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♦ Lectures from Math/Stat 341: Fall 2018:

Lecture 01: 09/07/18: Introduction: https://youtu.be/BCVNDfUKm7I
Lecture 02: 09/10/18: Hoops (and Geometric Series and Game Theory), Birthday Problem: https://youtu.be/DwyCFhzZEkQ
Lecture 03: 09/12/18: Paradoxes, Care with Infinities, Probability Wish List: https://youtu.be/6iVuKhMJY_g
Lecture 04: 09/14/18: Axioms of Probability, Consequences, Sniffing out Formulas: https://youtu.be/qiek1ZM_KLE
Lecture 05: 09/17/18: Factorial Function, Binomial Coefficients, Poker Hands, Pascal's Triangle Mod 2: https://youtu.be/pEoW_hX4-oo
Lecture 06: 09/19/18: Probability and Mathematical Modeling I (slides online here): https://youtu.be/mmsChVH7o_s
Lecture 07: 09/21/18: Probability and Mathematical Modeling II (slides online here): https://youtu.be/caFcPaQp9GU
Lecture 08: 09/24/18: Trump Splits, Conditional Probability, Bayes' Theorem: https://youtu.be/iQhgLd0lmv4
Lecture 09: 09/26/18: Independence, Derangements, Inclusion-Exclusion, Induction: https://youtu.be/kK7NVXvVgbs
Lecture 10: 09/28/18: Basics of pdfs and Random Variables, Coding: https://youtu.be/q8BJZHkkGro (code for aces up and pdf of code)
Lecture 11: 10/01/18: Review cont/discrete RV, expectation, moments, Cauchy, Taylor: https://youtu.be/fCQlNOiHolU
Lecture 12: 10/03/18: Joint pdfs, linearity of expectation: https://youtu.be/8ED51T8hdR0 (2015 lecture with detailed joint PDF example: http://youtu.be/gQzorseWuVc)
Lecture 13: 10/10/18: Introduction to Statistics and Modeling: https://youtu.be/ws2SkSngO5g (slides here)
Lecture 14: 10/12/18: Linearity of expectation, variances and covariances, power of linearity of expectation, bernoulli and binomial, convolution: https://youtu.be/LXbnSqpo4IE
Lecture 15: 10/15/18: CDF Method, Marriage Problem: https://youtu.be/1NV8w3z1cL8 (see http://youtu.be/wxOlDaA_cGs for two envelope problem: 18mins to 19:30mins)
Lecture 16: 10/17/18: Differentiating Identiteis (Geometric Series, GeomRV, Exp RV): https://youtu.be/vmdrj9m6k-c (Did the Poisson RV previous year: http://youtu.be/4EWY0U7LhX8)
Lecture 17: 10/19/18: Differentiating Identities: Binomial Distribution, Negative Binomial Distribution, Gaussian: https://youtu.be/1g9gq1OydQA
Lecture 18: 10/22/18: Sums of Uniform Random Variables, Sums of Gaussian Random Variables, Gamma Function: https://youtu.be/b_ZMk0wcGzo
Lecture 19: 10/24/18: Gamma Function, Chi-Square Distribution: https://youtu.be/NX_YUXKsPho
Lecture 20: 10/29/18: Markov and Chebyshev's inequalities, Divide and Conquer vs Newton's Method: https://youtu.be/09iNUteadas
Lecture 21: 10/31/18: Stirling's formula (justification, elementary arguments, integral test, Poisson and CLT): http://youtu.be/4KCjy1OsxaI
Lecture 22: 11/2/18: CLT for random walk of fair coin tosses, intro to generating fns via sums Poisson rvs: https://youtu.be/kVBIVl9uDTU
Lecture 23: 11/5/18: More on generating functions (examples, algebra) + standardization / change of basis: https://youtu.be/2mDwJ3ffSlU
Lecture 24: 11/7/18: Generating Functions III: Properties of MGF, Poisson and Normal Example, Issues with Interchanging Operators: http://youtu.be/Y7NppJoRoxQ (this is video watch at home)
- Lecture 24b: 11/7/18: Extra in-class lecture on problem solving and coding: https://youtu.be/mRYw-GHcgaw code: Mathematica File PDF of file
Lecture 25: 11/9/18: Guest Lecture: Josh McNutt '99: Intro to Data Science: https://youtu.be/3cU4YwE43Qk
Lecture 26: 11/12/18: M&M Game: Memoryless Processes, Geometric Series, Double Recurrences, Hypergeometric, ...: https://youtu.be/vmBUx0VhoEQ (slides here)
Lecture 27: 11/14/18: CLT for Sums of Poisson RV, CLT in General, Stirling from Poisson: https://youtu.be/kgrIXWcTs_U
Lecture 28: 11/16/18: Complex Analysis Introduction I: http://youtu.be/N0FRN-4neiA AND Coding general tic-tac-toe: https://youtu.be/zE0zc2hACg4 (code here, code pdf here)
Lecture 29: 11/19/18: Method of Least Squares: http://youtu.be/_L72XJXxGCc (2016 lecture)
Lecture 30: 11/26/18: Monte Carlo Integration: https://youtu.be/eOyGU8dDbVo (2016 has Buffon's needle: http://youtu.be/xdtA0F2NKb0): Mathematica Program here (pdf here)
Lecture 31: 11/28/18: Benford's law of Digit Bias: https://youtu.be/oM9O8C1y29o (slides here; you can also watch the version I gave at Brown: Brown talk available here).
Lecture 32: 11/30.18: Introduction to Complex Analysis II and Probability: http://youtu.be/SXikiKenyuc
Lecture 33: 12/3/18: More Sum Than Difference Sets: https://youtu.be/YZPgwR3e79g (Slides: slides for MSTD set lecture.)
Lecture 34: 12/5/18: Random Matrix Theory: https://youtu.be/SGnmEosshZg (slides here)

