(x,y)}$, zooming in to the origin of the plane
  • section 26.18: $\Spec k[x,y]_{(0)} = \Spec k(x,y)$, the stalk above the generic point
  • section 26.19: \problemhead
  • chapter 27: Affine schemes: the sheaf
  • section 27.1: A useless definition of the structure sheaf
  • section 27.2: The value of distinguished open sets (or: how to actually compute sections)
  • subsection 27.2.1: A basis of the Zariski topology
  • subsection 27.2.2: Sections are computable
  • subsection 27.2.3: They are affine
  • subsection 27.2.4: Classic example: the punctured plane
  • section 27.3: The stalks of the structure sheaf
  • subsection 27.3.1: They are localizations
  • subsection 27.3.2: Motivating local rings: germs should package values
  • section 27.4: Local rings and residue fields: linking germs to values
  • subsection 27.4.1: Localizations give local rings
  • subsection 27.4.2: Computing values: a convenient square
  • section 27.5: Recap
  • section 27.6: Functions are determined by germs, not values
  • section 27.7: \problemhead
  • chapter 28: Affine schemes: the Zariski topology
  • section 28.1: Some more advertising
  • section 28.2: The set of points
  • section 28.3: The Zariski topology on the spectrum
  • section 28.4: Krull dimension
  • section 28.5: On radicals
  • section 28.6: \problemhead
  • chapter 29: Affine varieties as ringed spaces
  • section 29.1: Synopsis
  • section 29.2: The Zariski topology on $\Aff^n$
  • section 29.3: The Zariski topology on affine varieties
  • section 29.4: Coordinate rings
  • section 29.5: The sheaf of regular functions
  • section 29.6: Regular functions on distinguished open sets
  • section 29.7: Baby ringed spaces
  • chapter 30: Differentiation
  • section 30.1: Definition
  • section 30.2: How to compute them
  • section 30.3: Local (and global) maximums
  • section 30.4: Rolle and friends
  • section 30.5: Smooth functions
  • section 30.6: \problemhead
  • chapter 31: Riemann integrals
  • section 31.1: Uniform continuity
  • section 31.2: Dense sets and extension
  • section 31.3: Defining the Riemann integral
  • section 31.4: Meshes
  • section 31.5: \problemhead
  • chapter 32: Limits and series
  • section 32.1: Completeness and inf/sup
  • section 32.2: Proofs of the two key completeness properties of $\RR$
  • section 32.3: Monotonic sequences
  • section 32.4: Infinite series
  • section 32.5: Series addition is not commutative: a horror story
  • section 32.6: Limits of functions at points
  • section 32.7: Limits of functions at infinity
  • section 32.8: \problemhead
  • chapter 33: Bonus: A hint of $p$-adic numbers
  • section 33.1: Motivation
  • section 33.2: Algebraic perspective
  • subsection 33.2.1: Definition of $\ZZ_p$
  • subsection 33.2.2: Base $p$ expansion
  • subsection 33.2.3: Constructing $\QQ_p$
  • section 33.3: Analytic perspective
  • subsection 33.3.1: Definition
  • subsection 33.3.2: Ultrametric space
  • subsection 33.3.3: More fun with geometric series
  • subsection 33.3.4: Completeness
  • subsection 33.3.5: Philosophical notes
  • section 33.4: Mahler coefficients
  • section 33.5: \problemhead
  • chapter 34: Power series and Taylor series
  • section 34.1: Motivation
  • section 34.2: Power series
  • section 34.3: Differentiating them
  • section 34.4: Analytic functions
  • section 34.5: A definition of Euler's constant and exponentiation
  • section 34.6: This all works over complex numbers as well, except also complex analysis is heaven
  • section 34.7: \problemhead
  • chapter 35: Abelian categories
  • section 35.1: Zero objects, kernels, cokernels, and images
  • section 35.2: Additive and abelian categories
  • section 35.3: Exact sequences
  • section 35.4: The Freyd-Mitchell embedding theorem
  • section 35.5: Breaking long exact sequences
  • chapter 36: Objects and morphisms
  • section 36.1: Motivation: isomorphisms
  • section 36.2: Categories, and examples thereof
  • section 36.3: Special objects in categories
  • section 36.4: Binary products
  • section 36.5: Monic and epic maps
  • chapter 37: Functors and natural transformations
  • section 37.1: Many examples of functors
  • section 37.2: Covariant functors
  • section 37.3: Covariant functors as indexed family of objects
  • section 37.4: Contravariant functors
  • section 37.5: Equivalence of categories
  • section 37.6: (Optional) Natural transformations
  • section 37.7: (Optional) The Yoneda lemma
  • chapter 38: Limits in categories (TO DO)
  • section 38.1: Equalizers
  • section 38.2: Pullback squares (TO DO)
  • section 38.3: Limits
  • section 38.4: \problemhead
  • chapter 39: Holomorphic functions
  • section 39.1: The nicest functions on earth
  • section 39.2: Complex differentiation
  • section 39.3: Contour integrals
  • section 39.4: Cauchy-Goursat theorem
  • section 39.5: Cauchy's integral theorem
  • section 39.6: Holomorphic functions are analytic
  • section 39.7: Optional: Proof that holomorphic functions are analytic
  • subsection 39.7.1: Proof of Cauchy-Goursat theorem
  • subsection 39.7.2: The rest
  • chapter 40: Holomorphic square roots and logarithms
  • section 40.1: Motivation: square root of a complex number
  • section 40.2: Square roots of holomorphic functions
  • section 40.3: Covering projections
  • section 40.4: Complex logarithms
  • section 40.5: Some special cases
  • chapter 41: Meromorphic functions
  • section 41.1: The second nicest functions on earth
  • section 41.2: Meromorphic functions
  • section 41.3: Winding numbers and the residue theorem
  • section 41.4: Argument principle
  • section 41.5: Digression: the Argument Principle viewed geometrically
  • section 41.6: Philosophy: why are holomorphic functions so nice?
  • chapter 42: Bonus: Topological Abel-Ruffini Theorem
  • section 42.1: The Game Plan
  • section 42.2: Step 1: The Simplest Case
  • section 42.3: Step 2: Nested Roots
  • section 42.4: Step 3: Normal Groups
  • section 42.5: Summary
  • chapter 43: Differential forms
  • section 43.1: Pictures of differential forms
  • section 43.2: Pictures of exterior derivatives
  • section 43.3: Differential forms
  • section 43.4: Exterior derivatives
  • section 43.5: Digression: $\bigwedge^k(V^\vee)$ versus $(\bigwedge^k(V))^\vee$
  • section 43.6: Tangential remark: Arc length $ds$ is not a $1$-form
  • section 43.7: Closed and exact forms
  • chapter 44: A bit of manifolds
  • section 44.1: Topological manifolds
  • section 44.2: Smooth manifolds
  • section 44.3: Regular value theorem
  • section 44.4: Differential forms on manifolds
  • section 44.5: Orientations
  • section 44.6: Stokes' theorem for manifolds
  • section 44.7: (Optional) The tangent and cotangent space
  • subsection 44.7.1: Tangent space
  • subsection 44.7.2: The cotangent space
  • subsection 44.7.3: Sanity check
  • chapter 45: Multivariable calculus done correctly
  • section 45.1: The total derivative
  • section 45.2: The projection principle
  • section 45.3: Total and partial derivatives
  • section 45.4: (Optional) A word on higher derivatives
  • section 45.5: Towards differential forms
  • chapter 46: Integrating differential forms
  • section 46.1: Motivation: line integrals
  • section 46.2: Pullbacks
  • section 46.3: Cells
  • section 46.4: Boundaries
  • section 46.5: Stokes' theorem
  • section 46.6: Back to Earth: A comparison to what you learned in vector calculus
  • chapter 47: Advice for the reader
  • section 47.1: Prerequisites
  • section 47.2: Deciding what to read
  • section 47.3: Questions, exercises, and problems
  • section 47.4: Paper
  • section 47.5: On the importance of examples
  • section 47.6: Conventions and notations
  • subsection 47.6.1: Natural numbers are positive
  • subsection 47.6.2: Sets and equivalence relations
  • subsection 47.6.3: Functions
  • subsection 47.6.4: Cycle notation for permutations
  • subsection 47.6.5: Rings
  • subsection 47.6.6: Choice
  • section 47.7: Further reading
  • chapter 48: Preface
  • section: About this book
  • section: Source code
  • section: Philosophy behind the Napkin approach
  • section: More pedagogical comments and references
  • section: Historical and personal notes
  • section: Acknowledgements
  • chapter 49: Sales pitches
  • section 49.1: The basics
  • section 49.2: Abstract algebra
  • section 49.3: Real and complex analysis
  • section 49.4: Algebraic number theory
  • section 49.5: Algebraic topology
  • section 49.6: Algebraic geometry
  • section 49.7: Set theory
  • chapter 50: Bonus: Cellular homology
  • section 50.1: Degrees
  • section 50.2: Cellular chain complex
  • section 50.3: Digression: why are the homology groups equal?
  • section 50.4: Application: Euler characteristic via Betti numbers
  • section 50.5: The cellular boundary formula
  • chapter 51: Singular cohomology
  • section 51.1: Cochain complexes
  • section 51.2: Cohomology of spaces
  • section 51.3: Cohomology of spaces is functorial
  • section 51.4: Universal coefficient theorem
  • section 51.5: Explanation for universal coefficient theorem
  • section 51.6: Example computation of cohomology groups
  • section 51.7: Visualization of cohomology groups
  • section 51.8: Relative cohomology groups
  • chapter 52: Application of cohomology
  • section 52.1: Poincar\'e duality
  • section 52.2: de Rham cohomology
  • section 52.3: Graded rings
  • section 52.4: Cup products
  • section 52.5: Relative cohomology pseudo-rings
  • section 52.6: Wedge sums
  • section 52.7: Cross product
  • subsection 52.7.1: Motivation
  • subsection 52.7.2: Cross product on singular homology
  • subsection 52.7.3: Cross product is not a $\ZZ$-module homomorphism
  • subsection 52.7.4: Cross product on cellular homology
  • subsection 52.7.5: Cross product on cellular cohomology
  • subsection 52.7.6: Motivation: cross product of differential forms
  • subsection 52.7.7: Piecing the cohomology groups together
  • section 52.8: K\"unneth formula
  • chapter 53: Excision and relative homology
  • section 53.1: Motivation
  • section 53.2: The long exact sequences
  • section 53.3: The category of pairs
  • section 53.4: Excision
  • section 53.5: Some applications
  • section 53.6: Invariance of dimension
  • chapter 54: The long exact sequence
  • section 54.1: Short exact sequences and four examples
  • section 54.2: The long exact sequence of homology groups
  • section 54.3: The Mayer-Vietoris sequence
  • chapter 55: Singular homology
  • section 55.1: Simplices and boundaries
  • section 55.2: The singular homology groups
  • section 55.3: The homology functor and chain complexes
  • subsection 55.3.1: Algebra of chain complexes
  • subsection 55.3.2: Geometry of chain complexes
  • section 55.4: More examples of chain complexes
  • chapter 56: Determinant
  • section 56.1: Wedge product
  • section 56.2: The determinant
  • section 56.3: Characteristic polynomials, and Cayley-Hamilton
  • chapter 57: Dual space and trace
  • section 57.1: Tensor product
  • section 57.2: Dual space
  • section 57.3: $V^\vee \otimes W$ gives matrices from $V$ to $W$
  • section 57.4: The trace
  • section 57.5: \problemhead
  • chapter 58: Eigen-things
  • section 58.1: Why you should care
  • section 58.2: Warning on assumptions
  • section 58.3: Eigenvectors and eigenvalues
  • section 58.4: The Jordan form
  • section 58.5: Nilpotent maps
  • section 58.6: Reducing to the nilpotent case
  • section 58.7: (Optional) Proof of nilpotent Jordan
  • section 58.8: Algebraic and geometric multiplicity
  • chapter 59: Bonus: Fourier analysis
  • section 59.1: Synopsis
  • section 59.2: A reminder on Hilbert spaces
  • section 59.3: Common examples
  • subsection 59.3.1: Binary Fourier analysis on $\{\pm1\}^n$
  • subsection 59.3.2: Fourier analysis on finite groups $Z$
  • subsection 59.3.3: Fourier series for functions $L^2([-\pi, \pi])$
  • section 59.4: Summary, and another teaser
  • section 59.5: Parseval and friends
  • section 59.6: Application: Basel problem
  • section 59.7: Application: Arrow's Impossibility Theorem
  • section 59.8: \problemhead
  • chapter 60: Inner product spaces
  • section 60.1: The inner product
  • subsection 60.1.1: For real numbers: bilinear forms
  • subsection 60.1.2: For complex numbers: sesquilinear forms
  • subsection 60.1.3: Inner product space
  • section 60.2: Norms
  • section 60.3: Orthogonality
  • section 60.4: Hilbert spaces
  • section 60.5: \problemhead
  • chapter 61: Duals, adjoint, and transposes
  • section 61.1: Dual of a map
  • section 61.2: (Optional) A cautionary tale on what goes wrong if you don't have a natural isomorphism $V \cong V^\vee$
  • section 61.3: Identifying with the dual space
  • section 61.4: The adjoint (conjugate transpose)
  • section 61.5: Eigenvalues of normal maps
  • section 61.6: \problemhead
  • chapter 62: Vector spaces
  • section 62.1: The definitions of a ring and field
  • section 62.2: Modules and vector spaces
  • section 62.3: Direct sums
  • section 62.4: Linear independence, spans, and basis
  • section 62.5: Linear maps
  • section 62.6: What is a matrix?
  • subsection 62.6.1: Extended example with $\RR^2$, suitable for the general public
  • subsection 62.6.2: General discussion, back to Napkin levels of abstraction
  • section 62.7: Subspaces and picking convenient bases
  • section 62.8: A cute application: Lagrange interpolation
  • section 62.9: Pedagogical digression: Arrays of numbers are evil
  • section 62.10: A word on general modules
  • section 62.11: \problemhead
  • chapter 63: Constructing the Borel and Lebesgue measure
  • section 63.1: Pre-measures
  • section 63.2: Outer measures
  • section 63.3: Carath\'{e}odory extension for outer measures
  • section 63.4: Defining the Lebesgue measure
  • section 63.5: A fourth row: Carath\'{e}odory for pre-measures
  • section 63.6: From now on, we assume the Borel measure
  • section 63.7: \problemhead
  • chapter 64: Large number laws (TO DO)
  • section 64.1: Notions of convergence
  • subsection 64.1.1: Almost sure convergence
  • subsection 64.1.2: Convergence in probability
  • subsection 64.1.3: Convergence in law
  • section 64.2: Weak law of large numbers
  • subsection 64.2.1: Application: Weierstrass approximation
  • section 64.3: Strong law of large numbers
  • subsection 64.3.1: Motivation: Biased random walk
  • subsection 64.3.2: Statement
  • subsection 64.3.3: Proof for finite-variance case
  • subsection 64.3.4: The general proof
  • section 64.4: \problemhead
  • chapter 65: Lebesgue integration
  • section 65.1: The definition
  • section 65.2: An equivalent definition
  • section 65.3: Relation to Riemann integrals (or: actually computing Lebesgue integrals)
  • section 65.4: \problemhead
  • chapter 66: Stopped martingales (TO DO)
  • section 66.1: How to make money almost surely
  • section 66.2: Sub-$\sigma$-algebras and filtrations
  • section 66.3: Conditional expectation
  • section 66.4: Supermartingales
  • section 66.5: Optional stopping
  • section 66.6: Fun applications of optional stopping (TO DO)
  • subsection 66.6.1: The ballot problem
  • subsection 66.6.2: ABRACADABRA
  • subsection 66.6.3: USA TST 2018
  • section 66.7: \problemhead
  • chapter 67: Measure spaces
  • section 67.1: Letter connotations
  • section 67.2: Motivating measure spaces via random variables
  • section 67.3: Motivating measure spaces geometrically
  • section 67.4: $\sigma$-algebras and measurable spaces
  • section 67.5: Measure spaces
  • section 67.6: A hint of Banach-Tarski
  • section 67.7: Measurable functions
  • section 67.8: On the word ``almost''
  • section 67.9: \problemhead
  • chapter 68: Bonus: A hint of Pontryagin duality
  • section 68.1: LCA groups
  • section 68.2: The Pontryagin dual
  • section 68.3: The orthonormal basis in the compact case
  • section 68.4: The Fourier transform of the non-compact case
  • section 68.5: Summary
  • section 68.6: \problemhead
  • section 68.7: Peter-Weyl
  • chapter 69: Random variables (TO DO)
  • section 69.1: Random variables
  • section 69.2: Distribution functions
  • section 69.3: Examples of random variables
  • section 69.4: Characteristic functions
  • section 69.5: Independent random variables
  • section 69.6: \problemhead
  • chapter 70: Swapping order with Lebesgue integrals
  • section 70.1: Motivating limit interchange
  • section 70.2: Overview
  • section 70.3: Fatou's lemma
  • section 70.4: Everything else
  • section 70.5: Fubini and Tonelli
  • section 70.6: \problemhead
  • chapter 71: Working with general schemes
  • chapter 72: Projective schemes
  • chapter 73: Quasicoherent sheaves
  • chapter 74: Sheaves of $\OO_X$-modules
  • chapter 75: Quantum circuits
  • section 75.1: Classical logic gates
  • section 75.2: Reversible classical logic
  • section 75.3: Quantum logic gates
  • section 75.4: Deutsch-Jozsa algorithm
  • chapter 76: Shor's algorithm
  • section 76.1: The classical (inverse) Fourier transform
  • section 76.2: The quantum Fourier transform
  • section 76.3: Shor's algorithm
  • chapter 77: Quantum states and measurements
  • section 77.1: Bra-ket notation
  • section 77.2: The state space
  • section 77.3: Observations
  • section 77.4: Entanglement
  • chapter 78: Some applications
  • section 78.1: Frobenius divisibility
  • section 78.2: Burnside's theorem
  • section 78.3: Frobenius determinant
  • chapter 79: Characters
  • section 79.1: Definitions
  • section 79.2: The dual space modulo the commutator
  • section 79.3: Orthogonality of characters
  • section 79.4: Examples of character tables
  • chapter 80: Representations of algebras
  • section 80.1: Algebras
  • section 80.2: Representations
  • section 80.3: Direct sums
  • section 80.4: Irreducible and indecomposable representations
  • section 80.5: Morphisms of representations
  • section 80.6: The representations of $\Mat_d(k)$
  • chapter 81: Semisimple algebras
  • section 81.1: Schur's lemma continued
  • section 81.2: Density theorem
  • section 81.3: Semisimple algebras
  • section 81.4: Maschke's theorem
  • section 81.5: Example: the representations of $\CC[S_3]$
  • chapter 82: Affine and projective plane curves
  • section 82.1: Affine plane curves
  • section 82.2: The projective line $\CP^1$
  • section 82.3: Projective plane curves
  • section 82.4: Filling in the holes
  • section 82.5: Nodes of a plane curve
  • chapter 83: Basic definitions of Riemann surfaces
  • section 83.1: Complex structures
  • section 83.2: Riemann surface
  • section 83.3: Complex manifold
  • section 83.4: Examples of Riemann surfaces
  • chapter 84: Differential forms
  • section 84.1: Differential form on $\CC$
  • section 84.2: Visualization of differential forms
  • subsection 84.2.1: Holomorphic forms
  • subsection 84.2.2: Putting the pieces together: $1$-forms on a Riemann surface
  • chapter 85: Line bundles
  • section 85.1: Overview
  • section 85.2: Definition
  • section 85.3: Visualizing a line bundle
