A basic course in number theory 2PDMAFPZ5Z

URI	`m2://res/2PDMAFPZ5Z`
Kind	course
Creators	Shripad Garge (instructor)
Date	2020-07-11
MSC	11-XX
Scope	in
Ids	course 02qyf5152:111101137

Expressions

e1: edition

Language	en
Date	2020-07-11

m1: page, IIT Bombay (record). nptel 111101137
m2: page, 2020-07-11 (record). nptel 111101137

Contents

part 1: Week 1
session 1: Lecture 1 : Integers
session 2: Lecture 2 : Divisibility and primes
session 3: Lecture 3 : Infinitude of primes
session 4: Lecture 4 : Division algorithm and the GCD
session 5: Lecture 5 : Computing the GCD and Euclid’s lemma
part 2: Week 2
session 6: Lecture 6 : Fundamental theorem of arithmetic
session 7: Lecture 7 : Stories around primes
session 8: Lecture 8 : Winding up on `Primes' and introducing `Congruences'
session 9: Lecture 9 : Basic results in congruences
session 10: Lecture 10 : Residue classes modulo n
part 3: Week 3
session 11: Lecture 11 : Arithmetic modulo n, theory and examples
session 12: Lecture 12 : Arithmetic modulo n, more examples
session 13: Lecture 13 : Solving linear polynomials modulo n - I
session 14: Lecture 14 : Solving linear polynomials modulo n - II
session 15: Lecture 15 : Solving linear polynomials modulo n - III
part 4: Week 4
session 16: Lecture 16 : Solving linear polynomials modulo n - IV
session 17: Lecture 17 : Chinese remainder theorem, the initial cases
session 18: Lecture 18 : Chinese remainder theorem, the general case and examples
session 19: Lecture 19 : Chinese remainder theorem, more examples
session 20: Lecture 20 : Using the CRT, square roots of 1 in ℤn
part 5: Week 5
session 21: Lecture 21 : Wilson's theorem
session 22: Lecture 22 : Roots of polynomials over ℤp
session 23: Lecture 23 : Euler 𝜑-function - I
session 24: Lecture 24 : Euler 𝜑-function - II
session 25: Lecture 25 : Primitive roots - I
part 6: Week 6
session 26: Lecture 26 : Primitive roots - II
session 27: Lecture 27 : Primitive roots - III
session 28: Lecture 28 : Primitive roots - IV
session 29: Lecture 29 : Structure of Un - I
session 30: Lecture 30 : Structure of Un - II
part 7: Week 7
session 31: Lecture 31 : Quadratic residues
session 32: Lecture 32 : The Legendre symbol
session 33: Lecture 33 : Quadratic reciprocity law - I
session 34: Lecture 34 : Quadratic reciprocity law - II
session 35: Lecture 35 : Quadratic reciprocity law - III
session 36: Lecture 36 : Quadratic reciprocity law - IV
part 8: Week 8
session 37: Lecture 37 : The Jacobi symbol
session 38: Lecture 38 : Binary quadratic forms
session 39: Lecture 39 : Equivalence of binary quadratic forms
session 40: Lecture 40 : Discriminant of a binary quadratic form
session 41: Lecture 41 : Reduction theory of integral binary quadratic forms
part 9: Week 9
session 42: Lecture 42 : Reduced forms up to equivalence - I
session 43: Lecture 43 : Reduced forms up to equivalence - II
session 44: Lecture 44 : Reduced forms up to equivalence - III
session 45: Lecture 45 : Sums of squares - I
session 46: Lecture 46 : Sums of squares - II
session 47: Lecture 47 : Sums of squares - III
part 10: Week 10
session 48: Lecture 48 : Beyond sums of squares - I
session 49: Lecture 49 : Beyond sums of squares - II
session 50: Lecture 50 : Continued fractions - basic results
session 51: Lecture 51 : Dirichlet's approximation theorem
session 52: Lecture 52 : Good rational approximations
part 11: Week 11
session 53: Lecture 53 : Continued fraction expansion for real numbers - I
session 54: Lecture 54 : Continued fraction expansion for real numbers - II
session 55: Lecture 55 : Convergents give better approximations
session 56: Lecture 56 : Convergents are the best approximations - I
session 57: Lecture 57 : Convergents are the best approximations - II
part 12: Week 12
session 58: Lecture 58 : Quadratic irrationals as continued fractions
session 59: Lecture 59 : Some basics of algebraic number theory
session 60: Lecture 60 : Units in quadratic fields: the imaginary case
session 61: Lecture 61 : Units in quadratic fields: the real case
session 62: Lecture 62 : Brahmagupta-Pell equations
session 63: Lecture 63 : Tying some loose ends

Catalogue records

nptel: 111101137 (manifestation)
nptel_video: 111101137 (manifestation)