♦ Lectures from Math/Stat 341: Spring 2015:

Lecture 01: 2/6/15: Introduction, Course Mechanics, Hedging: http://youtu.be/pVQL4ivA08w
Lecture 02: 2/9/15: Hoops (and Geometric Series and Game Theory), Birthday Problem: http://youtu.be/dmI9d-w-bM4
Lecture 03: 2/11/15: Paradoxes, Care with Infinities, Probability Wish List: http://youtu.be/Mg7xZqolBKE
Lecture 04: 2/13/15: Axioms of Probability, Consequences, Sniffing out Formulas: http://youtu.be/0Rp8KgWmLi0
Lecture 05: 2/16/15: Factorial Function, Binomial Coefficients, Poker Hands, Pascal's Triangle Mod 2: http://youtu.be/3iLIiZ9pOlo
Lecture 06: 2/18/15: In Lawrence 231: Probability and Mathematical Modeling I (slides online here): http://youtu.be/VwiX36gkDVI
Lecture 07: 2/23/15: In Lawrence 231: Probability and Mathematical Modeling II (slides online here): http://youtu.be/Jnqud_IcfAs
Lecture 08: 2/25/15: Trump Splits, Conditional Probability, Bayes' Theorem: http://youtu.be/8fYnAe7NZag
Lecture 09: 2/27/15: Independence, Derangements, Inclusion-Exclusion, Induction: http://youtu.be/dXBJ5F6pi5U
Lecture 10: 3/2/15: Basics of pdfs and Random Variables: http://youtu.be/Y4tqpC1pFo8
Lecture 11: 3/4/15: Review cont/discrete RV, expectation, moments, Cauchy, Taylor: http://youtu.be/zjwVClO1Zl8
Lecture 12: 3/9/15: Joint pdfs, linearity of expectation: http://youtu.be/gQzorseWuVc
Lecture 13: 3/11/15: Linearity of expectation, variances and covariances, power of linearity of expectation, bernoulli and binomial rv: http://youtu.be/OtQqAjBeq-k
Lecture 14: 3/13/15: CDF Method, Envelope Problem, Marriage Problem: http://youtu.be/wxOlDaA_cGs
Lecture 15: 3/16/15: Differentiating Identiteis (Geometric Series, GeomRV, Exp RV, Poisson RV): http://youtu.be/4EWY0U7LhX8
Lecture 16: 3/18/15: Guest Lecturer: William Arms: The Early Years of Academic Computing: http://youtu.be/JoGFR4cDRu0
Lecture 17: 3/20/15: Differentiating Identities: Binomial Distribution, Negative Binomial Distribution, Gaussian: http://youtu.be/10BwrNXa4qk
Lecture 21: 4/6/15: Sums of Uniform and Normal Random Variables, Introduction to Gamma Function: http://youtu.be/lBYA2hs_q1U
Lecture 22: 4/8/15: Gamma Function, Chi-Square Distribution: http://youtu.be/Ckp81hLLxWM
Lecture 23: 4/10/15: Guest Lecturer: Josh McNutt '99: Math in the NBA (business side): http://youtu.be/osTQa4Utd_g
Lecture 24: 4/13/15: Introduction to Statistics and Modeling: Video from 2013 version of the talk: https://www.youtube.com/watch?v=gFDly_6qOn4&feature=youtu.be