  • section 85.4: Morphisms between line bundles
  • section 85.5: Relation to invertible sheaves
  • chapter 86: Morphisms between Riemann surfaces
  • section 86.1: Definition
  • section 86.2: Functions to the Riemann sphere
  • section 86.3: Some other nice properties
  • section 86.4: Multiplicity of a map
  • section 86.5: The sum of the orders of a meromorphic function
  • section 86.6: The Hurwitz formula
  • section 86.7: The identity theorem
  • chapter 87: The Riemann-Roch theorem
  • section 87.1: Motivation
  • section 87.2: Divisors
  • section 87.3: Degree of a divisor
  • section 87.4: The principal divisor of a meromorphic function
  • section 87.5: The Riemann-Roch theorem
  • chapter 88: Breaking the continuum hypothesis
  • section 88.1: Adding in reals
  • section 88.2: The countable chain condition
  • section 88.3: Preserving cardinals
  • section 88.4: Infinite combinatorics
  • chapter 89: Cardinals
  • section 89.1: Equinumerous sets and cardinals
  • section 89.2: Cardinalities
  • section 89.3: Aleph numbers
  • section 89.4: Cardinal arithmetic
  • section 89.5: Cardinal exponentiation
  • section 89.6: Cofinality
  • section 89.7: Inaccessible cardinals
  • chapter 90: Forcing
  • section 90.1: Setting up posets
  • section 90.2: More properties of posets
  • section 90.3: Names, and the generic extension
  • section 90.4: Fundamental theorem of forcing
  • section 90.5: (Optional) Defining the relation
  • section 90.6: The remaining axioms
  • chapter 91: Inner model theory
  • section 91.1: Models
  • section 91.2: Sentences and satisfaction
  • section 91.3: The Levy hierarchy
  • section 91.4: Substructures, and Tarski-Vaught
  • section 91.5: Obtaining the axioms of $\ZFC$
  • section 91.6: Mostowski collapse
  • section 91.7: Adding an inaccessible
  • section 91.8: FAQ's on countable models
  • section 91.9: Picturing inner models
  • chapter 92: Ordinals
  • section 92.1: Counting for preschoolers
  • section 92.2: Counting for set theorists
  • section 92.3: Definition of an ordinal
  • section 92.4: Ordinals are ``tall''
  • section 92.5: Transfinite induction and recursion
  • section 92.6: Ordinal arithmetic
  • section 92.7: The hierarchy of sets
  • chapter 93: Zermelo-Fraenkel with choice
  • section 93.1: The ultimate functional equation
  • section 93.2: Cantor's paradox
  • section 93.3: The language of set theory
  • section 93.4: The axioms of $\ZFC$
  • section 93.5: Encoding
  • section 93.6: Choice and well-ordering
  • section 93.7: Sets vs classes
  • chapter 94: Interlude: Cauchy's functional equation and Zorn's lemma
  • section 94.1: Let's construct a monster
  • section 94.2: Review of finite induction
  • section 94.3: Transfinite induction
  • section 94.4: Wrapping up functional equations
  • section 94.5: Zorn's lemma
  • section 94.6: \problemhead
  • chapter 95: Compactness
  • section 95.1: Definition of sequential compactness
  • section 95.2: Criteria for compactness
  • section 95.3: Compactness using open covers
  • section 95.4: Applications of compactness
  • section 95.5: (Optional) Equivalence of formulations of compactness
  • section 95.6: \problemhead
  • chapter 96: Some topological constructions
  • section 96.1: Spheres
  • section 96.2: Quotient topology
  • section 96.3: Product topology
  • section 96.4: Disjoint union and wedge sum
  • section 96.5: CW complexes
  • section 96.6: The torus, Klein bottle, $\RP^n$, $\CP^n$
  • subsection 96.6.1: The torus
  • subsection 96.6.2: The Klein bottle
  • subsection 96.6.3: Real projective space
  • subsection 96.6.4: Complex projective space
  • chapter 97: Covering projections
  • section 97.1: Even coverings and covering projections
  • section 97.2: Lifting theorem
  • section 97.3: Lifting correspondence
  • section 97.4: Regular coverings
  • section 97.5: The algebra of fundamental groups
  • section 97.6: \problemhead
  • chapter 98: Fundamental groups
  • section 98.1: Fusing paths together
  • section 98.2: Fundamental groups
  • section 98.3: Fundamental groups are invariant under homeomorphism
  • section 98.4: Higher homotopy groups
  • section 98.5: Homotopy equivalent spaces
  • section 98.6: The pointed homotopy category
  • chapter 99: Properties of metric spaces
  • section 99.1: Boundedness
  • section 99.2: Completeness
  • section 99.3: Let the buyer beware
  • section 99.4: Subspaces, and (inb4) a confusing linguistic point
  • section 99.5: \problemhead
  • chapter 100: Metric spaces
  • section 100.1: Definition and examples of metric spaces
  • section 100.2: Convergence in metric spaces
  • section 100.3: Continuous maps
  • section 100.4: Homeomorphisms
  • section 100.5: Extended example/definition: product metric
  • section 100.6: Open sets
  • section 100.7: Closed sets
  • section 100.8: \problemhead
  • chapter 101: Topological spaces
  • section 101.1: Forgetting the metric
  • section 101.2: Re-definitions
  • subsection 101.2.1: Continuity
  • subsection 101.2.2: Closed sets
  • subsection 101.2.3: Properties that don't carry over
  • section 101.3: Hausdorff spaces
  • section 101.4: Subspaces
  • section 101.5: Connected spaces
  • section 101.6: Path-connected spaces
  • section 101.7: Homotopy and simply connected spaces
  • section 101.8: Bases of spaces
  • section 101.9: \problemhead

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

ItemKindWhereSource
12MSA2M4EVstatementcorollary, section 45.4napkin
12WPC853Y3definitiondefinition, section 97.4napkin
The $p$th power automorphismstatementtheorem, section 12.4napkin
13WBHY24CPexerciseques, section 9.9.1napkin
144J1893QJdefinitiondefinition, section 60.4napkin
1497QBT1DQstatementcorollary, section 27.2.2napkin
151VYQZ2TJproofproof, section 15.2napkin
152VSV417Nstatementtheorem, section 33.4napkin
155ZWKJJRWexampleexample, section 51.6napkin
16HTMXX8GHexerciseexercise, section 52.6napkin
16YNKCPMGHexerciseques, section 77.3napkin
Galois extensions are splittingstatementtheorem, section 14.5napkin
17DYM9QC3Cexampleexample, section 21.2napkin
Fundamental group of $S^1$exampleexample, section 97.3napkin
186RY9H314exampleexample, section 70.4napkin
197W7E1VKBexercisesproblem, section 16.5napkin
1A8KZNNS2Ndefinitiondefinition, section 101.6napkin
1AE87GK9QKexampleexample, section 65.3napkin
1AGAEDBHHPstatementtheorem, section 6.3napkin
1B5YMK01FGexampleexample, section 67.7napkin
1B9RA5AWX5exerciseques, section 29.6napkin
The dot product is the ``only'' inner formexampleexample, section 60.3napkin
1BJBJZH8N9definitiondefinition, section 60.1.3napkin
1BW634782Gexerciseques, section 13.4napkin
1C3G78PARYexerciseproblem, section 8.8napkin
A function that is not meromorphicexampleexample, section 41.2napkin
Transfinite inductionstatementtheorem, section 94.3napkin
1CXDPYE2Z2exerciseproblem, section 81.5napkin
1E0P85PY7Cproofproof, section 12.4napkin
1EX8JTR45Fexampleexample, section 21.4napkin
1EYZB2R63Zstatementtheorem, section 60.2napkin
1FBZN4B0MCexampleexample, section 60.1.1napkin
1FCRPPZSZ5exampleexample, section 52.6napkin
1FR5ZAWTX2exampleexample, section 92.6napkin
1GVYT7KH13exerciseproblem, section 41.6napkin
1GW8B5X7EMstatementtheorem, section 28.5napkin
The $n$ embeddings of a number fieldstatementtheorem, section 9.2napkin
1H21MKE02Cexampleexample, section 100.4napkin
The finite field of nine elementsexampleexample, section 12.1napkin
1HXWK9W912proofproof, section 3.2napkin
All polynomialsexampleexample, section 62.2napkin
1JJKK0YYKBproofproof, section 69.1napkin
1JT6XE8K13exerciseexercise, section 16.1napkin
1KJYWBEJ5Cexampleexample, section 24.2.2napkin
1M0NWHWGHZexampleexample, section 50.1napkin
1MRQ4NF6QJexerciseques, section 101.8napkin
1MW4K1XVZGexercisesproblem, section 29.7napkin
1N34WTA856exerciseproblem, section 3.6napkin
1N8JJADG46definitiondefinition, section 10.6napkin
1P2GN41SK3definitiondefinition, section 27.4.2napkin
1PGKF0WVAEexerciseproblem, section 7.3napkin
1Q5RZHBSWDexerciseexercise, section 9.9.1napkin
1Q84JSRSK4definitiondefinition, section 25.3napkin
Divisorsdefinitiondefinition, section 87.2napkin
Mayer-Vietoris long exact sequencestatementtheorem, section 54.3napkin
1QYD28ZDF7definitiondefinition, section 33.3.2napkin
1R1CF6H1XNstatementtheorem, section 63.4napkin
Cohomology ring of real and complex projective spaceexampleexample, section 52.4napkin
1RCVEME25Vdefinitiondefinition, section 9.5napkin
1RDX50VZRYexerciseproblem, section 66.7napkin
1RK1NDGQDMexerciseques, section 12.4napkin
1RP9DPWH5Cexercisedproblem, section 67.9napkin
1T56P466XPexerciseques, section 92.3napkin
$\aleph_0$ is regularexampleexample, section 89.6napkin
1VQY0A75JMexerciseexercise, section 10.5napkin
1VYA83XHQEexerciseques, section 3.4napkin
1VZQCH2Z9Fproofproof, section 53.5napkin
1WPTVYX3G7exerciseproblem, section 98.6napkin
1X4KAPK374exerciseques, section 34.5napkin
1XB0VX50DKexampleexample, section 68.2napkin
1YYF592SY7exampleexample, section 4.5napkin
1Z9GT292YNdefinitiondefinition, section 88.2napkin
203JB6CDWAproofproof, section 56.1napkin
Another holomorphic $1$-form: $d(z^2) = 2z \cdot dz$exampleexample, section 84.2napkin
The equivalent definitions of a Noetherian ringstatementproposition, section 5.9napkin
215ZMP2T1Kproofproof, section 22.5napkin
21HFVNVWAPproofproof, section 53.2napkin
21QX4WDGPMexerciseproblem, section 61.6napkin
224BZ2PP3Xdefinitiondefinition, section 4.5napkin
226WZH4FAQexerciseques, section 100.1napkin
22CNBCYEGZproofproof, section 19.5napkin
Isomorphism $\iff$ monic and epicstatementproposition, section 35.2napkin
22SRJG01JMexampleexample, section 66.4napkin
230RZ5A0CHstatementclaim, section 80.6napkin
238PPXHJFPexampleexample, section 67.6napkin
23D8F6851Wproofproof, section 33.2.3napkin
24KC2Y7944definitiondefinition, section 101.4napkin
25KM54V25Bproofproof, section 78.1napkin
Examples of cardinalsexampleexample, section 89.1napkin
Adjoining an algebraic numberexampleexample, section 16.3napkin
26TFRZX0J2definitiondefinition, section 52.3napkin
26VNS4BAR2exerciseproblem, section 9.9.3napkin
27676BMCDWproofproof, section 60.3napkin
27WVKCENJRdefinitiondefinition, section 32.1napkin
Area of a circleexampleexample, section 46.3napkin
295KBF3ZWKexampleexample, section 63.1napkin
2A6WR84RZJstatementtheorem, section 68.1napkin
Covering of $S^1$ by itselfexampleexample, section 97.1napkin
2AAWJ6SH2Fexampleexample, section 50.5napkin
2AGNNANESVexerciseproblem, section 19.8napkin
2AYYQ2RYT2exerciseexercise, section 100.7napkin
The interval is compactstatementtheorem, section 95.2napkin
2BA3MYE05Dstatementcorollary, section 95.4napkin
Splitting lemmastatementlemma, section 54.3napkin
2BQB6KBZX8exampleexample, section 29.5napkin
2C3F4PZ90Ndefinitiondefinition, section 55.1napkin
The hypothesis {$\EE[X_i]=0$} is importantexampleexample, section 64.3.2napkin
2CD0M73CN9definitiondefinition, section 12.3napkin
2CEWJE8YPAexampleexample, section 21.5napkin
2CFES8WBDBexerciseques, section 39.4napkin
2CG45K3DPEexerciseexercise, section 23.3napkin
2DB09B8TR1exerciseproblem, section 4.8napkin
2DFY4FP9QQstatementtheorem, section 13.3napkin
2E42PDK1AEexerciseproblem, section 5.10napkin
2EKPYAXJRCexerciseques, section 26.14.1napkin
2EYHZZ918Zstatementproposition, section 97.3napkin
2F9P5C9QDCstatementproposition, section 68.2napkin
2FD5WQW33Wstatementtheorem, section 6.6napkin
2FKB4V69F5proofproof, section 22.5napkin
2FX3Q0XHDTproofproof, section 89.4napkin
2GA7XMEYNXstatementtheorem, section 79.3napkin
2GFMQ6XCNKdefinitiondefinition, section 97.1napkin
2HK493JJFPexerciseproblem, section 19.8napkin
2HMK358S3Nstatementtheorem, section 95.5napkin
2HN30T8A7Vexampleexample, section 25.3napkin
2HP5TAWVDCexerciseques, section 9.3napkin
2HRGSBJRWPexercisedproblem, section 62.11napkin
2J7VVNES1Yexampleexample, section 21.4napkin
Relation with the original seriesstatementclaim, section 64.3.3napkin
2JN5V5YA5Dexerciseques, section 77.3napkin
2JQS19FGBKexerciseexercise, section 32.3napkin
2KR6Q8AXZBexampleexample, section 80.2napkin
Regular functions on $\CP^1$exampleexample, section 23.5napkin
2M9H2QGJ79exerciseexercise, section 9.2napkin
2MSPDXQ50Mexerciseexercise, section 91.3napkin
2MXXK2KJRXstatementproposition, section 29.3napkin
2NBSD11PBFexerciseexercise, section 58.7napkin
2NC2SATMK0definitiondefinition, section 80.1napkin
2NPJ0DW1E5exerciseproblem, section 13.8napkin
2NPQ8GR3YJexerciseexercise, section 4.3napkin
2P2B4KBQQ0exerciseques, section 62.7napkin
2PG7Q2JD3Nstatementlemma, section 8.6napkin
2RH7GQB3BKexerciseproblem, section 27.7napkin
2RKVD6SWN8exerciseproblem, section 4.8napkin
2RPT9J4EG2statementtheorem, section 27.4.2napkin
2RYGP6472Hexerciseques, section 14.6napkin
2S0AQGVCCZdefinitiondefinition, section 87.4napkin
2S1TVE5NY6exerciseexercise, section 3.3napkin
Holomorphic $1$-forms on the complex planedefinitiondefinition, section 84.2.1napkin
2S9R1WXW7Pexampleexample, section 8.7napkin
$H^n (-;G): \catname{hTop}\op \to \catname{Grp}$statementtheorem, section 51.3napkin
2SX3ZYVRC1proofproof, section 14.5napkin
2TQ870BSZFstatementlemma, section 14.7napkin
2VQWJM70Q0exampleexample, section 2.3napkin
2VZYWKYG51exampleexample, section 46.4napkin
Examples of inertial degreesexampleexample, section 18.3napkin
2W2D05EFZ0exerciseproblem, section 58.8napkin
2W3S81MFS5exerciseques, section 59.5napkin
2WSFQCA328definitiondefinition, section 80.1napkin
2X5H9VQEGSexampleexample, section 80.3napkin
2X6QPMZB49exerciseexercise, section 5.7napkin
2X9CMGP10Texercisedproblem, section 57.5napkin
2XEYZMPP39definitiondefinition, section 14.5napkin
Another explicit computationexampleexample, section 3.5napkin
Harmonic fanexerciseproblem, section 98.6napkin
2ZCMGKFBJFexerciseexercise, section 23.2napkin
2ZNAJQDR98exerciseexercise, section 42.3napkin
306NMEFYBGdefinitiondefinition, section 4.4napkin
306Y599N2Jstatementproposition, section 99.1napkin
30NRJCQ665exerciseproblem, section 30.6napkin
30WH7Y7QF1proofproof, section 100.3napkin
314WSW0FS4proofproof, section 30.3napkin
32KPMNT1PTexampleexample, section 30.5napkin
335PY6K029proofproof, section 81.2napkin
3454QPN42Gstatementlemma, section 52.3napkin
3603Q4V5F4statementproposition, section 20.2napkin
3645281BJ9exampleexample, section 5.6napkin
36NMWGANG2definitiondefinition, section 1.1napkin
371A6SCH1Qdefinitiondefinition, section 37.4napkin
37FWYHB1DTexampleexample, section 92.3napkin
$\ZZ$ is a Dedekind domainexampleexample, section 10.3napkin
388P2BV1PRstatementcorollary, section 4.4napkin
38GW6J2NZZstatementtheorem, section 33.3.4napkin
38MQMRAN32exerciseexercise, section 9.9.2napkin
38XM3F69EXdefinitiondefinition, section 44.2napkin
39608XPJ4Hexerciseexercise, section 38.1napkin
396PNP5H75definitiondefinition, section 36.4napkin
3AC4PK2KNJdefinitiondefinition, section 34.5napkin
3AGZXJDM77statementproposition, section 63.4napkin
3AW8A19KMCstatementtheorem, section 46.3napkin
Explicit exampleexampleexample, section 57.3napkin
Factoring $x^3-2 \pmod 5$exampleexample, section 13.7napkin
3C8YXQ7MYFdefinitiondefinition, section 28.3napkin
Properties of degreesstatementproposition, section 20.4napkin
3DP916N301exerciseproblem, section 20.5napkin
3DZQ04CFM3proofproof, section 6.2napkin
There is no set of all setsstatementtheorem, section 93.7napkin
3EP6EKE9PRexerciseexercise, section 67.5napkin
3EPBW726RSdefinitiondefinition, section 34.2napkin
Ordinals are strictly orderedstatementtheorem, section 92.3napkin
3FNFPQ35SFdefinitiondefinition, section 7.2.1napkin
3FR4AQ7Q30proofproof, section 4.7napkin
3FXGW06NZ7exercisedproblem, section 8.8napkin
3G65NNS5VAexerciseproblem, section 25.6napkin
3G7MVSZSNNproofproof, section 46.3napkin
3G7X4VXCQ6exerciseproblem, section 56.3napkin
3GHB3JB2RVproofproof, section 6.6napkin
3GM0TM9E2Mexerciseques, section 14.1napkin
$1$-densitydefinitiondefinition, section 43.6napkin
3H0P7HVCCSproofproof, section 58.6napkin
The finite field of order nine againexampleexample, section 12.3napkin
3J3V6GXW68statementtheorem, section 75.1napkin
Green's theoremexercisedproblem, section 46.6napkin
3JGCM25V51exerciseques, section 36.5napkin
3JRCB6Z8ECexampleexample, section 25.3napkin
3JRTKEGPBVproofproof, section 6.4napkin
3K5V4ABXRCexampleexample, section 62.2napkin
3K62HBMT9Pexerciseproblem, section 32.8napkin
3K73A6Q9E8statementtheorem, section 66.5napkin
3K91HJ1X00exerciseques, section 32.6napkin
3KG3TH5GMTstatementfact, section 2.4napkin
3KKJXFSZHFdefinitiondefinition, section 92.7napkin
The long exact sequence for $(X,A) = (D^2, S^1)$exampleexample, section 53.5napkin
3M9VT2MJ6Vexerciseproblem, section 36.5napkin
3MSWE2BGCVexerciseexercise, section 13.6.2napkin
3N1CN80G5Aexerciseques, section 92.4napkin
3NJVMDTS01statementlemma, section 88.4napkin
3NX8541G10exerciseques, section 9.8napkin
3PA7XK2JSJdefinitiondefinition, section 80.4napkin
3PKRS4X6K6exerciseques, section 90.2napkin
3QQY3X4KS5exercisesproblem, section 31.5napkin
3QZ5KYY4R8exercisedproblem, section 29.7napkin
3R0VNXF84Hexerciseques, section 51.3napkin
3S3YBSX1VVexerciseques, section 9.9.2napkin
Basis of the wedge productstatementproposition, section 56.1napkin
3SN6209DFFexampleexample, section 10.4napkin
3SYYAEDEC4exerciseproblem, section 34.7napkin
3T00ZF9HTTexampleexample, section 91.3napkin
3T2C2ZJ008definitiondefinition, section 79.3napkin
3TYBY0GE52proofproof, section 78.3napkin
3VF2BEVQASexerciseques, section 82.3napkin
3W64A1RQVTproofproof, section 76.2napkin
3WTRA8MS67exampleexample, section 27.3.1napkin
3WZCBGWM7Jstatementtheorem, section 80.6napkin
3WZRF8X96Hexerciseques, section 19.4napkin
3XBMD12TS7proofproof, section 15.1napkin
3XHSF5GKRSproofproof, section 81.3napkin
3XSW76CNRWexampleexample, section 57.1napkin
3YX0S7TV1Nexerciseproblem, section 92.7napkin
3Z4GE82F1Aproofproof, section 54.3napkin
3Z9AFVAYGKexerciseproblem, section 93.7napkin
3ZGRYK8WNVexampleexample, section 22.4.1napkin
41SJC87R36proofproof, section 34.3napkin
4236F3Y812exercisedproblem, section 15.4napkin
Examples of path-connected spacesexampleexample, section 101.6napkin
425FPC26XZexampleexample, section 19.5napkin
43EFAWCW6Texerciseexercise, section 51.7napkin
43T0P0TWZ3definitiondefinition, section 79.1napkin
43VWBAFGWVexerciseques, section 34.4napkin
43X2ZGHH3Fexerciseexercise, section 13.1napkin
44JNXASHFKproofproof, section 9.6napkin
4529FNM9Y4exerciseques, section 13.6.2napkin
45ZFPMPWPEstatementtheorem, section 31.3napkin
468ERW3P6Zexercisesproblem, section 5.10napkin
46MJHR0W7Jexampleexample, section 28.3napkin
472NHRXZAFdefinitiondefinition, section 98.1napkin
47690D80F1definitiondefinition, section 21.2napkin
478FX93YDGexerciseexercise, section 59.3.1napkin
47YF7J2V14statementtheorem, section 61.4napkin
48AES2JV1Qexerciseques, section 63.5napkin
48DTR4RBSRstatementcorollary, section 22.5napkin
48FJTCJCCPdefinitiondefinition, section 86.4napkin
48VDRVPFSHdefinitiondefinition, section 80.1napkin
Frobenius controls polynomial factorizationstatementtheorem, section 13.7napkin
49HTM1AEWDexampleexample, section 83.4napkin
4ABGG84Z3Jdefinitiondefinition, section 97.5napkin
4AGG8JPT84exerciseexercise, section 36.3napkin
