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