Lecture 25: 4/15/15: Markov and Chebyshev's inequalities, Divide and Conquer vs Newton's Method: https://youtu.be/l651t8fYTpM
Lecture 26: 4/17/15: Stirling's formula (justification, elementary arguments, integral test, Poisson and CLT): http://youtu.be/4KCjy1OsxaI
Lecture 27: 4/20/15: CLT for random walk of fair coin tosses, intro to generating fns via sums Poisson rvs: http://youtu.be/OpSmk0rGJF8
Lecture 28: 4/22/15: More on generating functions (examples, algebra) + standardization / change of basis: http://youtu.be/fBMYlrUnnv8
Lecture 29: 4/24/15: Generating Functions III: Properties of MGF, Poisson and Normal Example, Issues with Interchanging Operators:
- Video issues: had to redo lecture as recording didn't take: 24 minute version (largest block I could make today b/w meetings): http://youtu.be/Y7NppJoRoxQ
- Original video attempt: not sure if able to get YouTube to fix it, trying: http://youtu.be/Mr9x1ttIaIQ (NOT optimistic)
Lecture 30: 4/27/15: CLT for Sums of Poisson RV, CLT in General: http://youtu.be/0ftuzHhrHt0
Lecture 31: 4/29/15: M&M Game: Memoryless Processes, Geometric Series, Double Recurrences, Hypergeometric, ...: https://youtu.be/vmBUx0VhoEQ
Lecture 32: 5/4/15: Monte Carlo Integration, Buffon's needle: http://youtu.be/xdtA0F2NKb0: Mathematica Program here (pdf here)
Lecture 33: 5/6/16: Complex Analysis Introduction I: http://youtu.be/N0FRN-4neiA
Lecture 34: 5/8/16: Introduction to Complex Analysis II and Probability: http://youtu.be/SXikiKenyuc
Lecture 35: 5/11/16: Method of Least Squares: http://youtu.be/_L72XJXxGCc
Lecture 36: 5/13/16: Benford's law of Digit Bias: http://youtu.be/jvdgvQmHf7E (video might be hard to view: slides here: Theory and applications of Benford's law; as the slides are not viewable you should skim the slides first, or just go forward a slide as you listen to the audio, and that way you'll have a sense of when to advance. You can also watch the version I gave at Brown: video of a version of the talk that I gave at Brown is available here).
Lecture 37: 5/15/16: More Sum Than Difference Sets: http://youtu.be/gub8TS11Fr4 (Slides: slides for MSTD set lecture.)

♦ Links to lectures from 2013 (starts with Lecture 10 unfortunately)

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

Election fraud:

♦ Interesting videos

TED Lectures:

Did You Know (2009 version)

Yes, Prime Minister: Manipulation Polls (YouTube video)

♦ 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!