NOC:An Invitation to Mathematics


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