Math 2.0

Resources / course

An invitation to mathematics NVXJ3QBD9V

URIm2://res/NVXJ3QBD9V
Kindcourse
CreatorsSankaran Vishwanath (instructor)
Date2015-04-28
Scopein

Expressions

e1: edition

Languageen
Date2015-04-28
Contents
  • part 1: Week-1 Polynomials
  • session 1: Introduction
  • session 2: Long division
  • session 3: Applications of Long division
  • session 4: Lagrange interpolation
  • session 5: The 0-1 idea in other contexts - dot and cross product
  • session 6: Taylors formula
  • session 7: The Chebyshev polynomials
  • session 8: Counting number of monomials - several variables
  • part 2: Week-2 Combinatorics
  • session 9: Permutations, combinations and the binomial theorem.
  • session 10: Combinations with repetition, and counting monomials.
  • session 11: Combinations with restrictions, recurrence relations
  • session 12: Fibonacci numbers; an identity and a bijective proof.
  • session 13: Permutations and cycle type
  • session 14: The sign of a permutation, composition of permutations
  • session 15: Rules for drawing tangle diagrams
  • session 16: Signs and cycle decompositions
  • session 17: Sorting lists of numbers, and crossings in tangle diagrams
  • part 3: Week-3 Polynomials in Combinatorics
  • session 18: Real and integer valued polynomials
  • session 19: Integer valued polynomials revisited.
  • part 4: Week-4 Functions
  • session 20: Functions on the real line, continuity
  • session 21: The intermediate value property.
  • session 22: Visualizing functions.
  • session 23: Functions on the plane, Rigid motions.
  • session 24: More examples of functions on the plane, dilations.
  • session 25: Composition of functions
  • session 26: Affine and Linear transformations
  • session 27: Length and Area dilation, the derivative
  • part 5: Week-5 Conservation principles
  • session 28: Examples-I
  • session 29: Examples-II
  • part 6: Week-6 Matrices
  • session 30: Linear equations, Lagrange interpolation revisited
  • session 31: Completed Matrices in combinatorics
  • session 32: Polynomials acting on matrices
  • part 7: Week-7 Number theory
  • session 33: Divisibility, prime numbers
  • session 34: Congruences, Modular arithmetic
  • session 35: The Chinese remainder theorem
  • session 36: The Euclidean algorithm, the 0-1 idea and the Chinese remainder theorem

Catalogue records