The $n$ embeddings of any separable extensionstatementtheorem, section 14.4napkin
4AMF05QSNYexampleexample, section 24.2.2napkin
4BT4M9DYZBexercisedproblem, section 95.6napkin
4BX02GQ5VKexerciseproblem, section 5.10napkin
4C5WFRY80Bexerciseques, section 91.2napkin
4CVCD1B5GJproofproof, section 41.4napkin
4CZ4R6F7GCexerciseques, section 29.5napkin
4D29DVZHFVdefinitiondefinition, section 100.6napkin
4D7PK1WCYXexerciseques, section 7.1napkin
4EFFQWPF6Aexerciseexercise, section 56.1napkin
4EJY19QJA7exerciseexercise, section 5.6napkin
4EPMVA3VRPexampleexample, section 33.2.3napkin
4EQJPPP3MDexerciseproblem, section 37.7napkin
4EV9V2T18Bexerciseexercise, section 85.4napkin
4F3902KFMSexerciseproblem, section 89.7napkin
4FDK1W4VRAexerciseques, section 85.3napkin
Explicit example of element in $V^\vee$exampleexample, section 57.2napkin
Orbit-stabilizer theoremstatementtheorem, section 1.2napkin
4GTYN7AQ5Edefinitiondefinition, section 62.3napkin
4JCDKWYNPZexerciseexercise, section 99.1napkin
4JFBN7HC1Texampleexample, section 43.5napkin
4JGP0FY6ZYexerciseproblem, section 43.7napkin
4JR8W9C4M6exerciseproblem, section 60.5napkin
4KXS2FKAXJdefinitiondefinition, section 82.1napkin
4M5DV78CS0definitiondefinition, section 14.4napkin
4MFSXESSDYexercisedproblem, section 8.8napkin
4N1N831475exerciseexercise, section 100.6napkin
4NA1K20BEYdefinitiondefinition, section 80.4napkin
4NMAWZV0QJstatementtheorem, section 23.5napkin
Another non-holomorphic form: $\ol z \cdot dz$exampleexample, section 84.2napkin
4PGA3K28BWproofproof, section 34.5napkin
4R2ZZ7KM4Mexerciseexercise, section 61.2napkin
4R8VYK7Z0Rexampleexample, section 97.4napkin
$\aleph_\omega$ is not regularexampleexample, section 89.6napkin
4SZ1TDWHAZdefinitiondefinition, section 60.2napkin
Spherical coordinatesexerciseproblem, section 46.6napkin
Examples of minimal polynomialsexampleexample, section 16.1napkin
Sketch of Proofproofproof, section 80.3napkin
4W4Z1KC2KZexampleexample, section 58.3napkin
4W63VSZF71exampleexample, section 2.1napkin
4WKBWHR8BHexampleexample, section 54.1napkin
4WRK3Q1196definitiondefinition, section 77.3napkin
4X6Q2MAMV1definitiondefinition, section 76.2napkin
$V \cong V^\vee$ for real inner formsstatementtheorem, section 61.3napkin
4XM1ZSAS1Aexerciseques, section 61.3napkin
4XPA3FCXC2exerciseproblem, section 27.7napkin
4Y28JKQP81exampleexample, section 24.3napkin
An example of non-compactnessexampleexample, section 95.3napkin
4YR2B3VD50proofproof, section 59.7napkin
Sketch of Proofproofproof, section 9.4napkin
4Z5RVV1NJ9exerciseques, section 45.3napkin
4ZDQGVYF4Rexerciseques, section 63.2napkin
4ZPSCZY9A2exampleexample, section 89.6napkin
4ZWY78XMZYdefinitiondefinition, section 32.1napkin
4ZYE78EPVFexampleexample, section 6.6napkin
500QBEQAE6definitiondefinition, section 16.2napkin
507E4VEKG7exerciseproblem, section 58.8napkin
50SJ0V4JPFdefinitiondefinition, section 51.1napkin
516R7KFD5Vdefinitiondefinition, section 89.1napkin
51F9Y9JV8Rstatementtheorem, section 5.6napkin
WRONG Proof of False Theoremproofproof, section 61.2napkin
523TBTPPZ2exampleexample, section 1.4napkin
5258Q7KJN8definitiondefinition, section 75.3napkin
52DE15GENBexerciseques, section 36.2napkin
53BB9ETPZ8exerciseproblem, section 81.5napkin
542CQ5QVVDstatementtheorem, section 3.4napkin
546ADE36NXstatementtheorem, section 82.1napkin
54B3K0KBE4exerciseproblem, section 79.4napkin
55641KMJ9Zdefinitiondefinition, section 89.3napkin
55TRAH6E3Zdefinitiondefinition, section 31.1napkin
55W0VJ0R79definitiondefinition, section 100.3napkin
5611KPCNRJdefinitiondefinition, section 98.6napkin
56NSD6WEDBdefinitiondefinition, section 56.1napkin
Nonzero rationalsexampleexample, section 2.1napkin
56ZPGX9VM7definitiondefinition, section 46.3napkin
57TKMCC0YXexercisesproblem, section 62.11napkin
59JFZANC4Hexampleexample, section 23.1napkin
59SBV00WJQdefinitiondefinition, section 2.3napkin
59WHKYVZJ3statementtheorem, section 14.4napkin
5ABXNNC03Vdefinitiondefinition, section 3.3napkin
5AE81C4454proofproof, section 21.5napkin
5AE8TCJDCXexercisedproblem, section 1.4napkin
5AZGN6JAV6exampleexample, section 32.6napkin
Additive integersexampleexample, section 2.1napkin
5BDHTVW92Aexerciseexercise, section 98.2napkin
5C2CWYGGSZdefinitiondefinition, section 75.2napkin
5C2V684FTBdefinitiondefinition, section 44.1napkin
5CA137D6G7exerciseexercise, section 66.2napkin
Compact $\implies$ totally boundedstatementproposition, section 95.4napkin
Open set of a varietyexampleexample, section 29.3napkin
5E69F3ZBBJdefinitiondefinition, section 14.2napkin
5EFN878DNPexampleexample, section 34.4napkin
5F1AQ4H6Y2exerciseques, section 15.1napkin
$V \mapsto V^\vee$ is contravariantexampleexample, section 37.4napkin
5GD8CW481Yexerciseproblem, section 77.4napkin
5GNR23AS71exampleexample, section 62.2napkin
5GSG8CP5CXexerciseques, section 55.4napkin
5J242SB1AMexerciseques, section 37.7napkin
5J7GTDAZM8definitiondefinition, section 51.8napkin
5J953Z6D0Fexampleexample, section 100.4napkin
5JDWQHTS5Pdefinitiondefinition, section 6.1napkin
5JFVZRH6SRdefinitiondefinition, section 9.7napkin
5JGV6AQGFNdefinitiondefinition, section 100.6napkin
Zeros are isolatedexercisesproblem, section 39.7.2napkin
5JVFNNREQGexerciseproblem, section 37.7napkin
5JYBK2SYMSexampleexample, section 98.2napkin
5KJW4YTJBZexerciseproblem, section 53.6napkin
5KP2763FBNdefinitiondefinition, section 25.3napkin
Putnam 2014exerciseproblem, section 60.5napkin
5MH9KWH7RRproofproof, section 9.8napkin
5MKVXKNQ64exerciseques, section 69.1napkin
5NEGR6A5H2exampleexample, section 56.1napkin
Preserving cardinals $\iff$ preserving regular cardinalsstatementproposition, section 88.3napkin
5NN9JDCWTJexampleexample, section 28.3napkin
5NNK7HKYGYexerciseques, section 85.3napkin
5Q0W7FGZG5exampleexample, section 28.3napkin
Metric spaces of $\RR$exampleexample, section 100.1napkin
5QHZBM871Texampleexample, section 14.2napkin
5QTBPA6SD9statementcorollary, section 52.1napkin
5QX6TWEJREexercisedproblem, section 57.5napkin
5QX8CGY10Pexampleexample, section 19.5napkin
5R75PCGKSBexampleexample, section 8.5napkin
5RHZVS8NRPstatementproposition, section 6.2napkin
5RX93XPYBPdefinitiondefinition, section 101.7napkin
Reflectionexercisedproblem, section 91.9napkin
5SBBHWH4DWdefinitiondefinition, section 101.7napkin
5SGG10RYW2exerciseques, section 58.7napkin
5SQ0YMTFEXexampleexample, section 99.2napkin
5T0F16J3MMexampleexample, section 29.5napkin
5T8HNRPV64exampleexample, section 4.2napkin
5TVPKSABZHexerciseques, section 29.2napkin
5V9R0F5WFYexampleexample, section 21.3napkin
5VG6M0YMT5definitiondefinition, section 28.2napkin
5WP4KDTWE8exerciseproblem, section 77.4napkin
Branch cut functionsstatementtheorem, section 40.5napkin
5X3Z6DNZR0exerciseexercise, section 67.5napkin
5XE2H6JSJFexerciseproblem, section 5.10napkin
Ideal norm of $(5)$ in the Gaussian integersexampleexample, section 10.7napkin
5ZDNHW3PFFexerciseproblem, section 67.9napkin
5ZFSW0TF11exampleexample, section 5.5napkin
A parabolaexampleexample, section 82.1napkin
60FDRF6C73definitiondefinition, section 7.2.1napkin
60Z5TBXXWZexampleexample, section 28.2napkin
Completenessstatementcorollary, section 90.5napkin
61MJ7A1YD6definitiondefinition, section 23.4napkin
61QS7CNCR9exerciseexercise, section 5.6napkin
623K9MG1P4exerciseproblem, section 59.8napkin
62CNWAXWM2exampleexample, section 51.5napkin
62JZH5D4ECdefinitiondefinition, section 59.3.2napkin
62N0JRPDTVexerciseexercise, section 82.1napkin
633X42NV8Eexerciseproblem, section 101.9napkin
63433NRRVBexerciseques, section 10.5napkin
63MHMMN7PVproofproof, section 12.2napkin
63PGKWHZZGdefinitiondefinition, section 7.3napkin
Type $(1, 0)$ and type $(0, 1)$ $1$-formsdefinitiondefinition, section 84.2.1napkin
64SBHP123Fstatementtheorem, section 44.3napkin
64T4A76BXAexampleexample, section 24.4napkin
6542NKPA64definitiondefinition, section 81.3napkin
65GXJBC4WCexerciseexercise, section 100.3napkin
66XSFCAXX4exerciseques, section 17.1napkin
67FTWKMDS0proofproof, section 70.4napkin
67G1TCRFYDexampleexample, section 32.1napkin
Sketch of Proofproofproof, section 13.7napkin
67HXF7733Hdefinitiondefinition, section 5.7napkin
Lifting pathsstatementtheorem, section 97.2napkin
68B9NA2DBHstatementtheorem, section 21.7napkin
68D3S5EPG4statementproposition, section 86.5napkin
6969Y2N5QRexerciseques, section 55.2napkin
69CA4GHMA6exampleexample, section 2.1napkin
69E5REAGDDexerciseques, section 9.9.1napkin
69FXD33NDYexerciseproblem, section 95.6napkin
6AN0SH1ZGSproofproof, section 90.6napkin
6AP761C9BJexerciseproblem, section 62.11napkin
6BYQYQC0J4proofproof, section 27.3.1napkin
6BZNFK18R9definitiondefinition, section 29.4napkin
6C1VQ1TK67exampleexample, section 81.2napkin
6C2012Z6MJexampleexample, section 21.3napkin
6CH6FTTYKDproofproof, section 61.1napkin
6CK3AA7529definitiondefinition, section 62.5napkin
6DW3WK731Cstatementlemma, section 9.3napkin
6EH3T5W061definitiondefinition, section 63.5napkin
6EPMR7EM1Vstatementtheorem, section 53.6napkin
Proof of Cayley-Hamiltonproofproof, section 56.3napkin
6F6V6BQG24definitiondefinition, section 52.4napkin
6F7T69AJMSdefinitiondefinition, section 53.3napkin
6FDDS69FQNdefinitiondefinition, section 10.2napkin
6FNXQQ2S4Jexerciseques, section 52.4napkin
6FYQZW4ZFHexampleexample, section 62.2napkin
6G0FNHG1A3definitiondefinition, section 22.10napkin
Kronecker's theoremexerciseproblem, section 16.5napkin
6G5SMZERCDexercisesproblem, section 31.5napkin
6GGPPQ009Qstatementtheorem, section 33.4napkin
``Euclidean algorithm''statementclaim, section 6.6napkin
6GZ1M328K5definitiondefinition, section 101.1napkin
6HCVB5EGXEdefinitiondefinition, section 37.7napkin
$\frac52\ZZ$ is a fractional idealexampleexample, section 10.6napkin
Eigenvalues need not existexampleexample, section 58.3napkin
Finiteness of class groupstatementcorollary, section 9.7napkin
6J16N806JWexerciseproblem, section 28.6napkin
6K237A9KE1exerciseproblem, section 10.7napkin
6KGCGQTET4statementtheorem, section 22.10napkin
6KK9CM56CXexerciseproblem, section 32.8napkin
6KW8HYC7NNstatementtheorem, section 59.7napkin
6MCSK335D0statementproposition, section 66.5napkin
Short exact $\implies$ long exactstatementtheorem, section 54.2napkin
6MTCZBYPKVdefinitiondefinition, section 23.4napkin
6MZPRX8T0Kexampleexample, section 33.3.5napkin
Mayer-Vietoris long exact sequence, provisional versionexampleexample, section 54.2napkin
6N7QZJVVB1exerciseproblem, section 9.9.3napkin
6P3ZWKRBFKstatementtheorem, section 17.3napkin
Equalizers are monicexercisesproblem, section 38.4napkin
Kolmogorov's inequalitystatementtheorem, section 64.3.3napkin
Primes split before remaining inertexampleexample, section 18.5napkin
6Q2B3YN4S8exampleexample, section 91.3napkin
Factoring $77$: generating the periodic stateexampleexample, section 76.3napkin
6RHTY9F5WXdefinitiondefinition, section 34.5napkin
6RVV6XA0YGdefinitiondefinition, section 58.8napkin
6S2KNVQ6NYexampleexample, section 29.2napkin
6S3CDJPS5Dexerciseproblem, section 7.3napkin
6SJGKTVC8Jexampleexample, section 32.6napkin
6SW0KS3E62proofproof, section 95.2napkin
6T887AWYWTdefinitiondefinition, section 23.2napkin
Ramification in the Gaussian integersexampleexample, section 18.2napkin
6TNSB1PP5Jexampleexample, section 66.1napkin
6TQAH4FR4Wdefinitiondefinition, section 32.3napkin
6V62JESMYMexerciseexercise, section 80.4napkin
6VBEJNGXA9statementtheorem, section 37.2napkin
6VK6FX4Q3Cstatementtheorem, section 52.6napkin
6VND8EZZ6Sdefinitiondefinition, section 91.1napkin
6VNQ6ERF3Qstatementtheorem, section 32.1napkin
6VQ3RBW066exerciseques, section 27.6napkin
6VS6XN9SG4exerciseques, section 39.7.1napkin
6XABW24CFBexerciseproblem, section 43.7napkin
Prime ideal $\iff$ quotient is integral domainstatementtheorem, section 4.3napkin
6XZBAAWGWDdefinitiondefinition, section 95.1napkin
6YQAXWD3K2exampleexample, section 55.2napkin
6YW7YQSSKFexampleexample, section 22.6napkin
6ZDF125FTTdefinitiondefinition, section 7.3napkin
6ZEBQJZKT6statementtheorem, section 13.6napkin
6ZEHNBYZ86exampleexample, section 9.9.3napkin
701BNNMD9Xdefinitiondefinition, section 22.6napkin
Isomorphism of line bundlesdefinitiondefinition, section 85.4napkin
70TJ3BCH81statementlemma, section 95.5napkin
Basis of metric spacesstatementtheorem, section 101.8napkin
72T7ZM1CYPproofproof, section 36.4napkin
739P5974QKexampleexample, section 35.3napkin
73H4QB62QHproofproof, section 35.2napkin
741XFK0GRXdefinitiondefinition, section 100.2napkin
745W9V7VWSexerciseques, section 7.2.4napkin
74QYWSJ315exampleexample, section 55.4napkin
74SA6TE4K4exercisedproblem, section 6.6napkin
74W8B7T00Vexerciseproblem, section 58.8napkin
758G7GNX7Sdefinitiondefinition, section 4.6napkin
75G9G84JW7proofproof, section 90.3napkin
761KY6PRM6exampleexample, section 80.2napkin
7695TA9QASdefinitiondefinition, section 20.2napkin
773CE8HBXCexerciseproblem, section 37.7napkin
Inner product structure of tensorsexercisesproblem, section 60.5napkin
78BHZY0ZRPexerciseproblem, section 26.19napkin
78MRZXKXTMexampleexample, section 59.3.2napkin
78P6E766JXexerciseproblem, section 56.3napkin
More complicated $L(-)$ spacesexampleexample, section 87.1napkin
7999WHCSFNexerciseexercise, section 88.1napkin
7A1C4PA71Zdefinitiondefinition, section 64.1.2napkin
7A5JJGS3G0statementproposition, section 22.2napkin
7ADN07N6Z2exampleexample, section 75.2napkin
7AR2HAMPEDexampleexample, section 6.1napkin
7AS6C2NAF2exerciseexercise, section 30.2napkin
Sequentially compact $\iff$ compactstatementtheorem, section 95.3napkin
7CG391MDB3exerciseproblem, section 15.4napkin
7E87DJJGARexerciseques, section 97.4napkin
7EN8CBXFMVexerciseques, section 59.5napkin
7EQZRDR6KTexampleexample, section 100.1napkin
7F4MY9Z7GTstatementtheorem, section 20.2napkin
7F6A22EBD6exerciseproblem, section 22.9napkin
7F9GNC2EYVexerciseexercise, section 101.2.2napkin
7FB2W9KCS3definitiondefinition, section 88.2napkin
7FT2ZHQB10exercisesproblem, section 28.6napkin
7G5N7FYS2Cproofproof, section 10.2napkin
7GJ4VZ762Bproofproof, section 39.5napkin
7GP6BY6Z2Cstatementtheorem, section 29.6napkin
Non-examples of number fieldsexampleexample, section 16.3napkin
7HF7YTS2WQdefinitiondefinition, section 93.5napkin
7HZ9BMVZS6definitiondefinition, section 62.4napkin
Complete classification of finite fieldsstatementtheorem, section 12.3napkin
7J5MZGH56Zproofproof, section 6.5napkin
7JF02CJ9Y7exampleexample, section 80.3napkin
7K9YAV83P0statementtheorem, section 34.3napkin
The von Neumann hierarchy is completestatementtheorem, section 92.7napkin
7M940MBE0Gexerciseexercise, section 9.9.3napkin
7M98E7T0WKstatementproposition, section 22.11napkin
7MS0KJGP1Sdefinitiondefinition, section 67.5napkin
7N83ZEZ3EZexerciseproblem, section 54.3napkin
7NPEXHEEWKexampleexample, section 35.5napkin
7P1FX1S6KFexerciseproblem, section 34.7napkin
7P405EKWPCexerciseproblem, section 79.4napkin
7QBWHMXYYWstatementtheorem, section 9.6napkin
7QN96007MBproofproof, section 31.1napkin
The dual basis for $V^\vee$statementproposition, section 57.2napkin
7RAV8ZD65Jstatementtheorem, section 92.4napkin
{$\QQ[x]$ is a Euclidean domain}exampleexample, section 4.7napkin
7RQWZX64H0definitiondefinition, section 36.2napkin
7RZRKKKS8Sexampleexample, section 44.1napkin
7SY46Z06CFproofproof, section 88.2napkin
A set neither open nor closedexampleexample, section 100.7napkin
Klein four groupexampleexample, section 3.1napkin
7TK9AKTRBYexampleexample, section 32.1napkin
Cayley-Hamiltonstatementtheorem, section 56.3napkin
7TQW7SFN91statementtheorem, section 2.4napkin
7TYWSEMB0Aexerciseexercise, section 96.1napkin
7VJKQR6PGNexampleexample, section 50.5napkin
Examples of algebraic integersexampleexample, section 16.2napkin
7X3NE5M4GBdefinitiondefinition, section 43.3napkin
7XX3031941exampleexample, section 22.4.3napkin
7Y74NSD5Y2definitiondefinition, section 91.2napkin
7YD368TYSXdefinitiondefinition, section 1.4napkin
7Z0DRYSHWTexerciseques, section 58.3napkin
7ZADYNPYDVexerciseproblem, section 44.7.3napkin
7ZQK5SX9K3proofproof, section 68.2napkin
80844P09WWexercisedproblem, section 50.5napkin
Continuous on compact $\implies$ uniformly continuousstatementproposition, section 95.4napkin
80PB7MTKATexampleexample, section 55.1napkin
8182WHF7DMexampleexample, section 35.1napkin
82ZSHGJ03Rexerciseexercise, section 43.4napkin
83RKTPB3E9statementtheorem, section 94.5napkin
83WM9JV9S9exerciseexercise, section 36.2napkin
847Y9PCYKVexerciseexercise, section 19.4napkin
84HB1A9SWEexerciseproblem, section 6.6napkin
85AVDH37E8exerciseques, section 53.1napkin
85XN8SPGXTproofproof, section 22.7napkin
8648XCANQVexerciseexercise, section 80.5napkin
Cyclotomic Fieldexercisedproblem, section 15.4napkin
867MTJKM8Pexercisesproblem, section 101.9napkin
86EBCW8ZE4exampleexample, section 8.6napkin
86KX38R4JYexampleexample, section 2.1napkin
86WAM052AYstatementlemma, section 4.7napkin
Aleph numbers constitute all infinite cardinalsstatementlemma, section 89.3napkin
Polynomial ringexampleexample, section 5.3napkin
88SBQA754Pexerciseexercise, section 25.2.2napkin
89HQVBYFNMproofproof, section 60.4napkin
89NK0XMNN3exerciseproblem, section 46.6napkin
Examples of affine varietiesexampleexample, section 19.1napkin
8BE096E837exerciseproblem, section 69.6napkin
8CF2MEF5FCexampleexample, section 86.5napkin
8CM1K6GV2Dexerciseproblem, section 41.6napkin
8CS9SWMABGstatementproposition, section 63.3napkin
8D3K5V395Cexampleexample, section 99.2napkin
8D4TXQ9G37statementcorollary, section 59.5napkin
8DHBCS9APVstatementtheorem, section 3.6napkin
8DW6E9Z3ZYproofproof, section 60.2napkin
8DWTJNFWHSexerciseques, section 97.3napkin
Barenco et al, 1995; arXiv:quant-ph/9503016v1exercisedproblem, section 75.4napkin
8E88AP3C70statementproposition, section 22.5napkin
8EHWWSDQMQdefinitiondefinition, section 10.6napkin
8EMK4ZNW4Gexerciseques, section 99.2napkin
8EPEJAPTBVdefinitiondefinition, section 97.2napkin
8EVW4DDNVMexerciseproblem, section 99.5napkin
8HDEHXV9JJexerciseques, section 79.2napkin
8HWYJQ8BGGexerciseproblem, section 100.8napkin
Subgroups of $\ZZ$exampleexample, section 97.5napkin
8JANY0F9XPexampleexample, section 3.1napkin
Examples of $\mu(\OO_K)$exampleexample, section 17.2napkin
8M1VY29TQ5exampleexample, section 21.4napkin
8N3PRY6ZCDexerciseques, section 90.3napkin
8N8YDKFFKCexampleexample, section 9.7napkin
8P0H1F1SGWdefinitiondefinition, section 27.6napkin
Example of an interpretationexampleexample, section 90.3napkin
8Q82TGATS1exerciseexercise, section 64.3.3napkin
8Q8604VR72exerciseques, section 101.6napkin
8QAVXFAAG1proofproof, section 54.3napkin
8QCXV570XZexerciseproblem, section 35.5napkin
8QHE551SB8definitiondefinition, section 53.3napkin
8QRQE1A5S8statementlemma, section 51.6napkin
8R1VA4S0EMdefinitiondefinition, section 35.1napkin
8RD967947Yexerciseques, section 13.6.1napkin
8S4FR0HA9Gstatementtheorem, section 91.7napkin
8SWQSY0276exampleexample, section 100.4napkin
8T71SFR0XSexerciseques, section 80.1napkin
8V3D38MS0Jstatementlemma, section 53.2napkin
The homology groups of the figure eightstatementproposition, section 54.3napkin
8W765GX8KWstatementlemma, section 51.4napkin
Taiwan IMO campexerciseproblem, section 60.5napkin
8WHC10CF2Rexerciseproblem, section 88.4napkin
