♦ Lectures from Math/Stat 341: Fall 2021:
Lecture 01: 9/10/21: Introduction, Hoops Game: https://youtu.be/aD7tIO0CGyg (click here for first day slides)
Lecture 02: 9/13/21: Birthday Problem, Combinatorics, Institutionalization, Efficiency: https://youtu.be/_K0kOFa3x1g (slides)
Lecture 06: 9/22/21: German Tank Problem I: Theory: https://youtu.be/APsubcDVl1s (slides) (Lecture 06: 9/18/19: Probability and Mathematical Modeling I (slides online here): https://youtu.be/T-35mhZioeo)
Lecture 07: 9/24/21: GOAT of GOATs discussion: https://youtu.be/Ov0bYFbtHD4 (slides) (Lecture 07: 9/20/19: Probability and Mathematical Modeling II (slides online here): https://youtu.be/ZGM6be90XqA)
Lecture 10: 10/01/21: Mountain day - no class: watch this video for Monday: Independence, Derangements, Inclusion-Exclusion, Induction: https://youtu.be/lJKSKEUZ69k
Lecture 10: 10/04/21: Independence, Derangements, Inclusion-Exclusion, Induction: https://youtu.be/0mFJTq4ASRE (slides) (see video from previous year for fuller lecture: https://youtu.be/lJKSKEUZ69k)
Lecture 11: 10/06/21: PDFs and CDFs, the CDF Method, Sums of RV, Moments, Lineups: https://youtu.be/a6bwRbs5sow (slides) (coding: https://youtu.be/sSgjBysixdQ; code file here, pdf here)
Lecture 12: 10/08/21: Review cont/discrete RV, expectation, moments, Cauchy, Taylor: Lecture from 10/2/19: https://youtu.be/fCQlNOiHolU
Lecture --: 10/11/21: No class: Reading period
Lecture 13: 10/13/21: Joint PDFs, Convolutions, Linearity of Expectation, Buffon's Needle: https://youtu.be/Q-lp1yFdNvA (slides)
Lecture --: 10/15/21: No class: Take home exam
Lecture 14: 10/18/21: Sick, review class on midterm (not recorded)
Lecture 15: 10/20/21: Sick, lecture from 2019: Simpson's paradox, Ace of Hearts method: https://youtu.be/-on_cFHW66g (slides here)
Lecture 16: 10/22/21: Introduction to Statistics and Modeling: Pythagoras at the Bat: https://youtu.be/iJyoyUV2JWQ (slides here)
Lecture 17: 10/25/21: Linearity of expectation, variances and covariances, power of linearity of expectation, bernoulli and binomial, convolution: https://youtu.be/iltn3Oks-9k (slides)
Lecture 18: 10/27/21: Differentiating Identities, Marriage Problem, Estimating Solutions: https://youtu.be/Y6Lvb-ppyHE (slides)
Lecture 19: 10/29/21:
Lecture 20: 11/01/21: Sums of Uniform Random Variables, Sums of Gaussian Random Variables, Cauchy Distribution, Gregory-Leibnitz Formula: https://youtu.be/qW-3bHAwdPU (slides)
Lecture 21: 11/03/21: Pythagoras, Gamma Function, Chi-Square Distribution: https://youtu.be/9QQCnIrC53c (slides)
Lecture --: 11/05/21: No class: Watch Surface Area: https://youtu.be/X9Ujt8oicAI?t=2256 (starting here is 13.5 minutes)
Lecture 22: 11/8/21: Markov and Chebyshev's inequalities, Divide and Conquer vs Newton's Method: https://youtu.be/eBcKGUSB_vI (slides)
Lecture 23: 11/10/21: Poisson Random Variables, Exponential Function, Stirling's Formula, Dyadic Decomposition, CLT to Stirling: https://youtu.be/fY7teGfgxsY (slides)
Lecture 24: 11/12/21: CLT for random walk of fair coin tosses, intro to generating fns via sums Poisson rvs: https://youtu.be/i0NX8vb9rWU (slides)
Lecture 25: 11/15/21: Generating Functions and Moment Generating Functions: https://youtu.be/HgupUwwgQ7M (slides)
Lecture 26: 11/17/21: Generating Functions III: Properties of MGF, Poisson and Normal Example, Poisson to CLT: https://youtu.be/pk6BwJsDRjM (slides)
Lecture 27: 11/19/21: M&M Game: Memoryless Processes, Geometric Series, Double Recurrences, Hypergeometric, ...: https://youtu.be/IdGay1NGMBg (slides)
The M&M Game: From Morsels to Modern Mathematics (with Ivan Badinski, Nathan McCue, Cameron Miller, Kayla Miller and Michael Stone). Mathematics Magazine (90 (2017), no. 3, 197--207) pdf (pruned published version: pdf: Copyright [2017] Mathematical Association of America. All Rights Reserved.).
Lecture 28: 11/22/21: Method of Least Squares: https://youtu.be/ZKoBBt933Ac Handout here (slides)
Lecture 29: 11/29/21: Proof of the Central Limit Theorem: https://youtu.be/0t_I5j598vQ (slides)
Lecture 30: 12/01/21: German Tank Problem: (slides from Yale University, September 27, 2019): https://youtu.be/FPDiLprpr3A pdf (paper here)
Lecture 31: 12/03/21: Benford's Law of Digit Bias: Part I: https://youtu.be/GBV_LaWGjdo (slides here; you can also watch the version I gave at Brown: Brown talk available here).
Lecture 32: 12/06/21: Benford's Law of Digit Bias: Part II: https://youtu.be/qQjVN2C0gTg (slides here; you can also watch the version I gave at Brown: Brown talk available here).
