Math 408 Lectures

Day 1: 9-11-20: Introduction to the class: https://youtu.be/-wwoq_XhvrU (slides here) Markus 1

Day 2: 9-14-20: Packing in 1 and 2 dimensions, Intro to probability, Chi-square random variables: https://youtu.be/9ddyfqE559A: Jihoon 1

Day 3: 9-16-20: Chisquare random varianbles, volume of n-sphere, Heron's formula: https://youtu.be/yDKT_ovkU5g: Jihoon 2

Day 4: 9-18-20: Hexagonal lattice best in plane: https://youtu.be/rjrzcivn9Xg Markus 2

Day 5: 9-21-20: Voronoi cells, fractals, newton's method: https://youtu.be/9f4UVybADp8 Chenyang 1

Day 6: 9-23-20: Simple proof of Thue's Theorem?: https://youtu.be/CCmR_Nwhbe8 (slides here): Jihoon 3

Day 7: 9-25-20: Error detection/correction: https://youtu.be/uhlc5lk5kMw (slides here) Markus 3

Day 8: 9-30-20: Power sums, Vandermonde Determinants, Lagrange Interpolation: https://youtu.be/_E6dqbqXOCc Chenyang 2

Day 9: 10-2-20: Interpolating with values and derivatives: https://youtu.be/1ZkGmg71Xoo Clay 1

Day 10: 10-5-20: Taylor series, inner products, start of Fourier analysis: https://youtu.be/m3Q1ZPdcsCY : Stephen 1

Day 11: 10-7-20: Introduction to Fourier Analysis: https://youtu.be/6Q100j_Zo4o : Stephen 2

Day 12: :10-14-20: Dirichlet and Fejer Kernels, Approximations to the Idenity: https://youtu.be/NjKhA9_rsNg Sasha 1

Day 13: 10-16-20: Dirichlet's Theorem in Fourier Analysis: https://youtu.be/nXYy7a4j0ek (slides here) Sasha 2

Day 14: 10-19-20: Poisson Summation: https://youtu.be/RvuruTxPy7A Clay 2

Day 15: 10-21-20: Applications of Poisson Summation: Zeta(s): https://youtu.be/mDrItjsMyhE Sasha 3

Day 16: 10-23-20: Fourier Analysis and Interpolation I: https://youtu.be/EB9-cFsF2xM Isaac 1

Day 17: 10-26-20: Fourier Analysis and Interpolation I: https://youtu.be/Ab51YqqSG-Y Clay 3

Day 18: 10-28-20: Introduction to Modular Forms: https://youtu.be/LENIl17A2p4 Chenyang 3

Day 19: 10-30-20: Generation of SL(2,Z): https://youtu.be/wZEGsWkDunI Clay 4

Day 20: 11-2-20: Trying to find a weight 0 modular form: https://youtu.be/JgqkEZfFiys Stephen 3

Day 21: 11-4-20: Big Data lecture

Day 22: 11-6-20: Finding modular forms: https://youtu.be/X4-iR76MPvY Sasha 4

Day 23: 11-9-20: Lattices 1: https://youtu.be/yUmjuJQo0UM Chenyang 4

Day 24: 11-11-20: NO CLASS - work on writeups.

Day 25: 11-13-20: Hard problems, short vectors in lattices: https://youtu.be/19wogqVrKrc Markus 4

Day 26: 11-16-20: Real to discrete max, analytic density: https://youtu.be/wVpsnDNW_yQ Stephen 4

Day 28: 11-18-20: Roulette, Longest Run, Generating Function: https://youtu.be/DvhJ1nHCUFU Isaac 2

Day 29: 11-20-20: Runs II: https://youtu.be/qnK7rtgqN08 Isaac 3

Day 30: 11-23-20: Cancelled due to Prof Miller's illness

Day 31: 11-30-20: Gauss Circle I: https://youtu.be/i3MvCrMhXQU (slides here) Chenyang 5

Day 32: 12-02-20: Gauss Circle II: https://youtu.be/A5G0Y7EZk7c (slides here) Isaac 4

Day 34: 12-07-20: The Kepler Conjecture: https://youtu.be/NzqxeIdKuWA (slides here) Sasha 5

Day 35: 12-09-20: Cohn-Elkies I: https://youtu.be/7pho75IS7oA (slides here) Jihoon 4

Day 36: 12-11-20: DIfferentiation to Calculus of Variations: https://youtu.be/OSu5R0mt77U (slides here) Jihoon 5

Bonus lecture: 7-27-21: Finding functions with desired properties I: Uryshon's lemma: https://youtu.be/5v0vZGRXN7A

♦ Interesting news articles involving math (see also the course disclaimer about not suing me!)

Election fraud:

♦ Interesting videos

TED Lectures:

♦ Course disclaimer

I may occasionally say things such as `Probability is one of the most useful courses you can take' or 'If you know probability, stats and a programming language then you'll always be able to find employment'. I really should write `you should always be able to find employment', as nothing is certain. Thus, please consider yourself warned and while you may savor the thought of suing me and/or Williams College, be advised against this! I'm saying this because of the recent lawsuit of a graduate who was upset that she didn't have a job, and sued her school!