8WY4X1V9DXstatementtheorem, section 35.4napkin
8Y0S15R7T5exerciseproblem, section 25.6napkin
8Y92ZBSVF8exampleexample, section 66.3napkin
8YCPDQZJD8exerciseques, section 95.2napkin
8YHW23N8HPexampleexample, section 100.6napkin
8YQ8748ZR9exerciseexercise, section 80.4napkin
8YSX9NDNJ7proofproof, section 51.3napkin
Examples of open setsexampleexample, section 100.6napkin
90180MJZ9Tdefinitiondefinition, section 28.3napkin
9065K0W4HPexerciseproblem, section 46.6napkin
90CG1MT73Eexampleexample, section 77.3napkin
93MS8SDJCWstatementfact, section 2.4napkin
953ZZ1G6A9definitiondefinition, section 21.3napkin
95TAFR122Cstatementtheorem, section 52.2napkin
95WBSDH1QJexercisedproblem, section 10.7napkin
Even more signaturesexampleexample, section 9.3napkin
96JAG4TYF3proofproof, section 55.3.1napkin
981Z4T04NMstatementproposition, section 12.5napkin
99RV4Q6XSYexerciseexercise, section 25.4napkin
9A4V2X7SDZproofproof, section 22.7napkin
9AZJ0XN720proofproof, section 33.3.3napkin
9B1NYD8355exerciseexercise, section 9.9.3napkin
9B8W36Z432exerciseques, section 91.7napkin
9BCZECH2KRstatementfact, section 2.2napkin
9BT7QXW92Nexerciseques, section 8.7napkin
9D98YKFJ6Vexerciseproblem, section 14.6napkin
9DHA0VAHZNexerciseproblem, section 11napkin
Restatement of cardinality propertiesstatementproposition, section 89.2napkin
9DXT59WE58definitiondefinition, section 55.4napkin
The Frobenius elementstatementtheorem, section 13.1napkin
Ordinal multiplication is not commutativeexampleexample, section 92.6napkin
9ESPJ11MC3exercisesproblem, section 39.7.2napkin
9EWAE35XHMexampleexample, section 36.2napkin
9F8G8YSG1Cdefinitiondefinition, section 98.2napkin
9FM4HS4509statementtheorem, section 41.4napkin
9G91KS272Wexampleexample, section 5.4napkin
9GJKZJXH7Vproofproof, section 39.3napkin
9HE12PDD0Zexampleexample, section 51.6napkin
Orthogonal vectors are independentstatementlemma, section 60.3napkin
9J8V78Z2B4exerciseexercise, section 13.6.1napkin
9JZ77F6E2Vproofproof, section 58.3napkin
9M2JT3J8TAexerciseproblem, section 56.3napkin
9MCY9EHVSKstatementtheorem, section 20.4napkin
9N3GSY109Yexerciseexercise, section 3.2napkin
9N5MPDTW2Cexercisedproblem, section 34.7napkin
9P9NT880JZexampleexample, section 6.2napkin
9PA3ZR8569exampleexample, section 75.3napkin
9PR9QY9YJWexerciseques, section 77.3napkin
9PT94KTDGWexerciseexercise, section 37.3napkin
9PW947WP6Cdefinitiondefinition, section 62.10napkin
9Q972J5WD8exerciseproblem, section 19.8napkin
9QJRZAG5CKexerciseexercise, section 10.2napkin
9R6QJ9KDP4proofproof, section 63.3napkin
9R9WTH1KSTexampleexample, section 99.3napkin
9RFP3X86ANexerciseproblem, section 100.8napkin
9RK5NCWYRBdefinitiondefinition, section 90.1napkin
9SEBZW8KJBproofproof, section 14.2napkin
9SET2A9RNWexampleexample, section 29.3napkin
9T53BDZ005statementcorollary, section 44.3napkin
Gaussian integers {$\ZZ[i]$} form a UFDstatementtheorem, section 9.8napkin
9VZBMDPPZHproofproof, section 50.1napkin
9WC1K9KT7Texampleexample, section 2.2napkin
9WHPSJVDSXdefinitiondefinition, section 6.2napkin
9WM47JP3Q6statementtheorem, section 13.5napkin
9X17DCJFDMexerciseexercise, section 96.4napkin
9XCD7PV5ZDproofproof, section 97.3napkin
9XJF2Z035Dexampleexample, section 22.4.1napkin
9XRD2P57QSexerciseproblem, section 55.4napkin
9Y5EAW67S2exerciseexercise, section 52.6napkin
9YB5KG94MZdefinitiondefinition, section 43.7napkin
9YG1VTBQ80proofproof, section 9.8napkin
China TST 1998exerciseproblem, section 9.9.3napkin
Map of space $\implies$ map of singular chain complexesstatementlemma, section 55.3.2napkin
Discriminant of $K = \QQ(\sqrt2)$exampleexample, section 9.2napkin
9Z37QB1Y40exampleexample, section 100.1napkin
9ZMKY8Z78Rexerciseques, section 3.5napkin
A0CB47PFMNexerciseproblem, section 5.10napkin
The punctured plane is homotopy equivalent to $S^1$exampleexample, section 98.5napkin
A1CWDJE5EEstatementtheorem, section 6.2napkin
A1K859726Dproofproof, section 28.3napkin
A2KZTH9Y9Wexerciseexercise, section 59.3.1napkin
A36WEBMBVFdefinitiondefinition, section 97.5napkin
A38SJRVT0Jdefinitiondefinition, section 42.1napkin
A3ESPTV8YHstatementlemma, section 13.1napkin
Induced maps of relative homologystatementlemma, section 53.3napkin
A4K1FGQ82Qexerciseexercise, section 15.2napkin
General lifting criterionstatementtheorem, section 97.2napkin
A6526RR5PKexerciseproblem, section 52.8napkin
A6RPJQ7X0Rexerciseexercise, section 93.2napkin
A75B0572T6definitiondefinition, section 80.2napkin
A84YC8VSN3definitiondefinition, section 6.1napkin
A8C83G2MQ7exerciseexercise, section 92.6napkin
A8E3EK5CTBproofproof, section 88.3napkin
A8K56XYFKWproofproof, section 81.3napkin
A8QW467D9Yexerciseexercise, section 13.6.4napkin
A9BE1GGXHCdefinitiondefinition, section 100.4napkin
A9J9T2MD8Rexerciseproblem, section 95.6napkin
A9YTGEC2CBexerciseques, section 90.1napkin
AAR1WYK67Ystatementcorollary, section 34.3napkin
AB00MC8S4Vstatementtheorem, section 69.1napkin
Cubic Formulaexampleexample, section 42.3napkin
ACFF125QTSexercisedproblem, section 24.4napkin
ACG0TRNBE0exerciseexercise, section 2.3napkin
ACJKTRZ4HNdefinitiondefinition, section 95.3napkin
ACQ2C07ET6proofproof, section 20.4napkin
ACQ99D2Q8Ydefinitiondefinition, section 16.3napkin
ADGZAMWW3Wexerciseques, section 19.2napkin
$(z-i)^{-3} \cdot (z-\infty)^{-4}$ as a divisorexampleexample, section 87.2napkin
Examples of homeomorphismsexampleexample, section 100.4napkin
AF1X85SAM3exerciseques, section 89.6napkin
AFNA3RGJXWexerciseexercise, section 92.6napkin
Norm of $a+b\sqrt2$exampleexample, section 15.1napkin
AGCCJ58DZJexerciseexercise, section 2.1napkin
Norms and traces are rational integersstatementproposition, section 15.1napkin
Transitive sets inheriting $\ZFC$statementlemma, section 91.5napkin
AHZM2Q2VVQexerciseexercise, section 18.4napkin
AJ1PS11TVVstatementcorollary, section 20.5napkin
AJN4WPC7MMproofproof, section 62.4napkin
AKNH84X426exampleexample, section 65.3napkin
$\ZZ/5\ZZ$exampleexample, section 5.6napkin
Ideal norm of $(2+i)$ in the Gaussian integersexampleexample, section 10.7napkin
ANDB17X8H3exampleexample, section 55.2napkin
ANXZCV08E6definitiondefinition, section 22.1napkin
APAZH9MDG0exerciseproblem, section 30.6napkin
APF32X6P0Jdefinitiondefinition, section 3.1napkin
APTVKMRBK8exerciseques, section 13.2napkin
AS77DHKS83exerciseproblem, section 1.4napkin
AS865PTDW2definitiondefinition, section 15.2napkin
ASJ047ZEFMexerciseques, section 67.4napkin
AV9E34AWV0exampleexample, section 90.2napkin
AVA91Q3S6Gexerciseques, section 89.1napkin
AVD8RQT4TSproofproof, section 78.1napkin
AVHW4HS9PGproofproof, section 63.2napkin
An example of a $\ZZ$-moduleexampleexample, section 62.10napkin
AVXA7CBXX4proofproof, section 41.3napkin
AW5T21W7F9definitiondefinition, section 41.2napkin
AWCYQXTSNNexerciseproblem, section 2.8napkin
MathCounts Chapter Target Roundexerciseexercise, section 1.3napkin
AWMYT63GFTdefinitiondefinition, section 37.6napkin
AX54ZMPJFHdefinitiondefinition, section 30.1napkin
AX9JQVG8B2proofproof, section 81.4napkin
AXQA0MZTNYexerciseexercise, section 24.2.1napkin
Dihedral groupexampleexample, section 3.1napkin
AY95MW3A5Rproofproof, section 52.1napkin
AY9AZ5448Jstatementlemma, section 70.3napkin
AYJBPZKKJKexercisedproblem, section 34.7napkin
AZ2HTCYZ7Dexerciseexercise, section 60.1.1napkin
AZ4TM2P86Zexampleexample, section 79.4napkin
Metric spaces of $\RR^n$exampleexample, section 100.1napkin
AZE37RNTD9statementcorollary, section 40.5napkin
AZVD1JQEQ9exerciseexercise, section 20.2napkin
B0MWZFMCVBdefinitiondefinition, section 43.1napkin
B0NDAXWYWHexerciseexercise, section 28.3napkin
B0P4DX84FGexampleexample, section 21.2napkin
B1W5EW1PB5definitiondefinition, section 35.1napkin
Real functions vs.\ germsexampleexample, section 25.5napkin
B32GMT5ARBexerciseproblem, section 69.6napkin
B3KQVMZDVVdefinitiondefinition, section 44.7.1napkin
Decomposition group and Galois groupstatementtheorem, section 18.5napkin
B5M5D7SXG5exampleexample, section 61.1napkin
B5TCSYJPV1exampleexample, section 62.6.2napkin
Discriminant of $\QQ(i)$exampleexample, section 9.2napkin
B7BHPSPDS9statementproposition, section 66.3napkin
B832SSTVY1definitiondefinition, section 95.1napkin
B83REWSNSHdefinitiondefinition, section 62.6.1napkin
B88AG502RFexerciseques, section 62.2napkin
Maximums Occur On Boundariesexercisedproblem, section 39.7.2napkin
B8BQB5ZZE0statementproposition, section 33.2.3napkin
B8V1H8XNYJdefinitiondefinition, section 60.3napkin
$G$ encodes distinct real numbersstatementlemma, section 88.1napkin
Quotients and products don't necessarily cancelexampleexample, section 3.5napkin
B9YF5BCJWXexerciseproblem, section 55.4napkin
BA0T6AB7GJexampleexample, section 5.8napkin
BA6DDHGMZ8proofproof, section 9.7napkin
$e^x \ge 1+x$statementproposition, section 30.3napkin
BAQTX7BMTPexerciseques, section 92.7napkin
BB01X0BKEYexerciseproblem, section 39.7.2napkin
BBH70J7ACKexampleexample, section 2.1napkin
BBRBAR9NBTexerciseques, section 40.3napkin
BBYFHDVC1Yexampleexample, section 96.5napkin
BBZG2MF7VWexerciseproblem, section 16.5napkin
BC35B3HWA7exerciseproblem, section 98.6napkin
BC6X6234Y0exerciseproblem, section 94.6napkin
BCQNX9S5PHexerciseques, section 63.5napkin
BCVH4G392Bexampleexample, section 50.4napkin
Projection principlestatementtheorem, section 45.2napkin
$\RP^n$ as a cell complexexampleexample, section 96.6.3napkin
BDJA1XFHF2statementfact, section 3.2napkin
BE61XYAKM6exerciseexercise, section 52.4napkin
Base fieldexampleexample, section 12.1napkin
BESNB6RPHEstatementtheorem, section 50.5napkin
BFSH1CY2FCdefinitiondefinition, section 61.4napkin
BH6YHV1CX8exerciseproblem, section 95.6napkin
The $1$-form $dz$exampleexample, section 84.2napkin
BHV2FD7DPDproofproof, section 66.5napkin
BJ3WBS1H84statementlemma, section 70.3napkin
BJDM062Z9Fexerciseexercise, section 60.2napkin
The multiplicative group of $\FF_{17}$exampleexample, section 12.5napkin
BK14ZEM4Q8statementcorollary, section 66.5napkin
BK22REEMTDexerciseproblem, section 16.5napkin
BKET8S4GGZdefinitiondefinition, section 66.3napkin
Automorphism group of $\QQ(\sqrt2,\sqrt3)$exampleexample, section 14.5napkin
BMDA1Q2Y3Hproofproof, section 79.2napkin
BN6GM10KYZexerciseproblem, section 6.6napkin
BP8JHS0ADJexampleexample, section 54.1napkin
BPQBN3S4A1exampleexample, section 53.3napkin
BQX5GDYM76exerciseques, section 9.1napkin
BRJA78D1CTexampleexample, section 4.7napkin
Completion of a metric spaceexercisedproblem, section 99.5napkin
BRNA2BH8X8exerciseques, section 100.6napkin
Images of compacts are compactstatementtheorem, section 95.4napkin
BTDA6BX12Ndefinitiondefinition, section 20.2napkin
BTSXGM9SJVexerciseques, section 86.2napkin
BVPJ5M759Ddefinitiondefinition, section 33.4napkin
BWAEH5DRQ3exampleexample, section 98.2napkin
BWM9ESJCKFexampleexample, section 55.4napkin
BX2QP7HBCRstatementclaim, section 80.6napkin
BX9DW50Y4Aexerciseproblem, section 11napkin
BXEEZN6998statementtheorem, section 59.6napkin
BY82DV7P3Vexerciseproblem, section 56.3napkin
BYQZXM376Pproofproof, section 12.3napkin
BYTN0KG1STexampleexample, section 99.1napkin
BYVA9XNKX3proofproof, section 21.6napkin
BYXZBZKYR7exerciseexercise, section 4.4napkin
BZT4HB7W5Gexampleexample, section 79.4napkin
BZTTNZHNB4statementtheorem, section 9.4napkin
Functorial interpretation of fundamental groupsstatementtheorem, section 98.6napkin
C14K1XWANZstatementtheorem, section 18.4napkin
C1WTC6XS10definitiondefinition, section 18.5napkin
C1ZC54C9P0definitiondefinition, section 58.6napkin
C36NJTYQ9Zdefinitiondefinition, section 64.1.1napkin
C3NMDTNRM6statementproposition, section 3.2napkin
$\delta$ with cup productsstatementlemma, section 52.4napkin
C3V1Y43ER7statementproposition, section 33.3.3napkin
C4DB622Q6Aexerciseques, section 43.5napkin
C4EJ788XXRexampleexample, section 51.2napkin
C62Y1WYRVPstatementproposition, section 70.1napkin
C6FCP0GM4Eexampleexample, section 43.3napkin
C6P4PDZVFZproofproof, section 30.4napkin
C73Z2DWCQQexerciseques, section 89.2napkin
C7B8TY95R8statementcorollary, section 70.4napkin
C7BNFNJWBCproofproof, section 95.2napkin
Cohomology ring of $S^n$exampleexample, section 52.4napkin
Monic $\iff$ trivial kernelstatementproposition, section 35.2napkin
C8G1NV8EQBproofproof, section 5.6napkin
C8MJK1B26Sdefinitiondefinition, section 92.3napkin
C8PC5RVE9Eexampleexample, section 46.4napkin
C9D0K1XZY6statementtheorem, section 70.4napkin
C9VEVRZJQBexerciseques, section 101.7napkin
CA5EHHRB0Pexercisesproblem, section 1.4napkin
CAA20ZY7AHexercisedproblem, section 91.9napkin
Chain ruleexercisesproblem, section 45.5napkin
CBYATQBP2Tproofproof, section 100.5napkin
CCE35X2PQDexerciseproblem, section 30.6napkin
CCG5XX2DN2proofproof, section 22.7napkin
CCHT6113K6proofproof, section 20.2napkin
CCZQEFD58Cdefinitiondefinition, section 62.3napkin
CD94XJABV2exerciseques, section 61.5napkin
Open subsets of $\CC$exampleexample, section 83.4napkin
CE4J51J77Vdefinitiondefinition, section 88.3napkin
CFH3BKQ2QAexerciseexercise, section 76.3napkin
CFNM4WYNG3proofproof, section 29.4napkin
CG10AY6682statementlemma, section 91.6napkin
CG97KA4ZG6exerciseproblem, section 101.9napkin
CHCCM1HYVHproofproof, section 81.1napkin
CHNFH04DTGproofproof, section 59.3.2napkin
CHPQAB2K3Qexampleexample, section 97.1napkin
CHRGKSEXT8exerciseexercise, section 46.3napkin
CJ4ST236AYexerciseproblem, section 60.5napkin
CJG4YCFWSVdefinitiondefinition, section 53.3napkin
CJP9KR1TBFexercisedproblem, section 33.5napkin
CJT2JTF69Aexerciseques, section 16.1napkin
CJWFYEEC2Qexerciseexercise, section 9.9.2napkin
CJWZVK495Sstatementproposition, section 19.4napkin
CK3ZQY1HJBexerciseproblem, section 40.5napkin
CM6D751ZWEstatementtheorem, section 81.3napkin
CMGDYKKRCZexampleexample, section 22.4.1napkin
CMPCDG9PPWexampleexample, section 63.4napkin
CMPK85R02Adefinitiondefinition, section 66.2napkin
CMQW670NG0exampleexample, section 22.4.2napkin
CMVFRYY2F2exampleexample, section 8.7napkin
CP4MVZA66Texercisesproblem, section 15.4napkin
CP5SGDE8W4definitiondefinition, section 63.3napkin
CPGV6DR5XCexerciseques, section 7.3napkin
CPWX3T8E4Pexerciseproblem, section 16.5napkin
Consistency and Persistencestatementlemma, section 90.5napkin
CRPZY8Q7VJexampleexample, section 30.1napkin
CRQDQ829WQexerciseques, section 5.7napkin
CS20ZCWD98statementtheorem, section 30.2napkin
CSPHVMXM2Kexampleexample, section 22.6napkin
CV0505996Wexampleexample, section 32.3napkin
CV1915KQC5statementcorollary, section 22.7napkin
CV41MKTCG6exerciseproblem, section 2.8napkin
CVAHHQFZ65proofproof, section 92.4napkin
CVZ65BQX15statementtheorem, section 6.5napkin
CWA91HVD3Jstatementtheorem, section 68.4napkin
CWG6RNR1DKexampleexample, section 56.2napkin
CWJ27MY7Y2statementtheorem, section 23.3napkin
CXGC988PKQproofproof, section 13.1napkin
Intersections and unions of varietiesstatementtheorem, section 19.4napkin
CXHE24JDPKdefinitiondefinition, section 81.5napkin
CYG3D6WEQGproofproof, section 8.5napkin
Discriminant of cyclotomic fieldexercisesproblem, section 11napkin
CYN7A1X3VEproofproof, section 20.3napkin
Size of the mousetrapstatementlemma, section 9.5napkin
CYYATF9XXNexampleexample, section 21.6napkin
CZP096DNDVexerciseques, section 85.3napkin
CZZ5G4GA93proofproof, section 57.1napkin
D09Z3A8SQDexerciseques, section 60.2napkin
D0R0VZN05Adefinitiondefinition, section 79.2napkin
D0X3K10GBTexerciseexercise, section 59.3.2napkin
D11TG4AQZTexerciseexercise, section 42.3napkin
D13ADGQ8BYstatementtheorem, section 1.3napkin
An atlas on $S^1$exampleexample, section 44.1napkin
D1J9KQFVV9definitiondefinition, section 28.3napkin
Computing some exterior derivativesexampleexample, section 43.4napkin
D1VSGV6JEZdefinitiondefinition, section 79.3napkin
Cohomology is anticommutativestatementproposition, section 52.4napkin
D2Y59MPGE3statementtheorem, section 99.2napkin
D3GBGCE913exerciseques, section 26.14.4napkin
D4BGSEQGV5exampleexample, section 96.4napkin
D55JQ0E6FPexampleexample, section 15.2napkin
D595K3GK1Aexerciseques, section 18.4napkin
D5S6DP2PMNexampleexample, section 5.3napkin
Open set conditionstatementtheorem, section 100.6napkin
D69E6G1FYPstatementproposition, section 33.3.2napkin
The Riemann sphereexampleexample, section 83.4napkin
D71VQREWMTexercisedproblem, section 18.6napkin
D7E806Y54Bdefinitiondefinition, section 55.3napkin
D7HKCSRJR4exerciseques, section 101.2.1napkin
D7K9JQSQM0definitiondefinition, section 70.1napkin
D7KD5DDGFCexerciseques, section 19.4napkin
D7S6GG0VZVdefinitiondefinition, section 96.4napkin
D7ZNZC4M9Jexerciseproblem, section 95.6napkin
D8B27020CWexampleexample, section 23.5napkin
D9MS5WXB8Zproofproof, section 32.2napkin
D9NT9JNNYQdefinitiondefinition, section 83.2napkin
DA2RM1SZ7Pexerciseques, section 12.5napkin
DB1T6F421Rexerciseproblem, section 56.3napkin
DB8GTYMQFAstatementtheorem, section 7.3napkin
DB9SB2C1Z0statementtheorem, section 30.4napkin
DBJTH6PTTQexercisedproblem, section 63.7napkin
DBNHXM3MGNdefinitiondefinition, section 23.4napkin
DBRJWYN8VQexerciseques, section 95.5napkin
DCH7VGTRC4exerciseproblem, section 56.3napkin
DCKJAYD449exerciseproblem, section 1.4napkin
DD9A5VQ39Mexerciseexercise, section 5.6napkin
DDRRT7TD4Aexampleexample, section 22.4.4napkin
DDX2TVQFCPexerciseexercise, section 22.5napkin
DEGBRR0E3Fexerciseproblem, section 9.9.3napkin
DEKPJXRS8Zexerciseexercise, section 100.6napkin
DFKW63Q4ZKexerciseques, section 8.7napkin
DG38FGXQ9Pdefinitiondefinition, section 57.2napkin
DG3VX1AKJDexerciseexercise, section 39.7.2napkin
DGJQSBX67Dexerciseexercise, section 79.3napkin
DHGX2E9T0Sexerciseexercise, section 3.2napkin
DJNZNY212Rproofproof, section 6.2napkin
DJW3RMKTEPdefinitiondefinition, section 97.2napkin
DK8VYQB6JKexerciseproblem, section 9.9.3napkin
Covering projection of $S^1$exampleexample, section 97.1napkin
DKMHG5ZH8Kdefinitiondefinition, section 22.10napkin
DM13FXHREVexerciseproblem, section 66.7napkin
DMEXYR37R6exerciseproblem, section 66.7napkin
DN3FWEZR2Texerciseques, section 1.4napkin
DNM18D7MFAproofproof, section 92.4napkin
DP7VKH7RSPexerciseexercise, section 10.7napkin
DPC31M1B0Jexampleexample, section 43.5napkin
DPG6VSZZMJproofproof, section 53.6napkin
DQVFHJKF6Jexerciseproblem, section 58.8napkin
DR6DA63YHMstatementtheorem, section 8.6napkin
Basic examples of signaturesexampleexample, section 9.3napkin
DRAE5T8S6Kexerciseques, section 62.7napkin
DTRXJK4BN8exampleexample, section 2.1napkin
DTV4SXK4VZexercisesproblem, section 91.9napkin
DTZ6V8M9WXdefinitiondefinition, section 43.5napkin
Field characteristicsexampleexample, section 14.4napkin
Closed sets are complements of open setsstatementtheorem, section 100.7napkin
DW750RSPYSexampleexample, section 96.6.3napkin
DWBY0SZW6Pexerciseques, section 44.1napkin
DWCSZT5CSQdefinitiondefinition, section 66.4napkin
DWD854KRW2definitiondefinition, section 62.3napkin
DWJ38KY3V8exercisedproblem, section 98.6napkin
DWK1SR7P4Bexerciseques, section 92.7napkin
DWWD6G6MJ3exampleexample, section 62.6.2napkin
Countable transitive modelstatementtheorem, section 91.7napkin
DXA2QQ2RENexerciseques, section 88.2napkin
DXA85FKV58statementtheorem, section 92.5napkin
DXX078DF9Xdefinitiondefinition, section 22.3napkin
DXXK00RCQFexerciseproblem, section 14.6napkin