Lecture 33: 12/08/21: Monte Carlo Integration: https://youtu.be/GNKIJUZrb_A (slides) (2016 has Buffon's needle: http://youtu.be/xdtA0F2NKb0): Mathematica Program here (pdf here)
Lecture 34: 12/10/21: Introduction to Random Matrix Theory: https://youtu.be/r2e7NmPF3EE (slides)
♦ Lectures from Math/Stat 341: Fall 2019:
Lecture 01: 9/06/19: Introduction: https://youtu.be/HIv-HCVUfHM
Lecture 02: 9/9/19: Combinatorics, Birthday Problem, Pentium Bug, QWERTY, Programming, Babylonian Mathematics: https://youtu.be/4fzd-IRV2cE
Lecture 04': 9/13/19: Supplemental: Infinities, Generating Functions, Differentiating Identities: https://youtu.be/TQ20q4yZsho
Lecture 06: 9/18/19: Probability and Mathematical Modeling I (slides online here): https://youtu.be/T-35mhZioeo
Lecture 07: 9/20/19: Probability and Mathematical Modeling II (slides online here): https://youtu.be/ZGM6be90XqA
Lecture 08: 9/23/19: Card Shuffling (Guest Lecturer Francis Su): https://youtu.be/L_VTwdyyzUU
Lecture 10: 9/27/19: Independence, Derangements, Inclusion-Exclusion, Induction: https://youtu.be/lJKSKEUZ69k
Lecture 11: 9/30/19: Basics of pdfs and Random Variables: https://youtu.be/sn-hypa9tRY (coding: https://youtu.be/sSgjBysixdQ; code file here, pdf here)
Lecture 12: 10/02/19: Review cont/discrete RV, expectation, moments, Cauchy, Taylor: https://youtu.be/fCQlNOiHolU
Lecture --: 10/04/19: No class
Lecture 13: 10/07/19: Joint pdfs, linearity of expectation: https://youtu.be/6Yr5rTSoQrQ (2015 lecture with detailed joint PDF example: http://youtu.be/gQzorseWuVc)
Lecture 14: 10/09/19: Introduction to Statistics and Modeling: https://youtu.be/9iqLKlL-KHY (slides here)
Lecture 15: 10/11/19: Mountain Day
Lecture --: 10/14/19: Reading Period
Lecture 17: 10/16/19: Simpson's paradox, Ace of Hearts method: https://youtu.be/-on_cFHW66g (slides here)
Lecture 17: 10/18/19: Linearity of expectation, variances and covariances, power of linearity of expectation, bernoulli and binomial, convolution: https://youtu.be/WdITkk5zac0
Lecture 18: 10/21/19: Marriage Problem, Two Envelope Problem, Buffon's Needle: https://youtu.be/-36UUC_oPUs (see http://youtu.be/wxOlDaA_cGs for two envelope problem: 18mins to 19:30mins)
Lecture 19: 10/23/19: Differentiating Identiteis (Gaussian, Exponential, Geometric, Negative Binomial): https://youtu.be/T3PwM91_YaY
Lecture 20: 10/25/19: No class:
Lecture 21: 10/28/19: Sums of Uniform Random Variables, Sums of Gaussian Random Variables, Cauchy Distribution, Gregory-Leibnitz Formula: https://youtu.be/N0ye_W-2MD4
Lecture 22: 10/30/19: Pythagoras, Gamma Function, Chi-Square Distribution, Surface Area: https://youtu.be/X9Ujt8oicAI
Lecture 23: 11/01/19: Markov and Chebyshev's inequalities, Divide and Conquer vs Newton's Method: https://youtu.be/vuKCrS2on9Q
Lecture 24: 11/04/19: Poisson Random Variables, Exponential Function, Stirling's Formula, Dyadic Decomposition, CLT to Stirling: https://youtu.be/_-aGxDkNLHY
Lecture 25: 11/06/19: CLT for random walk of fair coin tosses, intro to generating fns via sums Poisson rvs: https://youtu.be/kVBIVl9uDTU
Lecture 26: 11/08/19: Generating Functions and Moment Generating Functions: https://youtu.be/GxohirsuMfM (didn't do standardization / change of basis)
Lecture 27: 11/11/19: M&M Game: Memoryless Processes, Geometric Series, Double Recurrences, Hypergeometric, ...: https://youtu.be/vmBUx0VhoEQ
Lecture 28: 11/13/19: Generating Functions III: Properties of MGF, Poisson and Normal Example, Poisson to CLT: video didn't record, last year didn't record, 24 minute version: http://youtu.be/Y7NppJoRoxQ
Lecture 29: 11/15/19: No Class
Lecture 30; 11/18/19: Method of Least Squares: http://youtu.be/_L72XJXxGCc
Lecture 31: 11/20/19: Proof of the CLT: https://youtu.be/4m77G15eINk
Lecture 32: 11/22/19: German Tank Problem: Yale University, September 27, 2019. pdf (video: https://youtu.be/nZJUbwC_bTw).
Lecture 33: 11/25/19: Coding examples: https://youtu.be/WX8PScrb8oM
Lecture 34: 12/02/19: Complex Analysis in a Day: https://youtu.be/WJdmu2vleTY
♦ Lectures from Math/Stat 341: Fall 2018:
Lecture 01: 09/07/18: Introduction: https://youtu.be/BCVNDfUKm7I
♦ Lectures from Math/Stat 341: Spring 2015:
♦ Links to lectures from 2013 (starts with Lecture 10 unfortunately)
♦ Interesting news articles involving math (see also the course disclaimer about not suing me!)
♦ Interesting videos
♦ Course disclaimer