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