Composition of continuous functions is continuousstatementproposition, section 100.3napkin
DY08MNT722definitiondefinition, section 88.4napkin
DY678JX2ZQexampleexample, section 5.3napkin
DY6A9TQE09exampleexample, section 62.6.2napkin
DYA46F1BJ3exampleexample, section 55.2napkin
DYD51SJTM6exampleexample, section 20.2napkin
$\omega^\omega$ is countableexampleexample, section 89.1napkin
Greek constructionsexerciseproblem, section 14.6napkin
DZ1QXSDJATexampleexample, section 8.5napkin
DZDMQHDP8Sstatementtheorem, section 79.2napkin
DZHJTTRRB4statementproposition, section 19.3napkin
DZJ511TSARexercisesproblem, section 51.8napkin
DZMY7RPNT3exampleexample, section 52.7.3napkin
DZS9PM7MBJproofproof, section 80.6napkin
Fredkin gateexerciseproblem, section 75.4napkin
E0MYXHMSK8exerciseques, section 85.3napkin
E0NEHCPRT2statementtheorem, section 4.4napkin
$V$ versus $V^\vee$ for complex inner formsstatementtheorem, section 61.3napkin
The determinant of a $2 \times 2$ matrixexampleexample, section 56.2napkin
E2F6CW58MFdefinitiondefinition, section 101.6napkin
E3CH1JH36Jexerciseproblem, section 30.6napkin
E3KG0W50KXstatementtheorem, section 13.7napkin
E416G64VM5definitiondefinition, section 67.4napkin
Finite fields are field extensions of $\FF_p$statementlemma, section 12.2napkin
E4ERW0DD44statementtheorem, section 27.2.1napkin
E51VW2W351exerciseproblem, section 5.10napkin
Column operationsexerciseproblem, section 56.3napkin
E6E72JW432exerciseques, section 8.7napkin
E6J7VZMWCZexampleexample, section 92.7napkin
E6M261HC4Fexerciseproblem, section 89.7napkin
E6S4DFTXCMexerciseques, section 22.11napkin
E74GJ1KXNGdefinitiondefinition, section 1.4napkin
E78JPM2F7Sproofproof, section 7.1napkin
E7G4N7GH92statementtheorem, section 80.5napkin
E7RJ7FAJR6exerciseproblem, section 95.6napkin
E83JRHEAT7exerciseexercise, section 14.7napkin
E847RNH6NKproofproof, section 35.2napkin
E92DD114J4definitiondefinition, section 97.1napkin
E95RD87GA5definitiondefinition, section 90.3napkin
E9CWBYKW80definitiondefinition, section 29.5napkin
E9GWXDH2JCproofproof, section 12.3napkin
Example of canonical embeddingexampleexample, section 9.3napkin
EA5V6E5XVXproofproof, section 4.4napkin
Chain conditions preserve regular cardinalsstatementtheorem, section 88.3napkin
$\CC$ is contractibleexampleexample, section 98.5napkin
ECN6ZSBKQQproofproof, section 23.3napkin
EDQZR8Z3N3definitiondefinition, section 91.4napkin
$\half$ isn't an algebraic integerexampleexample, section 15.2napkin
Examples of linear mapsexampleexample, section 62.5napkin
EEZA4NTEK6statementtheorem, section 20.3napkin
EF8CQDGNF9exerciseques, section 90.3napkin
Artin's primitive element theoremexerciseproblem, section 14.6napkin
EGW5V0V77Kexerciseproblem, section 2.8napkin
EHEFVS2EBGexerciseproblem, section 4.8napkin
EHTZ89K0B9definitiondefinition, section 25.4napkin
EJ31JHK1HAexerciseexercise, section 60.1.2napkin
EJJG704EZTproofproof, section 3.5napkin
EJSVXNKN0Rexerciseproblem, section 62.11napkin
Representation of $S_n$ decomposesexampleexample, section 80.4napkin
EKNF7H9T52proofproof, section 10.3napkin
EM0Y88V1BCstatementtheorem, section 52.7.2napkin
EMY3NT98HEdefinitiondefinition, section 100.1napkin
EN9MKGCCTSexerciseproblem, section 42.5napkin
ENGPS0CB4Texerciseques, section 100.6napkin
ENJEW81QZ3exerciseques, section 92.3napkin
ENTP1HBWB9statementtheorem, section 80.5napkin
EPBTXBSS60exerciseproblem, section 61.6napkin
EPNHR10QK2exampleexample, section 41.2napkin
EQBZAK02TTdefinitiondefinition, section 34.4napkin
ERB8SBZQNFproofproof, section 89.6napkin
ERDKXMQRK2definitiondefinition, section 22.3napkin
ESBKX5M7EPstatementtheorem, section 12.4napkin
ESMV54YNG6definitiondefinition, section 55.2napkin
EST1CW940Bstatementproposition, section 22.7napkin
ESVBDZ6J1Gexerciseques, section 91.2napkin
ETE1Z105MZexampleexample, section 41.2napkin
ETKWJ79MQ6proofproof, section 30.4napkin
EVJF75WZ50definitiondefinition, section 60.4napkin
EW5B09FSHGexerciseproblem, section 54.3napkin
EWBVGHGBA5statementtheorem, section 4.6napkin
$\alpha \in \ol\ZZ$ $\iff$ {$\ZZ[\alpha]$} finitely generatedstatementlemma, section 15.2napkin
EWT59EM0BFdefinitiondefinition, section 33.2.1napkin
EX5T0JF5P1definitiondefinition, section 19.5napkin
EXDFYZN1FRproofproof, section 33.4napkin
EXKR6JD1K8definitiondefinition, section 98.2napkin
Homology of wedge sumsstatementtheorem, section 53.5napkin
EY7FRYBM1Eexercisesproblem, section 41.6napkin
EYCG18KC6Ndefinitiondefinition, section 24.1napkin
EZD2J0VE7Hexerciseproblem, section 36.5napkin
Infinite binary treeexampleexample, section 90.1napkin
F1SAAE3579statementproposition, section 87.4napkin
F1V9AT2P4Hproofproof, section 27.2.2napkin
F1X3J880Y9exerciseques, section 55.4napkin
F21Y9EBAQHexampleexample, section 15.2napkin
F2BW3Z5NEEdefinitiondefinition, section 25.2.1napkin
F2Q1JYADN1statementtheorem, section 33.4napkin
F3FYVYJ8SEdefinitiondefinition, section 23.5napkin
F3J2WT5PPRstatementcorollary, section 30.2napkin
F4Y4JBS0S7statementproposition, section 4.7napkin
F55RPXJHB5statementproposition, section 63.1napkin
F5F9H0D568exampleexample, section 64.1.1napkin
F67XH6A1AZexampleexample, section 2.3napkin
F6SHMCN0FTexampleexample, section 58.5napkin
F6XEHTHDCEproofproof, section 18.4napkin
F738SFBDYBexerciseproblem, section 66.7napkin
F7APAF9876proofproof, section 9.8napkin
F7PQMB18KJproofproof, section 55.1napkin
F8HYGFTZESdefinitiondefinition, section 46.4napkin
F8JT8MYW9Cexampleexample, section 55.1napkin
F8X16SQPQ5proofproof, section 6.5napkin
F8ZM6QK53Jproofproof, section 58.8napkin
F999TMDGXGexerciseques, section 45.1napkin
FA1HJF78GTproofproof, section 45.3napkin
Triple product of primesstatementproposition, section 7.1napkin
FAF1TKR4GVexerciseques, section 23.2napkin
FAG5964BMYexerciseexercise, section 61.5napkin
FC10X45BBAexerciseques, section 13.8napkin
FC2DN5J85Ydefinitiondefinition, section 90.2napkin
FDDJ9Z3R5Gstatementtheorem, section 55.1napkin
FDSB9J4B1Yexerciseexercise, section 32.2napkin
FEJ2B9J7NQstatementlemma, section 50.2napkin
FEQ460AADXdefinitiondefinition, section 5.4napkin
Homology is a functor $\catname{hTop} \to \catname{Ab}$statementtheorem, section 55.3napkin
FFG9T4SN24definitiondefinition, section 6.2napkin
FFZHGC2KKRproofproof, section 59.5napkin
Trace representation of $\Delta_K$exercisesproblem, section 11napkin
FGRMPWJ4RAdefinitiondefinition, section 52.8napkin
FH49BD0A4Bdefinitiondefinition, section 55.4napkin
FHC9CJTRHPexerciseproblem, section 24.4napkin
FHDEEP6415statementtheorem, section 75.4napkin
Irreps give an orthonormal basisstatementcorollary, section 79.3napkin
FHWYMC16KPproofproof, section 90.2napkin
FJFJGVD72Zexerciseproblem, section 10.7napkin
Rational algebraic integers are rational integersstatementproposition, section 16.2napkin
FKKWKGTRXDdefinitiondefinition, section 96.3napkin
FKSR23SQN8exampleexample, section 4.5napkin
FKXAM4JHVGdefinitiondefinition, section 14.4napkin
FMGEHGRP05definitiondefinition, section 90.3napkin
FNEDDSHZQ0definitiondefinition, section 93.5napkin
FNQ2RD43TYstatementproposition, section 22.2napkin
FP0CHFAJ9Pexerciseques, section 79.1napkin
FPNV69KAPKdefinitiondefinition, section 91.2napkin
FQ5QPP0V36definitiondefinition, section 8.6napkin
FQ8SMXXH9Yexerciseques, section 5.3napkin
FQS8T3T1G1statementtheorem, section 70.4napkin
FQVFN38DV3exerciseproblem, section 61.6napkin
FQZ41S6NWKstatementproposition, section 89.3napkin
FRJ29J5Q1Wproofproof, section 9.8napkin
FRMGP93Q7Gexampleexample, section 22.4.2napkin
FRND6AQJS8proofproof, section 25.6napkin
FRTFE5KH9Vproofproof, section 101.8napkin
FRTMR4PCZMstatementproposition, section 21.6napkin
Infinite cardinals squaredstatementtheorem, section 89.4napkin
FSEY076ERXexerciseques, section 21.4napkin
Examples of graded ringsexampleexample, section 52.3napkin
Sections of a line bundledefinitiondefinition, section 85.2napkin
FV74BFZ247definitiondefinition, section 92.3napkin
FVSGN4QZH4definitiondefinition, section 80.3napkin
FW0073T8HNstatementtheorem, section 50.4napkin
FWM41G68BXstatementproposition, section 16.2napkin
FWN2AA4WJJexerciseques, section 62.5napkin
FX66BJ7SWBexerciseproblem, section 9.9.3napkin
$\RR^n$ and $\CC^n$ are normed vector spacesexampleexample, section 60.2napkin
Example of a non-normal subgroupexampleexample, section 3.5napkin
FYV1NN0FT8exercisesproblem, section 54.3napkin
FZ081PSAY9exerciseproblem, section 32.8napkin
FZXSV146WGdefinitiondefinition, section 19.1napkin
G0E8QX9X5Pproofproof, section 6.3napkin
G0W22QAPX4exampleexample, section 66.2napkin
G0WNGECA2Wstatementlemma, section 91.4napkin
G1DEKY4603statementtheorem, section 27.3.1napkin
G1G8VPT1GHexerciseproblem, section 60.5napkin
G1W0QRVPAXexampleexample, section 5.7napkin
G2AZDJ0JBPdefinitiondefinition, section 25.6napkin
$x^2-5y^2 = \pm 1$exampleexample, section 17.4napkin
G2VYC2DGE8exerciseproblem, section 34.7napkin
G3J1ER8Q8Bexerciseproblem, section 2.8napkin
Proof of \Cref{thm:uniqueness_primary_form_one_prime_torsion_module}proofproof, section 6.5napkin
G4EAV3JT5Jexerciseques, section 30.5napkin
G4XP4Y0AEYdefinitiondefinition, section 31.4napkin
Maximality and minimality of basesstatementtheorem, section 62.4napkin
G5MAXSFPC7statementproposition, section 21.5napkin
G5NF8966FQexerciseproblem, section 26.19napkin
G5Y8W9B75Cstatementcorollary, section 70.4napkin
G7BHHWGX76exerciseproblem, section 95.6napkin
G7BZW3R4AYstatementtheorem, section 68.2napkin
G7HPFRWDE7exampleexample, section 4.4napkin
G89B5DY49Gexerciseproblem, section 11napkin
G8D5EXECQ8definitiondefinition, section 80.5napkin
G8MBWDC1CCstatementfact, section 5.3napkin
Effect of the mousetrapstatementlemma, section 9.5napkin
GA75R8YX8Zproofproof, section 75.2napkin
GA8XH2ZNTTexercisedproblem, section 27.7napkin
GB224PAJ8Tdefinitiondefinition, section 100.5napkin
GBMV6VMEFMdefinitiondefinition, section 31.3napkin
GCYZ0P5W4Kexerciseques, section 22.7napkin
GD0EW9XZQSexampleexample, section 67.5napkin
GD1F3VGZMQproofproof, section 51.4napkin
GD93MP135Fstatementtheorem, section 25.3napkin
GDQNX5YMSAexerciseexercise, section 70.4napkin
GEKHTR54Y1exampleexample, section 100.7napkin
GEQT901ZESdefinitiondefinition, section 44.2napkin
GESCXA2E6Fexerciseproblem, section 3.6napkin
Important: prime ideals divide rational primesstatementtheorem, section 10.3napkin
Inertial degree and ramification indices are all equalstatementtheorem, section 18.4napkin
GGSZXB6TR0definitiondefinition, section 63.1napkin
GGVFQG4QBNproofproof, section 90.2napkin
A conic in $\CP^2$, or a cone in $\CC^3$exampleexample, section 23.2napkin
GHQN1E627Ystatementproposition, section 34.4napkin
GHSQC51FFRstatementproposition, section 75.2napkin
GHV6ZAVQZVexerciseexercise, section 26.16napkin
GHYAFGWRTKdefinitiondefinition, section 66.5napkin
GJ4ZP16V2Ddefinitiondefinition, section 30.3napkin
GJG07PNWX6exampleexample, section 20.2napkin
GK4N51H9WZexampleexample, section 59.3.2napkin
GK825Y5J5Cstatementtheorem, section 63.2napkin
GKPVBGWENCexerciseproblem, section 68.6napkin
GMHNG8FAZ3exerciseproblem, section 32.8napkin
Root representation of $\Delta_K$exercisesproblem, section 11napkin
GMPKK2G1SDexerciseproblem, section 50.5napkin
Ordinals represent all order typesstatementtheorem, section 92.3napkin
GN88TAMJFTexercisesproblem, section 61.6napkin
GNEYGF4C9Texerciseproblem, section 81.5napkin
GPGYHQ02ZFexampleexample, section 58.5napkin
Field extensions have multiplicative degreestatementtheorem, section 14.2napkin
GQS1KBB4ECexerciseproblem, section 99.5napkin
Kernelsexampleexample, section 62.7napkin
GR3XXZ27B9exampleexample, section 1.2napkin
GRP5M7DXP1exerciseproblem, section 64.4napkin
GS2PVT50ZJstatementtheorem, section 27.6napkin
GSPR9GKF41definitiondefinition, section 8.5napkin
GSZT3QTE1Bexercisedproblem, section 62.11napkin
GT3ZPPRTTXexerciseques, section 80.1napkin
Eigenvalues always exist over algebraically closed fieldsstatementtheorem, section 58.3napkin
$\RR^n$ and $\CC^n$ have standard basesexampleexample, section 60.3napkin
GTTFVSQYG3exerciseques, section 58.8napkin
GVD95CRBSWexerciseexercise, section 33.2.1napkin
Regular functions on distinguished open setsexampleexample, section 29.6napkin
GWA19N3Z3Wexampleexample, section 68.1napkin
GX1AGC4CCXexerciseques, section 58.4napkin
Graded quotients are graded toostatementlemma, section 23.1napkin
GXBXEP87VFproofproof, section 92.3napkin
GXPWW1G7JJdefinitiondefinition, section 97.3napkin
Orders of groupsexampleexample, section 2.4napkin
GYPBKX03MSdefinitiondefinition, section 101.5napkin
GZ4YBBCNXHstatementlemma, section 68.7napkin
Basis of $\RR$exampleexample, section 101.8napkin
GZRXRPV0JFexerciseexercise, section 90.1napkin
H02ZA3Z75Kexerciseques, section 101.7napkin
H04GRTQXK7exercisedproblem, section 16.5napkin
H06J18WF37exampleexample, section 55.4napkin
H0FK19T440statementtheorem, section 12.2napkin
H0YZSPNMA5exerciseproblem, section 25.6napkin
H15FNAVTD3exerciseproblem, section 96.6.4napkin
H1DBBV5SKWexercisesproblem, section 4.8napkin
More product spacesexampleexample, section 96.3napkin
H22D6WAGQFexercisesproblem, section 35.5napkin
H2HGNSX900definitiondefinition, section 3.3napkin
H2JN8N17EQproofproof, section 34.5napkin
Burnsidestatementtheorem, section 78.2napkin
H2TQ1RQ0Y9exerciseproblem, section 16.5napkin
H2WJVWFCCVdefinitiondefinition, section 31.4napkin
Old examples of automorphism groupsexampleexample, section 14.5napkin
H56DC5X61Zexerciseexercise, section 33.3.2napkin
H5F9G28HYGexerciseques, section 36.3napkin
H6ABBGN2NTexerciseques, section 50.2napkin
H6HCK4T1QRexerciseques, section 9.5napkin
H6PFEMQ5KGstatementtheorem, section 37.7napkin
H72CEBCV1Adefinitiondefinition, section 41.2napkin
Sketch of Proofproofproof, section 13.7napkin
H7CAH90G6Cexerciseexercise, section 26.12napkin
H80N0414S3definitiondefinition, section 3.3napkin
H8T0P11ZGGdefinitiondefinition, section 28.3napkin
H8TTCRZS0Yproofproof, section 29.6napkin
H992SCAVXQexampleexample, section 70.4napkin
H9FWCEZ0KEproofproof, section 61.3napkin
$K = \QQ \cdot \OO_K$statementtheorem, section 15.2napkin
H9X9HXGXJDproofproof, section 9.8napkin
HA5AM349Z3definitiondefinition, section 52.8napkin
The homology groups of $S^m$statementtheorem, section 54.3napkin
HB257T7P4Ndefinitiondefinition, section 51.8napkin
HB52Z8SX63definitiondefinition, section 23.4napkin
HBA8N9MCQYdefinitiondefinition, section 43.7napkin
HCJ0CHD6Y6proofproof, section 15.2napkin
Rasiowa-Sikorski lemmaexerciseproblem, section 90.6napkin
HCPMRN583Jdefinitiondefinition, section 101.3napkin
HD1XHK6KD2definitiondefinition, section 57.1napkin
HD3QP9MK4Sexerciseproblem, section 5.10napkin
HD723CGM0Sexampleexample, section 76.1napkin
Factoring $6$ in the integers of $\QQ(\sqrt{-5})$exampleexample, section 10.5napkin
HDSETTYXAJexampleexample, section 34.2napkin
HE6QX26A97proofproof, section 93.2napkin
HEVH007X6Gdefinitiondefinition, section 5.3napkin
Elements of \tempuuujbhtkx\ are integralstatementlemma, section 78.1napkin
HEZ4SK79N4proofproof, section 57.3napkin
HF6JYQZ4W0exampleexample, section 21.4napkin
HFQKTK406Gexercisedproblem, section 80.6napkin
Examples of compact spacesexampleexample, section 95.1napkin
HG7VCGWS26exerciseexercise, section 56.2napkin
HGEGDJGFWCexerciseques, section 6.2napkin
HGJWJYES92exerciseproblem, section 10.7napkin
HGVWWW5WHWexampleexample, section 32.3napkin
HH4D28QNDDexampleexample, section 45.3napkin
Separability in characteristic zerostatementlemma, section 14.4napkin
HH9R8Z2S78exerciseproblem, section 40.5napkin
$\RR^2$exampleexample, section 100.5napkin
HKK80KK9Q9statementproposition, section 5.7napkin
HKQGEZ5006proofproof, section 30.3napkin
HM2KCHT076definitiondefinition, section 34.2napkin
HM8BZG4Y4Hexerciseexercise, section 27.1napkin
HMF5HKD6P3definitiondefinition, section 37.7napkin
HN4B2G33S5exampleexample, section 14.5napkin
HNF123ENKAexerciseques, section 42.1napkin
HNRDCXHPE0exerciseproblem, section 100.8napkin
HP4WR6S6JEdefinitiondefinition, section 67.8napkin
HPQRD23XD7exampleexample, section 80.2napkin
HQ4N5XW231definitiondefinition, section 5.6napkin
HQT7KJCG33statementtheorem, section 16.4napkin
B\'ezout's theorem for curvesstatementcorollary, section 20.5napkin
Kernel and image are subrepresentationsexerciseexercise, section 80.5napkin
HRZAJFJXAJdefinitiondefinition, section 61.1napkin
HSENKQMCRFstatementtheorem, section 8.7napkin
HSVHEQEYQ0exerciseproblem, section 5.10napkin
HSYYE5V1YKexerciseproblem, section 57.5napkin
HT8YR2GG81exerciseques, section 63.4napkin
HV4TR00328proofproof, section 100.5napkin
HVKPS51WBSproofproof, section 100.3napkin
HVVVY54AZXexerciseexercise, section 89.3napkin
Prime factorization worksstatementtheorem, section 10.4napkin
HWAT348VKQexercisesproblem, section 2.8napkin
HWKXXTRGDDexampleexample, section 90.3napkin
HX04AJACA2exerciseques, section 60.1.2napkin
HYCWWR9CX1definitiondefinition, section 62.10napkin
HYXWKH9Y8Gexerciseproblem, section 100.8napkin
HZ4P4AYHSDexerciseques, section 18.1napkin
HZQYQJHZK7proofproof, section 68.7napkin
Factoring algorithm / Dedekind-Kummer theoremstatementtheorem, section 10.5napkin
HZTKBCCPEAexampleexample, section 32.7napkin
J03Y2Z6M84exampleexample, section 37.2napkin
J05J6NJB9Wstatementtheorem, section 68.3napkin
J08PZT5MY1exerciseques, section 100.2napkin
J0E77HH2GKexerciseproblem, section 33.5napkin
Fractional ideals form a groupstatementtheorem, section 10.6napkin
J0XPQ8ZV1Qexerciseproblem, section 58.8napkin
J14EHWKSE9statementproposition, section 86.3napkin
J1CPGKMHX3statementproposition, section 33.3.2napkin
J1DP4FNKS2statementtheorem, section 32.3napkin
J1GAH028RFexerciseproblem, section 80.6napkin
J1ZB0T22XNdefinitiondefinition, section 96.2napkin
The singlet stateexampleexample, section 77.4napkin
J3Q9893XNSexampleexample, section 5.5napkin
Examples of ordersexampleexample, section 2.4napkin
J43KG4BHDRexerciseexercise, section 66.2napkin
Example of an antichainexampleexample, section 88.2napkin
J5GB5S833Eexampleexample, section 7.3napkin
J6FGXTGGHYexerciseproblem, section 26.19napkin
J6XNV15P53exerciseexercise, section 78.3napkin
J7CT5XXBKEdefinitiondefinition, section 86.4napkin
Cellular chain complex gives $H_n(X)$statementtheorem, section 50.2napkin
The $n$ embeddings of a number fieldstatementtheorem, section 14.3napkin
A hyperelliptic curveexampleexample, section 82.3napkin
Cyclotomic Frobenius elementsstatementlemma, section 13.4napkin
J8YH5C4JZPexerciseproblem, section 90.6napkin
Examples of cross product of differential formexampleexample, section 52.7.6napkin
J91F7NBJFRexerciseproblem, section 10.7napkin
J94BK6JNHNexampleexample, section 8.5napkin
J97XMDKREPdefinitiondefinition, section 43.4napkin
JA5RM2X7F4statementproposition, section 28.5napkin
JAD51QV8KKexampleexample, section 28.2napkin
JAVP7R4DNYdefinitiondefinition, section 3.2napkin
JAW0H8C0XTstatementlemma, section 53.2napkin
JB73V9RZ0Fexerciseques, section 101.5napkin
Example of a finite subcoverexampleexample, section 95.3napkin
JCE3HCFP45exampleexample, section 20.3napkin
Proof using coversproofproof, section 95.4napkin
JCW8ZAT7YCstatementtheorem, section 62.4napkin
JDB7PDQWXHexerciseproblem, section 95.6napkin
