IIT Madras Mathematical Thinking Lectures
BSMA200198 lectures12 weeks
Weeks
- Week 19 lecturesTriangular numbers · Sigma notation for summation · Sequences · Peano's axioms for the natural numbers · Set theory - the language of mathematics · Hilbert hotel · Bijections and cardinality · The natural numbers · The integers
- Week 27 lecturesA trip to Cantorsville · Cantor's diagonalization argument · Towards the real numbers · Ordered field · Completeness axiom · The least upper bound property · Mathematical Logic and Statements
- Week 36 lecturesCurrency game · Divisibility · Greatest common divisor · The Euclidean Algorithm · Proof of the euclidean algorithm · Test for divisibility
- Week 46 lecturesFermat's little theorem · Fundamental theorem of arithmetic · Modular arithmetic · Arithmetic with congruences · Infinitude of primes · Inclusion–exclusion principle
- Week 57 lecturesSieve of eratosthenes · Proof of the inclusion–exclusion principle · Pigeonhole principle · Pigeonhole principle - applications part i · Pigeonhole Principle - Applications Part II · More on the infinitude of primes · Gaps between primes
- Week 610 lecturesWhy study Sequences · Binomial coefficients · Binomial theorem · Lattice paths · Random sampling · Permutations · Inversion of a permutation · The poincaré polynomial · Self reciprocal polynomials · Inclusion–exclusion principle examples 1
- Week 710 lecturesEuler's totient function · Graph theory introduction · Connectedness in graphs · Distance in graphs · Reconstruction problem · Tree · Adjacency matrix · Sperner’s lemma · Sperner’s lemma - version 2 · Properties of trees
- Week 88 lecturesPascal's triangle and the sierpi_ski gasket · Properties of trees - part 2 · Properties of trees - part 3 · Properties of trees - part 4 · Planar graphs · Graph coloring · Chromatic index · Triangle inequality
- Week 910 lecturesLimit of a sequence · Properties of limits · Sandwich lemma · Shifting lemma · Cauchy sequences · Bolzano–weierstrass theorem · Convergence of infinite series · Limit of a function · Continuity of functions · Intermediate value theorem
- Week 105 lecturesContinuity of trigonometric functions · Sequential continuity and continuous functions on a closed interval · Applications of intermediate value theorem · Fibonacci numbers and the golden ratio · Lamé's formula
- Week 119 lecturesEuclidean algorithm on square root of 2 - i · Euclidean algorithm on square root of 2 - ii · Continued fractions · Derivatives · Faà di bruno's formula - i · Faà di bruno's formula - ii · Extrema of continuous functions · Local maximum and local minimum · Mean value theorem
- Week 128 lecturesRiemann integrals - i · Riemann integrals - ii · Uniform continuity and integrals - i · Uniform continuity and integrals - ii · Properties of riemann integrals · Fundamental theorem of calculus · The derivative determines a function (up to a constant) · The natural logarithms