JDMMA4F3YVproofproof, section 64.3.3napkin
Hermitian matrices have real eigenvaluesstatementtheorem, section 61.5napkin
JEW9QH70PGexampleexample, section 36.2napkin
JEXTCZFXCEdefinitiondefinition, section 46.2napkin
JF2ENKX2F1proofproof, section 64.3.3napkin
{The ring $\ZZ[\frac{1 + \sqrt{-19}}{2}]$ is not a Euclidean domain}exampleexample, section 4.7napkin
JFY1GDVK3Gdefinitiondefinition, section 35.2napkin
JG74T58KZXproofproof, section 30.2napkin
JGRY7K968Kdefinitiondefinition, section 52.3napkin
JGWN2H0M76exerciseexercise, section 12.2napkin
Factoring $5$ in a Galois/non-Galois extensionexampleexample, section 18.4napkin
JHCR86GHXQproofproof, section 28.3napkin
JHYB4Q3KK3exampleexample, section 62.2napkin
JJWX5SJRZMexerciseques, section 55.3.1napkin
JKAX1DT9M1exampleexample, section 20.3napkin
Example of Cayley-Hamilton using determinant definitionexampleexample, section 56.3napkin
JM2BEV0RVJexerciseques, section 10.7napkin
JM63F1JRRBstatementproposition, section 60.4napkin
JMTQZH8SBCstatementtheorem, section 95.2napkin
JN57ETW6C8exerciseexercise, section 9.9.2napkin
JN815N1BZAstatementproposition, section 9.8napkin
JNAHS3PHFFdefinitiondefinition, section 80.2napkin
Infinite cardinal arithmetic is trivialstatementtheorem, section 89.4napkin
JNS2X56BNFexerciseproblem, section 94.6napkin
$\aleph_1$ is regularexampleexample, section 89.6napkin
JPG0036358definitiondefinition, section 95.3napkin
JPJCZJY9FZexerciseques, section 89.4napkin
JQ15K9Q6B2definitiondefinition, section 57.3napkin
JQ1ZKEBABRexampleexample, section 6.5napkin
JQZWDYJB6Nexerciseques, section 101.2.2napkin
JR49Z37KZGproofproof, section 22.11napkin
JRMN8WHTJQexerciseproblem, section 93.7napkin
JRY50D8PXKexerciseques, section 85.3napkin
JS07JS6NX1statementcorollary, section 95.4napkin
JS0GPWQ7BXexerciseexercise, section 9.9.1napkin
JS4DBZNMNEproofproof, section 78.2napkin
JSJ1WZSXWVexerciseques, section 97.2napkin
JT1QPE328Nexampleexample, section 76.3napkin
JT49STSTMDexerciseques, section 57.3napkin
JT4KW6DX72statementproposition, section 8.7napkin
JTQTYY97TFexampleexample, section 8.3napkin
JTSFG4BDPAexercisedproblem, section 50.5napkin
JV1S00DD5Mexerciseques, section 98.5napkin
JVB8CJW09Dexercisedproblem, section 13.8napkin
The Riemann-Roch theoremstatementtheorem, section 87.5napkin
The partial ordering of divisorsdefinitiondefinition, section 87.4napkin
JVK78VPSJWexerciseques, section 22.7napkin
JVME6TAHKQexerciseques, section 76.2napkin
JVS0AYSVVPstatementproposition, section 59.3.2napkin
JW06GBFFNNproofproof, section 91.4napkin
JW142CN6V1exerciseproblem, section 2.8napkin
JW5EXGZA67proofproof, section 63.5napkin
JX7MM77D49exampleexample, section 51.6napkin
JY2N6A0SA1exerciseproblem, section 89.7napkin
These conditions are weakexampleexample, section 97.5napkin
K03TYRBDX6exampleexample, section 17.1napkin
K0J5V3CP5Xstatementproposition, section 24.3napkin
K15RGPXT50exercisedproblem, section 96.6.4napkin
Sketch of proofproofproof, section 56.1napkin
K2K0RDKZ52proofproof, section 21.5napkin
K2MQ8VC3FKexerciseques, section 20.5napkin
K30MS665FTexerciseproblem, section 57.5napkin
K31SEK509Gdefinitiondefinition, section 23.1napkin
K39S83BDT0exerciseproblem, section 28.6napkin
K3JTP27MZ7statementtheorem, section 27.2.2napkin
Proof using coversproofproof, section 95.4napkin
K3XSV528W1statementtheorem, section 68.7napkin
K45GQR37J2proofproof, section 28.5napkin
K4CKTMM971exerciseques, section 86.2napkin
K5WZBNHMMHproofproof, section 95.2napkin
K6221CF0KTdefinitiondefinition, section 8.3napkin
K6M2DPYJ6Xexampleexample, section 32.1napkin
K6Q49Z33EAdefinitiondefinition, section 63.4napkin
K6SKNW3DKCexerciseques, section 22.10napkin
K72CRWBM27statementproposition, section 76.2napkin
K7XHSTG5N8definitiondefinition, section 101.2.1napkin
Definition of wedge product using the cross productdefinitiondefinition, section 52.7.6napkin
K8DN53NDV6exerciseexercise, section 32.5napkin
K8J4AHCYCNdefinitiondefinition, section 9.3napkin
KA37NDCZKCexercisesproblem, section 91.9napkin
KA4R996V29definitiondefinition, section 89.6napkin
KAWM70BGDMexampleexample, section 33.2.1napkin
KB22GK556Sexampleexample, section 65.1napkin
KB7JXXW6WYstatementtheorem, section 89.6napkin
Uniform continuityexampleexample, section 95.4napkin
KCKN4MZXGRexerciseproblem, section 20.5napkin
KCZ83XS361exerciseproblem, section 94.6napkin
KDCQYBFHKZexampleexample, section 5.8napkin
KDDSFKF5QPstatementtheorem, section 33.4napkin
KDF7DZRPMYproofproof, section 13.4napkin
KEC7EFPMTBstatementcorollary, section 30.2napkin
KEH1MBM018definitiondefinition, section 53.6napkin
KERF6X9P6Estatementproposition, section 33.2.3napkin
KEWYP0C5G9definitiondefinition, section 52.3napkin
KF3FDKVZ58proofproof, section 28.5napkin
KFF5X4EY46proofproof, section 27.2.1napkin
KFQE3BNN5Jproofproof, section 20.2napkin
KGK15DAG8Pproofproof, section 14.7napkin
KGR1PK88Z0definitiondefinition, section 32.7napkin
Two non-entangled qubitsexampleexample, section 77.4napkin
KGW3FCGTDEexampleexample, section 25.4napkin
KGXB0SPJRTstatementproposition, section 54.3napkin
KH7B6ZXGZTproofproof, section 80.6napkin
KHAZ6H4WTZexerciseproblem, section 22.9napkin
KHYGKRMXR5proofproof, section 24.2.1napkin
KJRQC31CQ7proofproof, section 8.7napkin
KK0PJ2H4NQstatementlemma, section 60.2napkin
KKF9ZZEPAVexerciseexercise, section 46.1napkin
On $\gcd(|C|, \dim V) = 1$statementlemma, section 78.2napkin
KKQA4PS5KGstatementlemma, section 14.5napkin
KKR7RV8H6Nexerciseexercise, section 16.3napkin
KMN6WS9HABdefinitiondefinition, section 25.5napkin
Hatcher \S2.1 exercise 18exerciseproblem, section 53.6napkin
KMS3S3SN0Hexampleexample, section 22.6napkin
KN5MKWT40Adefinitiondefinition, section 93.5napkin
KNC8F8CWTNexerciseproblem, section 30.6napkin
KNE2Y9KFEEexerciseques, section 44.1napkin
Properties obtained from filtersstatementlemma, section 90.3napkin
KP101BFRJSdefinitiondefinition, section 25.3napkin
KPSYE22WDTexampleexample, section 8.6napkin
Intertwining operatorsexampleexample, section 80.5napkin
KQKHHA4TX0exerciseproblem, section 25.6napkin
KRBWQ8FPF6exerciseproblem, section 35.5napkin
KRC4VCF35Qexerciseexercise, section 63.4napkin
KRFE940GHCexerciseques, section 100.3napkin
KT36QWHVVKdefinitiondefinition, section 55.1napkin
The circleexampleexample, section 82.1napkin
First few levels of the name hierarchyexampleexample, section 90.3napkin
Fundamental groups don't depend on basepointstatementtheorem, section 98.2napkin
KWADJMEF3Jexampleexample, section 14.2napkin
KWQKN28V2Zexerciseexercise, section 52.8napkin
KWRGN5BDWGexerciseques, section 88.1napkin
KWT0CHFRFBexerciseproblem, section 92.7napkin
KX9W1C9Y3Adefinitiondefinition, section 63.1napkin
KXFMYFXT41definitiondefinition, section 89.2napkin
KXJ90YVV0Yexampleexample, section 27.2.2napkin
KXNJNKNKPPexampleexample, section 80.1napkin
KY9SV1886Mdefinitiondefinition, section 27.2napkin
Generic filters on the infinite chainexampleexample, section 90.1napkin
Cauchy's integral formulastatementtheorem, section 39.5napkin
KZWSVBTFY5exerciseproblem, section 28.6napkin
M0NWNA9RCSexerciseexercise, section 14.4napkin
M0S0D84WAAexerciseexercise, section 51.5napkin
M15MS90YRDproofproof, section 13.2napkin
M1CDYEMDN5proofproof, section 88.4napkin
M1FQDBN5H9proofproof, section 31.2napkin
M2GAWPSRN5exerciseproblem, section 21.8napkin
M331S1GDQWstatementtheorem, section 78.3napkin
M56WEWKQTZexampleexample, section 79.1napkin
Prime $\iff$ irreduciblestatementtheorem, section 19.5napkin
Conjugacy in abelian groups is trivialstatementcorollary, section 1.4napkin
M5XA611AN9definitiondefinition, section 16.2napkin
Long exact sequence for relative homologystatementtheorem, section 54.2napkin
M6883Y2E7Nexampleexample, section 14.1napkin
M68KBQHPVHdefinitiondefinition, section 2.4napkin
M6CAWYHX88definitiondefinition, section 44.4napkin
The generic extension satisfies $\ZFC$statementtheorem, section 90.6napkin
M73TSC5P0Hexerciseproblem, section 19.8napkin
Gram-Schmidtstatementtheorem, section 60.3napkin
M78MW08JDQstatementproposition, section 67.7napkin
M7EYN8YT1Aexerciseproblem, section 32.8napkin
M7T53WHDCCexerciseques, section 1.2napkin
M8155MV4GEexampleexample, section 8.3napkin
M8TTF8NBSHdefinitiondefinition, section 4.3napkin
Interval modulo endpointsexampleexample, section 96.2napkin
Typical example of liftingexampleexample, section 97.2napkin
M9382T04F0exerciseques, section 82.3napkin
M94JENQDRPexerciseproblem, section 9.9.3napkin
MA1M431FGTstatementtheorem, section 46.5napkin
MACSJKYFEWexampleexample, section 2.5napkin
Disconnected and connected spacesexampleexample, section 101.5napkin
MBWPKTSM2Hexampleexample, section 54.1napkin
MCMB35K9MKexampleexample, section 37.2napkin
MDC82J2ZQ2definitiondefinition, section 99.2napkin
MEHJFKAZQ1exerciseproblem, section 81.5napkin
MEJJBNA0DSexampleexample, section 44.3napkin
MEXW4N0N9Estatementtheorem, section 31.4napkin
MEYFT4Y7PKdefinitiondefinition, section 92.3napkin
MF62374F94exercisedproblem, section 6.6napkin
Examples of generated idealsexampleexample, section 5.7napkin
Subgroup generated by an elementexampleexample, section 2.5napkin
Sequential continuitystatementtheorem, section 100.3napkin
MGA8WKJ8BWproofproof, section 88.1napkin
MGJ42TD3JYdefinitiondefinition, section 34.4napkin
MH06Q5B2YQstatementtheorem, section 52.7.3napkin
MH1CDPR31Jproofproof, section 53.4napkin
MHJV1W3N8Xexercisedproblem, section 80.6napkin
MHY3VJ9D9Cexerciseexercise, section 99.1napkin
MJD4RYBTZ9exampleexample, section 8.2napkin
MJXYN96EE2exerciseproblem, section 24.4napkin
MJYS2VXH7Pproofproof, section 14.3napkin
MKD36T1AESproofproof, section 31.4napkin
MKEVXXHR8Aproofproof, section 52.3napkin
MKH1PJV91Zexerciseproblem, section 16.5napkin
MKYQBWJPPPexampleexample, section 3.1napkin
MM74WNC3G7proofproof, section 55.3.2napkin
MMJNWP7JPDexampleexample, section 44.5napkin
MMQBXYE9WJexercisesproblem, section 15.4napkin
MMTESGS1NYexerciseproblem, section 13.8napkin
MN06Q50S39exampleexample, section 79.2napkin
MN7R3KCN78proofproof, section 32.5napkin
Cardinal arithmeticdefinitiondefinition, section 89.4napkin
Some type $(1, 0)$ $1$-formsexampleexample, section 84.2.1napkin
Closed subsets of compactsstatementproposition, section 95.1napkin
MPGQMZ7XDWstatementtheorem, section 53.4napkin
MQCVNCWFM5definitiondefinition, section 99.4napkin
Modding out in the product groupexampleexample, section 3.5napkin
MQNNX1VB4Texampleexample, section 59.3.1napkin
MR2621WNBCstatementtheorem, section 8.5napkin
MR3EBTRHEXexerciseques, section 50.1napkin
MRFPHG2Z93proofproof, section 90.5napkin
MRQEPCB9APdefinitiondefinition, section 89.6napkin
MRQGPZR6RCexerciseproblem, section 68.6napkin
MTYJ95Z9JAexerciseexercise, section 97.1napkin
MV3GVB2YTDexerciseques, section 4.6napkin
Pullback and $d$ commuteexerciseproblem, section 46.6napkin
MWRQWW2WE2exerciseques, section 51.3napkin
MX6M82R3R3exerciseexercise, section 100.5napkin
MX7YV3975Hstatementtheorem, section 44.7.3napkin
MXHATGQETPdefinitiondefinition, section 65.1napkin
MXWE46YZNYexercisedproblem, section 33.5napkin
MYM4KVSTA9exerciseexercise, section 81.5napkin
MYRDB0WG8Cdefinitiondefinition, section 79.3napkin
MYYY9SWESSdefinitiondefinition, section 96.4napkin
MZ6YJ3YT2Bstatementtheorem, section 41.3napkin
Euclidean planeexampleexample, section 62.3napkin
N0BWXWM98Aexerciseques, section 98.1napkin
N0EQ1QRCK5statementproposition, section 58.8napkin
N1D00K02Y8exerciseques, section 5.9napkin
N1E16GPP5Eproofproof, section 25.3napkin
N1V33HNK7Qdefinitiondefinition, section 96.2napkin
Continuous partials implies differentiablestatementtheorem, section 45.3napkin
Quadratic Formulaexampleexample, section 42.3napkin
N2ZTP04NYKdefinitiondefinition, section 33.3.1napkin
N36FQXWT1Pexerciseques, section 14.2napkin
N39PABCVT3exerciseexercise, section 77.4napkin
Weirder quotient spacesexampleexample, section 96.2napkin
N45S8TFSFFexampleexample, section 23.3napkin
N48QPQNK8Rexercisedproblem, section 32.8napkin
N4B0D2NNABdefinitiondefinition, section 69.1napkin
N54RPQTA37statementtheorem, section 22.7napkin
N55HWZFK28exercisesproblem, section 54.3napkin
N5BRSYHB03definitiondefinition, section 42.4napkin
N5YBQB2ED2exampleexample, section 36.3napkin
N626HY3S21definitiondefinition, section 33.2.3napkin
N67YBVEV4Kexampleexample, section 91.1napkin
N6G4RTGKSRexercisedproblem, section 79.4napkin
N6YZ4NERVBdefinitiondefinition, section 14.5napkin
Galois group of the cyclotomic fieldexercisesproblem, section 14.6napkin
A non-holomorphic form: $d \ol z$exampleexample, section 84.2napkin
N7TM9T2SE0exerciseproblem, section 56.3napkin
Ordinal arithmetic is not commutativeexampleexample, section 92.6napkin
N8GSD8C089exerciseques, section 14.6napkin
N8XC3S7592definitiondefinition, section 32.1napkin
N8ZF58MKDQexampleexample, section 77.4napkin
N9JG5C171Pproofproof, section 52.4napkin
N9XS75EHC0exerciseexercise, section 30.1napkin
NA8KWYGJPHproofproof, section 2.2napkin
NARY3SNT5Eexampleexample, section 98.5napkin
NAWFE3M3YVproofproof, section 91.7napkin
NAXB0G87X3proofproof, section 32.4napkin
NBBF7TPTP9exampleexample, section 30.2napkin
NBH0XPF3FQdefinitiondefinition, section 44.5napkin
NBSNTNMRT2exerciseques, section 51.4napkin
NBV4SVHBAZdefinitiondefinition, section 58.3napkin
NBZ754EBGEdefinitiondefinition, section 58.3napkin
NC4J2M9Y07exampleexample, section 4.6napkin
Typical ringsexampleexample, section 5.3napkin
ND68MXMC3Kexerciseexercise, section 36.4napkin
NDBFEXXNW1exerciseproblem, section 3.6napkin
NDQCR1JTPFexercisesproblem, section 89.7napkin
NDQER2C3A9proofproof, section 66.5napkin
NECW2D4QY6definitiondefinition, section 24.3napkin
NEDRMZN9MGexampleexample, section 25.6napkin
NEH05EQTSGexercisesproblem, section 65.4napkin
NEJA174G3Hdefinitiondefinition, section 89.4napkin
NEVAT10XQ4exerciseques, section 43.7napkin
NEXE10MW79statementtheorem, section 50.5napkin
NFK2V6WC5Hproofproof, section 8.6napkin
NFSD4DQWMXexerciseques, section 77.3napkin
NFSXGFYHHNstatementtheorem, section 32.5napkin
NFV31C33HJproofproof, section 4.7napkin
Homology groups split into path-connected componentsstatementproposition, section 55.2napkin
NG5DSZEJZFproofproof, section 28.5napkin
NG7CY1TSX4definitiondefinition, section 65.1napkin
NGN99YE09Kstatementtheorem, section 58.4napkin
NH27VPSJPTdefinitiondefinition, section 36.2napkin
NH8502XEJZexampleexample, section 2.1napkin
NJ2BN2F5NSexerciseques, section 4.7napkin
NJ7P6G4RQMexerciseques, section 35.1napkin
Cantor's diagonal argumentstatementlemma, section 93.2napkin
NJP2JE6G21exampleexample, section 13.2napkin
NKEG25WV1Qstatementtheorem, section 23.5napkin
NKM2Z1SVSPdefinitiondefinition, section 92.7napkin
NKPYFPWYYFstatementtheorem, section 63.3napkin
NKW48677C2statementcorollary, section 70.4napkin
NMK0JBE3XGexampleexample, section 57.2napkin
NMQAP6HG8Jstatementlemma, section 35.4napkin
NNEY20VWRYexerciseproblem, section 41.6napkin
NP0SJDHCQPproofproof, section 89.3napkin
NPJMMBP89Bdefinitiondefinition, section 35.1napkin
Embeddings are evenly distributed over conjugatesstatementtheorem, section 14.3napkin
NQ6PRPZY96exerciseexercise, section 4.3napkin
NQW74NXA5Jdefinitiondefinition, section 59.3.3napkin
$\OO_K$ integrally closed and Noetherianstatementproposition, section 10.3napkin
NR6FKVJJFBexerciseexercise, section 5.3napkin
NSEHCCVWNDdefinitiondefinition, section 30.5napkin
NSMRW3Z12Vexerciseexercise, section 54.2napkin
Examples of abelian categoriesexampleexample, section 35.2napkin
NTXM036WC9exercisedproblem, section 65.4napkin
NTZWB85J14exerciseques, section 98.5napkin
NV0JP9BV8Hexerciseproblem, section 4.8napkin
NV5BGFJYXQstatementproposition, section 34.4napkin
NVPZXECABDstatementlemma, section 88.4napkin
NVZ02D8KK0exerciseques, section 56.2napkin
NW4Z9XBQ78exerciseexercise, section 96.3napkin
NWENTG9RKJexerciseproblem, section 32.8napkin
NWRE39CSPDproofproof, section 5.7napkin
NWTWSVQ5CEstatementtheorem, section 81.3napkin
Local rings in non-algebraic geometry sheavesexampleexample, section 27.4.1napkin
NXYMQVJE8Tdefinitiondefinition, section 5.5napkin
NYR3TD2TH0exampleexample, section 61.4napkin
NYV63ZGK01definitiondefinition, section 55.3.1napkin
Sketch of Proofproofproof, section 9.3napkin
P19TQZ94W9statementtheorem, section 63.5napkin
P2ND23SSTHstatementproposition, section 28.3napkin
P2TMXCHKM2definitiondefinition, section 3.2napkin
Open cover homology theoremstatementtheorem, section 54.3napkin
P3MGN4FZ9Sexampleexample, section 52.4napkin
P3NVGAFVPSexerciseproblem, section 10.7napkin
P3Z8MFP6AAexercisesproblem, section 60.5napkin
P4B7RNTGWEexerciseexercise, section 35.2napkin
P4TDVYNDE4exampleexample, section 4.7napkin
P4W3GB71KHexerciseques, section 28.3napkin
P5HY5V6KDFexerciseexercise, section 3.1napkin
P5Q2YWQHX9exampleexample, section 43.5napkin
P5S0VZCFT9exampleexample, section 36.3napkin
P6BR3E6Q9Pexerciseexercise, section 92.3napkin
P6FXT8XAJBstatementtheorem, section 61.5napkin
P6M69CEJN7exerciseproblem, section 63.7napkin
P6MGFW6145proofproof, section 4.4napkin
P6VE0VMS27exerciseproblem, section 30.6napkin
P77W566Y7Tdefinitiondefinition, section 50.2napkin
P78P1MQJK8exerciseexercise, section 98.2napkin
P7JAXFQNDNdefinitiondefinition, section 4.5napkin
P7MFAN3F5Cstatementcorollary, section 81.2napkin
P7SJYC63M6statementtheorem, section 81.1napkin
P7W2MQHR0Pstatementproposition, section 100.6napkin
P9AP097KMDexercisesproblem, section 80.6napkin
P9CZNA51ZMdefinitiondefinition, section 5.3napkin
P9NYEY1VCJproofproof, section 64.3.3napkin
PB7FX9HB5Fdefinitiondefinition, section 15.1napkin
PBBCECPT79exerciseques, section 37.2napkin
PBQF0QWR8Jexerciseques, section 97.2napkin
Coordinate rings correspond to idealstatementtheorem, section 29.4napkin
More examples of basesexampleexample, section 62.4napkin
PDMF3PPDPBexerciseques, section 95.5napkin
PDSG7E89FGexerciseques, section 15.2napkin
PDXZ1T9E48exerciseques, section 3.3napkin
PFFBTC6EBAproofproof, section 22.2napkin
PGAQ2J79TPstatementproposition, section 59.2napkin
PHYVZYTVGWdefinitiondefinition, section 25.2.1napkin
PJ47QYQSC5exerciseproblem, section 21.8napkin
Morally correct definition of norm and tracestatementtheorem, section 15.1napkin
Strong law of large numbersstatementtheorem, section 64.3.2napkin
PK7HS9402Sproofproof, section 22.2napkin
PKDBS30V50exerciseques, section 58.8napkin
PKSNAC4WVXproofproof, section 9.2napkin
PKZGACV379exerciseexercise, section 6.1napkin
PM0A78A5MXexampleexample, section 5.4napkin
PM2D4AAMR3definitiondefinition, section 58.6napkin
PMFDJCGJJBexampleexample, section 12.4napkin
PMRWTNFHNEexerciseproblem, section 30.6napkin
Irreducible polynomials have distinct rootsstatementlemma, section 15.1napkin
PN969VJ5TTexampleexample, section 92.3napkin
PNCMDH69BWproofproof, section 27.2.2napkin
PNCVCAT0ERexerciseques, section 2.1napkin
PNFSR0H7RVdefinitiondefinition, section 92.3napkin
$h_I$ eventually constant when $\dim \Vp(I) = 0$statementcorollary, section 20.2napkin
PNVDJ4RNM2proofproof, section 61.5napkin
PPD8101X5Gexampleexample, section 21.5napkin
PPWK8R3GTYdefinitiondefinition, section 91.2napkin
PQ7ZP6JYYWstatementtheorem, section 39.6napkin
PR464PD374proofproof, section 61.4napkin
PRJG0N2BHZstatementtheorem, section 30.4napkin
PTZQAK2X5Hdefinitiondefinition, section 37.6napkin
PVJ1BH0MS4exerciseexercise, section 39.7.1napkin
PVM75DNYNXexerciseexercise, section 33.4napkin
PW0XCT98GDexampleexample, section 28.3napkin
PW2ZMH0AM7exerciseexercise, section 39.7.1napkin
PW6JW2XVTKdefinitiondefinition, section 25.2.1napkin
TSTST 2014exerciseproblem, section 62.11napkin
PWB93PYNFCexampleexample, section 82.1napkin
Homotopy equivalent spaces have isomorphic fundamental groupsstatementtheorem, section 98.5napkin
PWX4SCVF0Kdefinitiondefinition, section 8.3napkin
PX8G1V5MGTexerciseexercise, section 42.4napkin
PX907WEAXSstatementtheorem, section 59.3.3napkin
PXP6ZH4JYWdefinitiondefinition, section 4.2napkin
PXQQ81Y24Rdefinitiondefinition, section 96.5napkin
Reversible gatesexampleexample, section 75.2napkin
Complex $n$-manifolddefinitiondefinition, section 83.3napkin
PYDDVJYYBMexampleexample, section 28.4napkin
Proof of density theoremproofproof, section 81.2napkin
$V^\vee \otimes W$ $\iff$ linear maps $V \to W$statementtheorem, section 57.3napkin
Q0CBBXG6A0exerciseexercise, section 92.4napkin
Q0JH5YFHZ5exercisedproblem, section 61.6napkin
Q0XW5YY88Xexerciseproblem, section 16.5napkin
Q0YWZBVM2Zdefinitiondefinition, section 21.2napkin
Q16772PP7Wstatementtheorem, section 65.3napkin
Examples of Hilbert functions in zero dimensionsexampleexample, section 20.2napkin
Q1D00JGEESstatementproposition, section 100.5napkin
Q1DKPACRC4statementproposition, section 58.6napkin
Q1NDH0HAECdefinitiondefinition, section 4.2napkin
Q1P9S38HVCexampleexample, section 66.4napkin
Q2CSQA65MBexampleexample, section 95.4napkin
Q2NZK7QR48exampleexample, section 41.2napkin
Q2S90MW3WAexampleexample, section 5.9napkin
Q322M6Y4C0definitiondefinition, section 9.2napkin
Q36KYGBYTSexercisesproblem, section 7.3napkin
Q3AN178F0Xexerciseproblem, section 100.8napkin
Q3GF8Z961Nexampleexample, section 32.4napkin
Q3NM61WS1Eexerciseexercise, section 8.7napkin
Q3QHT73Y62definitiondefinition, section 42.3napkin
Q3TPC1A6HDexerciseproblem, section 24.4napkin
Q46XFEZK06exampleexample, section 66.2napkin
$H_n(X, A)$ where $A$ is open in $X$exampleexample, section 53.1napkin
Q4Z4YB4890exampleexample, section 36.5napkin
Q512JWR648proofproof, section 34.2napkin
Q598AHZ1TRexerciseexercise, section 37.4napkin
Q5DCP1H68Zexerciseques, section 27.4.1napkin
Q5JN4ARM0Vproofproof, section 95.5napkin
Q669TZ09C1exercisesproblem, section 62.11napkin
Q68XNJE92Rexampleexample, section 9.2napkin
More quotient spacesexampleexample, section 96.2napkin
Hurewicz theoremstatementtheorem, section 55.2napkin
Q73A2QQCVDexerciseexercise, section 82.3napkin
Q7KFK4DN5Gexerciseproblem, section 3.6napkin
Q7NHQDD781definitiondefinition, section 90.5napkin
Q7SSHK9KTEexercisedproblem, section 36.5napkin
Group theory via covering spacesstatementtheorem, section 97.5napkin
Q8C3EPEZSEstatementcorollary, section 34.5napkin
Q8FYMJ2MPDstatementtheorem, section 39.3napkin
Q94Q2KK9NQexerciseproblem, section 61.6napkin
Sketch of Proofproofproof, section 62.7napkin
Q9SYKQNQDXstatementtheorem, section 18.2napkin
QA3NQR7PG0proofproof, section 75.1napkin
QA4EEEEG0Vexerciseques, section 1.4napkin
Furstenbergexerciseproblem, section 101.9napkin
Factoring $3$ in the integers of $\QQ(\sqrt{-17})$exampleexample, section 10.5napkin
QBCG85TAK3exerciseques, section 9.7napkin
QCXHMRV0C9exampleexample, section 70.4napkin
QDXHXTG0AEproofproof, section 19.3napkin
QDZGBQ6RBEstatementcorollary, section 81.1napkin
Algebraic integers are closed under $+$ and $\times$statementtheorem, section 15.2napkin
QE98CAXQKEexampleexample, section 27.4.1napkin
QERJRZ2FE1proofproof, section 18.4napkin
Total derivative of $f(x,y) = x^2+y^2$exampleexample, section 45.1napkin
QGBJS22JEJexerciseexercise, section 96.6.3napkin
QH2X2C70E5exampleexample, section 31.2napkin
QH5V1ECZ5Adefinitiondefinition, section 20.2napkin
QHHNXBN2ESstatementtheorem, section 81.2napkin
QHM995DAEQexerciseexercise, section 68.2napkin
QHVAV83RD8definitiondefinition, section 98.2napkin
QHXSQ5NTR2definitiondefinition, section 5.6napkin
QJ5BYVMPCVexerciseques, section 88.1napkin
QJ76T4XVQDdefinitiondefinition, section 56.1napkin
QJ8NQPFCZCdefinitiondefinition, section 46.4napkin
QJZ9BR5YBBexerciseexercise, section 92.6napkin
QKGJ6PRP10exerciseexercise, section 78.2napkin
QKMGVT4RDTexerciseproblem, section 92.7napkin
QKYGPKV6S1proofproof, section 20.5napkin
QMB83K815Bstatementtheorem, section 78.1napkin
QMHHDHS9KVexampleexample, section 99.1napkin
Contravariant Yoneda functorexampleexample, section 37.4napkin
QMXH5D9EYXexerciseques, section 95.4napkin
QNC48EV0YEstatementclaim, section 64.3.3napkin
QP3QPPDHP3exerciseproblem, section 93.7napkin
QPM854K3VVstatementclaim, section 3.5napkin
QQJW2GFCKMdefinitiondefinition, section 80.4napkin
QQSYJ5KKMWdefinitiondefinition, section 9.8napkin
QRF0BKNNSZexerciseques, section 29.3napkin
QRHPXHXX9Adefinitiondefinition, section 66.2napkin
The ring of Gaussian integers is a Euclidean domainexampleexample, section 4.7napkin
QSBJ7JKW45exerciseproblem, section 14.6napkin
QSVMGQNHXYexerciseexercise, section 81.4napkin
QT2CCADEZYstatementtheorem, section 28.5napkin
Differential $1$-forms on $\CC$definitiondefinition, section 84.1napkin
QTFBY55XVEdefinitiondefinition, section 22.10napkin
QV1R9Q55BEstatementproposition, section 97.5napkin
Exterior derivative vanishesstatementtheorem, section 43.4napkin
QV2A4K66FXstatementtheorem, section 93.6napkin
QVCHVGRA19proofproof, section 61.5napkin
QVJCBQR4Z4exampleexample, section 46.3napkin
QW27YZYEJYdefinitiondefinition, section 60.1.1napkin
QW2VJXBZ7Hexerciseques, section 95.3napkin
QW85Q1775Hexerciseexercise, section 4.2napkin
QW9WYYN7MHexampleexample, section 27.6napkin
QWGMWV0MYVdefinitiondefinition, section 28.4napkin
QWH0VEHYJ7statementtheorem, section 39.7.1napkin
QWT3E4B9KQstatementtheorem, section 58.5napkin
QWYWND6KTGdefinitiondefinition, section 67.4napkin
QXEGYXV1YSexerciseques, section 3.2napkin
QXWYMPFFBVexerciseexercise, section 79.3napkin
The boundary of the boundary is emptystatementtheorem, section 46.4napkin
QY2ZVGJ2E6exerciseproblem, section 75.4napkin
QY7BMWEZT5exerciseproblem, section 31.5napkin
QY91NYVFENdefinitiondefinition, section 101.1napkin
QYG77MSNRGexerciseproblem, section 60.5napkin
QYH8KRKCCYdefinitiondefinition, section 10.3napkin
QYZH0MMGFRexampleexample, section 92.3napkin
QZ2BZBJVGRexercisesproblem, section 39.7.2napkin
R04E53H116exampleexample, section 41.2napkin
Moore spacesexerciseproblem, section 50.5napkin
R1DM5GC715exerciseques, section 19.2napkin
R21Z9E1DPGproofproof, section 31.3napkin
R2NWMWCWYGproofproof, section 13.5napkin
R2Z63XZ006proofproof, section 94.5napkin
R394JATBWEdefinitiondefinition, section 6.5napkin
R4NRTCQBSTexerciseproblem, section 4.8napkin
Infinite chainexampleexample, section 90.1napkin
R4WAB804CEdefinitiondefinition, section 91.4napkin
R53P8QETFKexampleexample, section 28.2napkin
R5HXWPXXAFstatementtheorem, section 31.2napkin
R5M2DQAAGFexerciseques, section 6.6napkin
R5QVG19G3Pexampleexample, section 39.1napkin
R61DHP5CYEexerciseexercise, section 51.3napkin
R6N7A7SDNHstatementtheorem, section 34.2napkin
Generic filters on the infinite binary treeexampleexample, section 90.1napkin
R7H7HJVHY4statementtheorem, section 40.4napkin
R7JK7DK707statementtheorem, section 27.4.1napkin
R7WT4SA4D2proofproof, section 45.2napkin
Examples and non-examples of well-orderingsexampleexample, section 93.6napkin
R9AAAQ3S0Yproofproof, section 1.2napkin
RAG2S1HQ68definitiondefinition, section 51.1napkin
RAS2X8FFKSexampleexample, section 55.2napkin
RASXF90228exercisedproblem, section 51.8napkin
RB61KS1SPFdefinitiondefinition, section 10.2napkin
RBAJCMWW9Bexampleexample, section 31.4napkin
RBBQE69Y3Zstatementtheorem, section 6.5napkin
Fundamental theorem of Galois theorystatementtheorem, section 14.6napkin
RBF1H322PCexerciseques, section 9.4napkin
RBY8W17MG2exampleexample, section 58.1napkin
RBYV8S7P7Hexampleexample, section 38.1napkin
Hilbert's Nullstellensatzstatementtheorem, section 19.3napkin
RCR91X8W0Yexerciseexercise, section 9.9.3napkin
RD6FQ4ZHSHexerciseproblem, section 93.7napkin
RDHFAMXBKVexerciseques, section 9.8napkin
RE3BFSFK7Tdefinitiondefinition, section 89.5napkin
REN9ZG90EGexampleexample, section 30.3napkin
RF8W6C073Fexerciseexercise, section 36.4napkin
RFDAPAEXCMstatementlemma, section 6.5napkin
RFJX6DSQ7Dexerciseproblem, section 3.6napkin
RFX7WW4S7Texerciseproblem, section 100.8napkin
RGEZREKTMVproofproof, section 4.7napkin
RGNHYJTHBRdefinitiondefinition, section 23.1napkin
RGS00J8HXYdefinitiondefinition, section 5.4napkin
RH2CMEAEVYdefinitiondefinition, section 79.3napkin
RH8SXZVR36definitiondefinition, section 98.5napkin
RHK2YG4AETstatementtheorem, section 6.5napkin
``First isomorphism theorem'' in abelian categoriesstatementproposition, section 35.5napkin
Examples of splitting fieldsexampleexample, section 14.5napkin
RKYH1AYVFCexerciseproblem, section 81.5napkin
RMR74K85ZMexampleexample, section 36.2napkin
RMY72D66R3exampleexample, section 52.7.4napkin
RNCX55NQ3Estatementcorollary, section 21.5napkin
RPD0RZXJ6Pproofproof, section 20.4napkin
RPNZJ3PC1Cstatementcorollary, section 64.3.3napkin
RPZV0VYPCSstatementtheorem, section 50.1napkin
RQ7401WB6Nexerciseexercise, section 14.6napkin
RQ95W68R8Adefinitiondefinition, section 6.4napkin
RQBTBP7W90exampleexample, section 28.3napkin
RR34CM4RG0proofproof, section 20.5napkin
RRJF5530K7exampleexample, section 24.1napkin
RSJ5Q27W81exampleexample, section 14.5napkin
RSKVN35N6Vdefinitiondefinition, section 32.5napkin
Non-examples of subgroupsexampleexample, section 2.5napkin
RW60K3ZMNZproofproof, section 14.3napkin
Degree of a divisordefinitiondefinition, section 87.3napkin
RWTPGKFC18exerciseproblem, section 79.4napkin
RX3K0RPS3Nstatementlemma, section 8.5napkin
Fixed field theoremstatementtheorem, section 14.7napkin
RXY8JS5TZCstatementtheorem, section 40.3napkin
RXZYR4X1RKexampleexample, section 86.4napkin
RY26J282J9exerciseexercise, section 35.3napkin
RYM6X4KGSSexerciseques, section 97.3napkin
RYQZ9GVTYKdefinitiondefinition, section 14.6napkin
Divisor of a meromorphic functiondefinitiondefinition, section 87.4napkin
RZG86B70Z3statementtheorem, section 66.4napkin
Inverse of productsstatementproposition, section 2.2napkin
RZZDX8VWFGdefinitiondefinition, section 41.2napkin
S0BR12FFGDexampleexample, section 28.5napkin
S0D0EWZEJ9exerciseproblem, section 101.9napkin
S18RFVN4JQexerciseques, section 90.1napkin
S1MEN93VACdefinitiondefinition, section 31.3napkin
S1RBJSAJSSexerciseproblem, section 64.4napkin
Rationalizing the denominatorexampleexample, section 15.2napkin
S2549TF3N5definitiondefinition, section 20.4napkin
S25YHTZJ2Hdefinitiondefinition, section 44.2napkin
S2JPXWVY9Jstatementtheorem, section 81.4napkin
S2MFDHFP4Cexerciseques, section 98.2napkin
S2Q930YF6Nexerciseproblem, section 52.8napkin
S2TX1NRSQ9definitiondefinition, section 62.7napkin
S3D7XD9Z80statementtheorem, section 25.5napkin
S3F27DS7BZexerciseexercise, section 82.1napkin
S3FHQZKN0Hdefinitiondefinition, section 55.2napkin
S3RMJ95350exampleexample, section 60.1.2napkin
S3S0X4QB5Mstatementtheorem, section 65.3napkin
S3W0W2Q36Rexampleexample, section 99.2napkin
S3Z3Y64SRKexerciseexercise, section 76.2napkin
S42H2F9C03proofproof, section 79.3napkin
S4D9AJ5NKTproofproof, section 98.2napkin
S4GXGX3Z24exerciseques, section 39.5napkin
S4W6F0VAPYexerciseproblem, section 36.5napkin
S4Z1SP3VTAstatementtheorem, section 20.5napkin
S54X090HSPexerciseques, section 100.6napkin
S5EGKGN8AYexerciseproblem, section 62.11napkin
S5HCXX5G7Sexampleexample, section 2.1napkin
S65VMGWZDQstatementtheorem, section 61.2napkin
S78KNTRE7Hdefinitiondefinition, section 60.3napkin
S78QHFNY5Tstatementtheorem, section 33.3.3napkin
S7EGCH7QEGexampleexample, section 95.1napkin
S7EY24ZRSTproofproof, section 27.4.1napkin
S7VC7W9AHTexampleexample, section 91.1napkin
S8G0RY4326exerciseproblem, section 101.9napkin
S8NWVT2KMDexerciseques, section 1.4napkin
S9A8AQMBDFexampleexample, section 9.9.3napkin
SA01S8QWJQstatementtheorem, section 31.1napkin
SA2JZ82CXVexampleexample, section 85.4napkin
SA4EMSCPX2statementproposition, section 4.7napkin
SB48E6HAE7statementtheorem, section 39.4napkin
SB75FK837Xstatementtheorem, section 19.7napkin
SBAA7Y23TWexerciseexercise, section 31.2napkin
SBBJ3JEZK0definitiondefinition, section 53.3napkin
SBDHFVPB4Ydefinitiondefinition, section 45.1napkin
SBDY2F0V2Rexerciseques, section 10.5napkin
SBNS5NP1BVexerciseques, section 98.4napkin
$\mathbb {RP}^2$exampleexample, section 97.4napkin
SC6DFB86XEexerciseques, section 51.4napkin
SCVAQZGYR2exerciseques, section 22.11napkin
SD5WZB0E4Tproofproof, section 61.2napkin
SDC2BYTTNRstatementtheorem, section 24.2.2napkin
SENF14PKHWstatementlemma, section 9.3napkin
Fermat's theorem on sums of two squaresstatementtheorem, section 8.7napkin
SG0BZS1E7Wexerciseproblem, section 53.6napkin
SG64ZFT6G3exampleexample, section 2.3napkin
SGH85DJ2DTproofproof, section 16.2napkin
SGY7WDDKWDdefinitiondefinition, section 29.2napkin
SHSKJ7KZ04exerciseexercise, section 99.4napkin
SJ73PYTNYRdefinitiondefinition, section 44.7.1napkin
SKB9YFND87exerciseques, section 17.1napkin
SKG0Q89F6Nproofproof, section 91.6napkin
SKYEM6D2Y7exampleexample, section 58.4napkin
SM1A5YP7SYstatementproposition, section 30.2napkin
Examples of pre-sheavesexampleexample, section 25.2.1napkin
SN5EGT6JSMproofproof, section 98.2napkin
SN9FS1Q2FMstatementproposition, section 32.5napkin
Spansexampleexample, section 62.7napkin
SNZWPPPNHNexampleexample, section 63.1napkin
SPXYZXWBT9statementtheorem, section 92.4napkin
SQ7A88S58Yexerciseproblem, section 50.5napkin
SQCA26BPW5exerciseproblem, section 66.7napkin
SRGFCV9HGEexampleexample, section 5.3napkin
SSCW7HZ84Jexampleexample, section 14.5napkin
SSNVTCAKMXexerciseproblem, section 3.6napkin
STNQSKJTVNexampleexample, section 37.2napkin
SVA8AVPZ8Bexerciseexercise, section 63.5napkin
SVJQYQHM43exampleexample, section 32.6napkin
SVPEPXXTKHexerciseques, section 3.1napkin
Examples and non-examples of prime idealsexampleexample, section 4.3napkin
Ideal classes in $\QQ(\sqrt{-5})$exampleexample, section 9.1napkin
SW330FCHP3proofproof, section 70.4napkin
SW745HX5VDexampleexample, section 8.4napkin
SWRJKS27G2exerciseexercise, section 41.2napkin
SXZW1Q5PMKproofproof, section 15.1napkin
SY0X8HN43Wexerciseproblem, section 99.5napkin
SZ74XJ9ZB8exerciseexercise, section 2.2napkin
Chain homotopic maps induce the same map on homology groupsstatementproposition, section 55.3.1napkin
SZMXXRDRTEstatementcorollary, section 59.5napkin
SZXR5N7KV4definitiondefinition, section 17.2napkin
SZYAAPA4RMproofproof, section 62.7napkin
Primitive rootsexampleexample, section 2.4napkin
T0ZCKVTYRTstatementproposition, section 32.4napkin
T31BPM4JNNexerciseexercise, section 32.3napkin
Non-Examples of groupsexampleexample, section 2.1napkin
T43GSBAVMVexerciseproblem, section 26.19napkin
T4CVX5D4KFdefinitiondefinition, section 25.2.2napkin
Splitting posets omit generic setsstatementlemma, section 90.2napkin
T4SGQ9F6RQexampleexample, section 24.1napkin
T4SHJHCPGYexampleexample, section 21.3napkin
Abelian groups are $\ZZ$-modulesexampleexample, section 62.2napkin
T5Q6WNTRS3exerciseques, section 88.2napkin
T67P8GQEQNdefinitiondefinition, section 68.1napkin
T6ENY5STE9exerciseques, section 46.4napkin
T6KHVERFTKproofproof, section 18.4napkin
$(3)\inv$ in $\ZZ$exampleexample, section 10.6napkin
T9KXG231S1definitiondefinition, section 32.4napkin
T9PX877F9Jexerciseques, section 41.3napkin
T9TQHRNEJXdefinitiondefinition, section 41.3napkin
T9Z5MYGWV3exerciseques, section 2.4napkin
Example of a traceexampleexample, section 57.4napkin
Representation of $S_n$ decomposesexampleexample, section 80.3napkin
TBD8HQQYFSexampleexample, section 31.2napkin
TBSVFKMKKYexerciseexercise, section 33.2.3napkin
TC32WQW830definitiondefinition, section 10.3napkin
TCMC34WH1Mdefinitiondefinition, section 15.1napkin
TCT4YCANERstatementtheorem, section 8.6napkin
TCVYGQKJGRdefinitiondefinition, section 29.5napkin
TD489K7XQFexercisesproblem, section 80.6napkin
TD6CM6C7NDexerciseproblem, section 1.4napkin
TD6JZR6N9Pdefinitiondefinition, section 62.2napkin
Aleph fixed pointexampleexample, section 89.7napkin
TDPPRAW1KZexerciseexercise, section 87.4napkin
TE2ZXRFG7Bproofproof, section 62.4napkin
TF4KRS43DJexampleexample, section 98.5napkin
de Rham cohomologyexampleexample, section 51.1napkin
TFP9E5G301definitiondefinition, section 80.1napkin
$n$-dimensional vector spaces are isomorphicstatementproposition, section 62.5napkin
TG4KT21BMKproofproof, section 59.5napkin
TGM8EDHFHCexerciseproblem, section 52.8napkin
THPSXRR4WKexerciseproblem, section 46.6napkin
THRPJE5D25proofproof, section 89.3napkin
More exact sequencesexampleexample, section 35.3napkin
TJCD7NB8YPdefinitiondefinition, section 89.1napkin
TJFYAC8KT5statementtheorem, section 44.6napkin
TK4X75041Tproofproof, section 33.3.2napkin
The ring of Eisenstein integers is a Euclidean domainexampleexample, section 4.7napkin
Sketch of Proofproofproof, section 95.4napkin
Regular representationexampleexample, section 80.2napkin
TMWHWJVET8statementproposition, section 56.1napkin
TNDVVSDMWAproofproof, section 30.2napkin
TNFT5QXSJ4exampleexample, section 2.1napkin
TNHCKKMJHFexerciseproblem, section 63.7napkin
TPM71BZS00definitiondefinition, section 18.3napkin
The torusexampleexample, section 97.4napkin
TRC63CF6Y2exampleexample, section 55.2napkin
TRVSXMK57Texerciseproblem, section 2.8napkin
$(0, 2)$ is a topological $1$-manifoldexampleexample, section 83.1napkin
TSS0GJ5QZCexampleexample, section 5.9napkin
TSX5WW7QHNexerciseques, section 90.3napkin
TT2NAJH5EEexampleexample, section 23.4napkin
TT30XX1Y67exercisedproblem, section 2.8napkin
TV5WSFPG9Sexerciseexercise, section 43.5napkin
TVH520FTBPexampleexample, section 31.1napkin
TW1DKNJHK7statementtheorem, section 30.3napkin
TWRSTJ0Y7Jexercisedproblem, section 93.7napkin
TWRTB82EA0exampleexample, section 1.4napkin
$\pi_n(S^m)$ is trivial when $n < m$exampleexample, section 98.4napkin
TX706BGBE1exampleexample, section 39.2napkin
TXC4WR4RMRexerciseexercise, section 36.5napkin
TXD53TCGH4exercisesproblem, section 53.6napkin
TYECCNAR36exampleexample, section 55.2napkin
TZKPYEPXYXexercisesproblem, section 4.8napkin
Removable singularity theoremexerciseproblem, section 39.7.2napkin
Loops in $S^2$ are nulhomotopicexampleexample, section 98.2napkin
TZWP92KX5Vexerciseproblem, section 101.9napkin
TZXQJB3MRZdefinitiondefinition, section 44.6napkin
V06G7YVX0Ddefinitiondefinition, section 63.3napkin
V0CTHTAG1Mproofproof, section 97.5napkin
V105A7M9A2statementtheorem, section 6.1napkin
V237RFD18Fdefinitiondefinition, section 86.3napkin
V2TXEVF21Wstatementtheorem, section 32.5napkin
V2WP76601Pstatementtheorem, section 22.5napkin
V30JWAJPMDdefinitiondefinition, section 35.3napkin
Proof using sequencesproofproof, section 95.4napkin
V3FB5S94SHexerciseques, section 95.1napkin
V3Z8TYP0REproofproof, section 12.2napkin
V40X2DC40Vexerciseexercise, section 37.2napkin
V4WR72DF8Bproofproof, section 51.6napkin
Order of a meromorphic functiondefinitiondefinition, section 87.1napkin
V6PC2P6XMYexerciseques, section 40.4napkin
V6VSMS33QSdefinitiondefinition, section 76.1napkin
Solutionproofproof, section 13.8napkin
V77AF60E3Jproofproof, section 54.2napkin
Cubic Legendre symbol subsumed by Artin symbolexampleexample, section 8.5napkin
V83ZMGMTE4exerciseques, section 2.1napkin
V9D7S2H1SKstatementcorollary, section 59.5napkin
V9R8NC2QJGexerciseques, section 7.2.1napkin
V9ZK4NVWSBexampleexample, section 66.2napkin
Ideal arithmetic via generatorsstatementproposition, section 10.2napkin
VAD44P58AXexampleexample, section 23.5napkin
VAS6ZDFFGCproofproof, section 12.4napkin
VBBX902QZZexerciseproblem, section 53.6napkin
VBJJHETZD8exerciseques, section 85.3napkin
VBN2VDPVVEdefinitiondefinition, section 1.2napkin
VBYYJ3DYJYproofproof, section 30.2napkin
VCH7WJW823exampleexample, section 86.1napkin
$\RR \to S^1$ is regularexampleexample, section 97.4napkin
VECSKX0NHEexerciseques, section 36.5napkin
VESANEWNR6statementtheorem, section 62.7napkin
VF3TVKQ9JKexerciseproblem, section 13.8napkin
Fictitious account of the battle of Hastingsexerciseproblem, section 17.4napkin
VFSMA70MVDexerciseexercise, section 37.7napkin
VFXZZ8EBP5exampleexample, section 70.1napkin
Explicit computation of matrices for $a+b\sqrt2$exampleexample, section 15.1napkin
VG2EM7REFTdefinitiondefinition, section 75.2napkin
VGKRZWAKPBdefinitiondefinition, section 56.2napkin
VGQ726V8QBdefinitiondefinition, section 36.5napkin
VGYQYNSTXBexampleexample, section 86.3napkin
VJ6CJCATBAexerciseexercise, section 9.9.1napkin
Zariski topology on $\Aff^2$exampleexample, section 29.2napkin
VJYB4G21SZdefinitiondefinition, section 39.3napkin
VK202K4AYCexerciseexercise, section 92.6napkin
VK2RFERZ4Pexerciseproblem, section 27.7napkin
VKDYT2N2B4exerciseques, section 85.4napkin
VKGJD4WMNDdefinitiondefinition, section 99.2napkin
VKJ7ECGJ39definitiondefinition, section 32.3napkin
Uniqueness of productsstatementproposition, section 36.4napkin
VMQ2SYD7VVexampleexample, section 53.4napkin
VMS3JN8TRAdefinitiondefinition, section 69.1napkin
VMSAZTGV03exampleexample, section 46.2napkin
VPEY486ZMNexampleexample, section 43.3napkin
VQAT07Y3FZstatementtheorem, section 24.2.1napkin
VQFDPAN49Fexerciseques, section 25.6napkin
VQFQWKK3XCexampleexample, section 27.3.1napkin
VQTH44VG3Kexerciseexercise, section 59.2napkin
$\OO_K$ is a free $\ZZ$-module of rank $n$statementtheorem, section 15.2napkin
VRSZ1ES3R8exerciseexercise, section 15.2napkin
A distribution with finite mean but infinite varianceexampleexample, section 64.3.3napkin
VTCR50P09Pdefinitiondefinition, section 68.2napkin
VTGA7ZZ24Edefinitiondefinition, section 36.5napkin
VTH2GP3ZATexerciseques, section 9.7napkin
VVEPE8S4X6exampleexample, section 80.1napkin
VVM0VEED95exercisedproblem, section 61.6napkin
VVTE50D3G3proofproof, section 20.2napkin
VVWN63CMJ0exerciseexercise, section 59.3.3napkin
VW4W0YEVDTproofproof, section 86.4napkin
VWAP70HDMWproofproof, section 9.3napkin
VWVRM9MAJMstatementtheorem, section 52.4napkin
VWZEA9S9DDstatementtheorem, section 8.7napkin
VX9CCTVEV0exerciseproblem, section 54.3napkin
VXCEKB5FB5definitiondefinition, section 35.2napkin
VYK7ZC7PJ9proofproof, section 30.4napkin
VZ1KVQVHSCproofproof, section 78.2napkin
VZGTD961Y2definitiondefinition, section 29.7napkin
W06T8NDBMEexampleexample, section 39.2napkin
Frobenius determinantsexampleexample, section 78.3napkin
The complex torusexampleexample, section 83.4napkin
W1CW326PG7definitiondefinition, section 32.6napkin
W1R7FVY7SYproofproof, section 12.2napkin
W24C2MTZRMproofproof, section 100.6napkin
W2E56Q86TPexercisesproblem, section 21.8napkin
W2GHABK3APexerciseques, section 1.2napkin
W33SYGAG2Gdefinitiondefinition, section 81.1napkin
W4H691WB11exerciseproblem, section 17.4napkin
Legendre symbol subsumed by Artin symbolexampleexample, section 8.5napkin
W5GSFFWCDWdefinitiondefinition, section 28.3napkin
W5WG0FAJRKdefinitiondefinition, section 43.1napkin
W6A22PMBY0statementproposition, section 100.5napkin
W702AXZQ6Bexerciseques, section 89.7napkin
W7BKCAG59Xexerciseques, section 12.5napkin
W7JZW59WYKexampleexample, section 59.3.2napkin
W8BQWRAFGXdefinitiondefinition, section 27.1napkin
W8Z3B9ZYPMexerciseproblem, section 3.6napkin
Basis of $V \otimes W$statementproposition, section 57.1napkin
W96F10X27Pexerciseques, section 15.1napkin
W985KGGWBZexerciseexercise, section 17.2napkin
HMMT 2017exercisedproblem, section 12.5napkin
WAFEX9TF5Zexerciseproblem, section 96.6.4napkin
WAQKZE1TP5proofproof, section 70.4napkin
WAWRZ33X23exampleexample, section 32.4napkin
$\ZZ$ is the infinite cyclic groupexampleexample, section 3.1napkin
The ring {$\ZZ[\sqrt{11}]$} is a Euclidean domainexampleexample, section 4.7napkin
WCBK21JAV7definitiondefinition, section 51.2napkin
WCKCHZ1W40exampleexample, section 1.3napkin
WD2VKFFER8definitiondefinition, section 66.2napkin
WDBM34HNDMdefinitiondefinition, section 92.3napkin
WDBWJ0Q9M2proofproof, section 2.2napkin
WDS4AVRZE8exampleexample, section 3.2napkin
WDYBWVKAASexerciseproblem, section 2.8napkin
WE9B7WBCCRstatementproposition, section 30.4napkin
WF0V01325Aproofproof, section 62.8napkin
A non-example: Representation of $\Mat(V)$exampleexample, section 80.5napkin
WFY3F7VDFHdefinitiondefinition, section 2.1napkin
WG6ZQW325Fproofproof, section 93.7napkin
{$\ZZ[\sqrt7]$} is a UFDstatementproposition, section 9.8napkin
WGC82CAP0Xexerciseexercise, section 55.3.1napkin
WJ9Q78SSTNexercisedproblem, section 41.6napkin
WJBS2Y2P7Wproofproof, section 92.7napkin
WKGF8PY64Kexerciseproblem, section 59.8napkin
WM0CMGKA4Ndefinitiondefinition, section 61.5napkin
WM36SCTYGMdefinitiondefinition, section 29.3napkin
The elliptic curve $y^2 = x^3 - x$exampleexample, section 82.1napkin
WMW8V3YW5Nexampleexample, section 67.4napkin
WNHMBFJV4Eexercisedproblem, section 52.8napkin
WNNQQB5NA3definitiondefinition, section 86.1napkin
WP66KPB119definitiondefinition, section 23.2napkin
WPDQN7HK6Cdefinitiondefinition, section 45.3napkin
WPFXRY6VHXexerciseexercise, section 58.5napkin
Bolzano-Weierstra\ssstatementtheorem, section 95.2napkin
WQ3XX5AP5Sdefinitiondefinition, section 101.8napkin
WQGNWQ22G3definitiondefinition, section 90.1napkin
WQZKNWB5B6proofproof, section 63.4napkin
WR52QXMVXRexerciseproblem, section 15.4napkin
WR78HK45A2proofproof, section 35.4napkin
WRGKM1A877exampleexample, section 4.4napkin
WRX94KNG77exerciseexercise, section 82.2napkin
WRYHTSSXX8exerciseques, section 4.2napkin
WS5HSB7G1Nexercisesproblem, section 79.4napkin
WSFCGPZNDZdefinitiondefinition, section 23.3napkin
WSGW2BSCTEexerciseques, section 8.7napkin
$\Zc2$-cohomology of $\RP^n$exerciseproblem, section 51.8napkin
WSY8JTG7JXstatementtheorem, section 45.4napkin
WT0306ZNRZexerciseproblem, section 33.5napkin
Examples of topologiesexampleexample, section 101.1napkin
WT4D1H2NCMexerciseexercise, section 19.4napkin
WT63CK1J4Qexerciseexercise, section 62.4napkin
WTGA6G3M28proofproof, section 98.3napkin
WTJ2WKDF2Dexerciseproblem, section 13.8napkin
WTJNKSF31Gexampleexample, section 24.3napkin
Taxicab on $\RR^2$exampleexample, section 100.1napkin
WTV5ZZWABTexerciseques, section 39.3napkin
WW6B7JJ7K1exampleexample, section 43.7napkin
WWCY8CEC2Dstatementtheorem, section 51.4napkin
WWDJ2ZXR25exampleexample, section 100.7napkin
WWHZ7ZB7V8statementproposition, section 86.2napkin
WWPTDBEFP7definitiondefinition, section 19.3napkin
The space of functions with pole of order at most $4$ on $\CC_\infty$exampleexample, section 87.1napkin
WX2Q1GS604definitiondefinition, section 99.1napkin
WX6DWQH9S2exercisedproblem, section 29.7napkin
WXH0G5Q5M4definitiondefinition, section 43.3napkin
WXYBCY287Jexerciseques, section 101.3napkin
WYGMK9YJ5Bproofproof, section 67.7napkin
WYX19F3V9Sexerciseques, section 43.4napkin
Ideals divide their normsstatementlemma, section 9.8napkin
X08M9DD0Z9definitiondefinition, section 52.6napkin
X0FFFNV5QTexampleexample, section 25.3napkin
X0HR4S395Gdefinitiondefinition, section 93.6napkin
X0ZS8KREFDdefinitiondefinition, section 35.4napkin
X200TS9Z8Mexampleexample, section 22.4.2napkin
Banach fixed point theoremexercisedproblem, section 99.5napkin
X2GPJ9D7HTdefinitiondefinition, section 31.2napkin
X2KN8FJD5Cstatementproposition, section 86.4napkin
X2RJHP6HYDexerciseques, section 62.8napkin
X38ZYNR1GEexampleexample, section 66.3napkin
X3MEACFD1Yproofproof, section 95.5napkin
X3NPS21ASDexampleexample, section 100.2napkin
X4GF5JVVSGexerciseques, section 3.5napkin
X4TP40P82Ndefinitiondefinition, section 55.3.1napkin
X565KB16DVdefinitiondefinition, section 2.4napkin
X5VHYSP2GJstatementtheorem, section 75.2napkin
X6SH641V2Adefinitiondefinition, section 100.7napkin
X76Z0G0J49definitiondefinition, section 14.4napkin
X7WE71ZWJ8definitiondefinition, section 67.7napkin
X83KCPD2KKdefinitiondefinition, section 98.5napkin
X85KQ276S8exerciseexercise, section 91.5napkin
X8EMVPGT05proofproof, section 86.5napkin
X8S466Z2EQproofproof, section 79.3napkin
X8TWQGB1CYdefinitiondefinition, section 90.1napkin
$V_\alpha$ for $\alpha \le 3$exampleexample, section 92.7napkin
Riemann surfacedefinitiondefinition, section 83.2napkin
XAVE8Z7WX2definitiondefinition, section 85.2napkin
XB2W074RR2exerciseexercise, section 2.5napkin
XBJ26KMCGYstatementtheorem, section 12.3napkin
XBRQZMD74Pexerciseques, section 100.3napkin
Picking a basis for linear mapsstatementtheorem, section 62.7napkin
Possible values argumentstatementlemma, section 88.2napkin
XCJ4DW3ZVYstatementtheorem, section 32.1napkin
Sketch of Proofproofproof, section 60.3napkin
XDM12ZDC6Sexerciseproblem, section 61.6napkin
XE8J43ANPMexampleexample, section 17.2napkin
XER7239CQBdefinitiondefinition, section 98.2napkin
XFQFWN49ZTexampleexample, section 91.1napkin
The shrinking wedge of circlesexampleexample, section 53.1napkin
XH2Y78H55Adefinitiondefinition, section 30.3napkin
XH8X2C89W5exercisesproblem, section 4.8napkin
XHYZTM44NRproofproof, section 41.4napkin
XJ3TGNZ8ETexerciseproblem, section 31.5napkin
XJ6ZH46P3Sstatementtheorem, section 24.4napkin
XJT2ZQC7RPdefinitiondefinition, section 89.3napkin
Graphs are metric spacesexampleexample, section 100.1napkin
XMEA3GG2CTdefinitiondefinition, section 62.4napkin
XMG9C6XNJMexerciseques, section 75.4napkin
Sketch of Proofproofproof, section 75.2napkin
XP2Q0YX4NCexerciseexercise, section 99.4napkin
XPHZF65GRYdefinitiondefinition, section 63.2napkin
XQJ1ZJ4G3Sproofproof, section 66.3napkin
Properties of the absolute normstatementlemma, section 10.7napkin
XSB4283SZ8exampleexample, section 2.1napkin
XSGWCFDAX9exerciseexercise, section 101.6napkin
Direct sum of Noetherian modules is Noetherianstatementlemma, section 6.4napkin
XTQZ71TB54proofproof, section 37.2napkin
The proposition does not hold for smooth compact manifoldsexampleexample, section 86.3napkin
$\pi_n(S^n) \cong \mathbb Z$exampleexample, section 98.4napkin
XV6C8HVJBJexerciseques, section 95.1napkin
XVT41T7CPEexampleexample, section 55.2napkin
Representations of $A \oplus B$ are $V_A \oplus V_B$statementproposition, section 80.3napkin
XWSXTM73SCexerciseexercise, section 9.9.3napkin
Class group of $\QQ(\sqrt{-17})$statementproposition, section 9.8napkin
XX8TSP0Q6Jexercisedproblem, section 4.8napkin
XY23VJMAZ5definitiondefinition, section 63.4napkin
Chebyshev's inequalitystatementtheorem, section 64.3.3napkin
XYRXAC4GD7definitiondefinition, section 91.2napkin
XYZSF5BVGTstatementtheorem, section 13.6.2napkin
XZB6CE60T3exerciseques, section 36.2napkin
XZR2XJCRYSstatementtheorem, section 30.4napkin
Y0C6H60W2Wexerciseexercise, section 52.7.2napkin
Y0CXYE4KCGexerciseexercise, section 66.5napkin
Y116GWEQBMexampleexample, section 63.2napkin
Algebraic closuresstatementtheorem, section 14.2napkin
Prototypical exampleexampleexample, section 16.3napkin
Y1KPGNNSJ6exampleexample, section 92.3napkin
Y2SXM3BPT4statementlemma, section 12.2napkin
Y3KNBTCDEKstatementproposition, section 34.5napkin
Y3VRZY2VGMdefinitiondefinition, section 98.3napkin
Y4K9T9DXC2exerciseexercise, section 65.1napkin
Y4PB88319Pexerciseexercise, section 25.5napkin
Y526KPHZQ6definitiondefinition, section 65.1napkin
Y5QG60G8FCdefinitiondefinition, section 46.3napkin
Y6QPAP2EJQexerciseques, section 6.4napkin
Y6SNZ1QNHEdefinitiondefinition, section 41.3napkin
Y794J9M6K2proofproof, section 34.3napkin
Y7DKBR1AS2exerciseexercise, section 22.3napkin
Y7EMA5YCZBproofproof, section 50.2napkin
Closed and bounded but not compactexampleexample, section 95.2napkin
Y7GZDRE6BJdefinitiondefinition, section 95.4napkin
Y7K8NRHMQ4exerciseques, section 58.6napkin
Y82N2CJYN4definitiondefinition, section 101.2.1napkin
Y9AJ2BZ49Gstatementtheorem, section 28.3napkin
Y9FB2QQTWMdefinitiondefinition, section 10.7napkin
Y9KFQ0T4C4exampleexample, section 33.1napkin
$(0, 2)$ is a smooth $1$-manifoldexampleexample, section 83.1napkin
YAHM374Z2Astatementtheorem, section 62.8napkin
YAQE0RXSCRexerciseques, section 19.2napkin
YAQR9QYQ77statementtheorem, section 52.5napkin
YB3M20E6T3exampleexample, section 66.3napkin
YBAZMEHDQFstatementproposition, section 66.6.1napkin
YBBMJ2Y7D9definitiondefinition, section 22.11napkin
Algebraic condition for normal subgroupsstatementtheorem, section 3.5napkin
YBM4EWFZB0proofproof, section 54.3napkin
YBZK1TN8YTstatementcorollary, section 6.3napkin
YC5BJ906YHexerciseproblem, section 17.4napkin
YCF7MP6DJNexerciseproblem, section 45.5napkin
YCG7JZ83NDdefinitiondefinition, section 93.7napkin
YDAB13T37Cstatementtheorem, section 52.8napkin
Examples of group actionsexampleexample, section 1.1napkin
YG49G76Z1Dexerciseexercise, section 1.1napkin
YG6GCGK602exampleexample, section 96.6.4napkin
YGWH2VPRG4proofproof, section 66.5napkin
Partial derivatives of $f(x,y) = x^2+y^2$exampleexample, section 45.3napkin
YH0KHZC104proofproof, section 88.4napkin
YHE83AYYQMexampleexample, section 96.5napkin
YJJ6T3030Bstatementclaim, section 61.5napkin
Deutsch-Jozsaexerciseproblem, section 75.4napkin
YMMCTF6K6Bstatementproposition, section 41.4napkin
YMSB2RH5VPdefinitiondefinition, section 5.6napkin
YP7XG57D3Vdefinitiondefinition, section 58.5napkin
Basis completionstatementtheorem, section 62.7napkin
YQ8ZT0JT33definitiondefinition, section 68.1napkin
YQ9AZZJX80definitiondefinition, section 97.5napkin
YQBQZR2JEPexerciseques, section 52.2napkin
YQCMWYBEE9exerciseproblem, section 32.8napkin
YQEJ0VR4YHexampleexample, section 2.5napkin
YR2KAPZH6Eexerciseproblem, section 66.7napkin
YSJHVYVWSSexerciseexercise, section 36.5napkin
YSYCEPA8MAexerciseques, section 3.2napkin
YTAF66FKAFexercisedproblem, section 101.9napkin
YXENV1NTXXdefinitiondefinition, section 55.3.1napkin
YXQAVJY8W6definitiondefinition, section 101.2.2napkin
YXTN54T477definitiondefinition, section 58.4napkin
YXXWN8HRD7exerciseproblem, section 58.8napkin
Arc length isn't a formexerciseproblem, section 46.6napkin
YY0FYV41KEexerciseproblem, section 35.5napkin
The unit squareexampleexample, section 96.3napkin
YYPMPQYVBJexerciseques, section 22.11napkin
YZ9KA609C4definitiondefinition, section 37.2napkin
Z0B9TANR6Mproofproof, section 97.2napkin
Rasiowa-Sikorski lemmastatementlemma, section 90.2napkin
Hilbert basis theoremstatementtheorem, section 5.9napkin
Metric spaces of $\RR^2$exampleexample, section 100.1napkin
Complex structure of $\CP^1$definitiondefinition, section 82.2napkin
Z2GRMKN6W0statementtheorem, section 90.4napkin
Z2WJEYHXNFexerciseexercise, section 100.7napkin
Z43K36JK5Pproofproof, section 10.3napkin
Z4K7EBYDQFproofproof, section 50.2napkin
An elliptic curve, againexampleexample, section 82.3napkin
Z4Z39JP034statementtheorem, section 17.2napkin
Z5K65SHEX0proofproof, section 98.5napkin
Z5QG73ZT91exampleexample, section 66.6.1napkin
Z5VWYH08N8exerciseques, section 62.4napkin
Z5Y37GNNB8exerciseexercise, section 36.5napkin
Z6C2SFY6PFexampleexample, section 5.3napkin
Z6PFA8T29Tstatementlemma, section 39.5napkin
Z7PA28N64Yexampleexample, section 36.4napkin
Left multiplication is a bijectionstatementlemma, section 2.2napkin
Z85N52GRMCstatementtheorem, section 61.1napkin
The Riemann sphere, againexampleexample, section 82.3napkin
Z9DX1DFSX0exerciseques, section 58.3napkin
$f_\sharp$ is homotopy invariantstatementlemma, section 98.3napkin
Z9RMZZ6H0Rdefinitiondefinition, section 21.4napkin
Klein bottleexercisesproblem, section 54.3napkin
ZAB07964YXstatementtheorem, section 13.2napkin
ZAHFGDK3N2definitiondefinition, section 99.1napkin
{Norm of $a+b\sqrt[3] 2+c \sqrt[3] 4$}exampleexample, section 15.1napkin
ZB1WG8S5S4exerciseexercise, section 53.3napkin
ZBNZZNH1XSexerciseproblem, section 3.6napkin
Examples of degreesexampleexample, section 20.4napkin
ZBWH7Z6RX0proofproof, section 75.4napkin
Infinite binary tree is (very) splittingexampleexample, section 90.2napkin
ZCRWEQY11Ndefinitiondefinition, section 60.1.2napkin
ZCV189XBW5exampleexample, section 3.2napkin
Explicit computationexampleexample, section 57.1napkin
ZDGF5D1C0Zexerciseques, section 6.2napkin
ZDGN24HK6Mexerciseproblem, section 7.3napkin
ZE13AJJWQRexampleexample, section 23.1napkin
ZFA656X3H7statementlemma, section 78.2napkin
ZFJ526GR9Kdefinitiondefinition, section 27.4.1napkin
ZFTBWAP2TBexerciseques, section 43.6napkin
ZG515V60S2exercisedproblem, section 6.6napkin
ZGAQHC2T5Fstatementlemma, section 12.2napkin
ZGD4SP169Gexerciseproblem, section 21.8napkin
Frobenius elements of the Gaussian integersexampleexample, section 13.1napkin
ZH01QXG05Rdefinitiondefinition, section 89.3napkin
ZH1V2ZB03Mdefinitiondefinition, section 23.2napkin
ZH98ZE164Sexerciseques, section 79.2napkin
ZHGYY3AEDNproofproof, section 50.4napkin
Tautological covering projectionexampleexample, section 97.1napkin
ZHYSM4YXVWdefinitiondefinition, section 2.5napkin
More examples of multiplicity of a map at a pointexampleexample, section 86.4napkin
ZJPEKBEV0Bstatementtheorem, section 52.1napkin
Orthogonalitystatementtheorem, section 79.3napkin
ZNFMQTT6KFdefinitiondefinition, section 85.4napkin
ZQCN9QP92Texerciseexercise, section 15.1napkin
ZR0NWHFWZHdefinitiondefinition, section 54.1napkin
ZRKH5GK0BTexerciseques, section 7.3napkin
ZRMT0A719Vexerciseproblem, section 27.7napkin
ZRQAVXN5GBproofproof, section 89.4napkin
ZTVYV00FYFexampleexample, section 23.2napkin
ZV4KN9W6MFdefinitiondefinition, section 27.1napkin
ZV6HVTMJ3Qexerciseproblem, section 62.11napkin
ZVEN04AFSVexampleexample, section 36.2napkin
ZVPS69AVT7definitiondefinition, section 6.2napkin
ZW9SNB3ZX4exerciseproblem, section 58.8napkin
ZWBYY8AZR8exampleexample, section 58.8napkin
Different primes have different $K^D$exampleexample, section 18.5napkin
Transfinite inductionstatementtheorem, section 92.5napkin
ZXNY22BAJGproofproof, section 21.7napkin
ZXQSED6MEQstatementtheorem, section 86.7napkin
ZXZ1452K6Mproofproof, section 30.4napkin
The Sylow theoremsstatementtheorem, section 7.1napkin
ZY2TR6ZVZNexampleexample, section 70.1napkin
ZY4AMVGZCNdefinitiondefinition, section 24.1napkin
ZY8PW9060Nstatementlemma, section 25.6napkin
ZY98TFE1ECexerciseproblem, section 95.6napkin
ZYRJWXM33Rexerciseexercise, section 82.2napkin
ZYXHW1FZW7statementtheorem, section 53.4napkin
ZZ0S3WNSWAexerciseexercise, section 25.5napkin
ZZJVC7BAAFexerciseexercise, section 66.6.1napkin
ZZR3K9ZK28exerciseproblem, section 7.3napkin

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