♦ Lectures from Math/Stat 341: Fall 2016:

• Lecture 01: 9/9/16:  Introduction: click here for first day slides                click here for first day's handout        first day's video:  https://youtu.be/bzilA8-4g4w
• Lecture 02: 9/12/16: Basketball and Birthday Problems, Russell's Paradox: https://youtu.be/L_HbCDXqCIY
• Lecture 03: 9/14/16: Mathematical Rigor: Countable/Uncountable, Axioms, Infinities: https://youtu.be/ybboE1tEjGM
• Lecture 04: 9/16/16: Kolmogorov's Axioms, Expected Counts, Roulette, Double Plus One, Fibonacci Numbers: https://youtu.be/mrB6N7MjYt8
• Lecture 05: 9/19/16: Binomial Coefficients, Proof by Story, Tic-Tac-Toe, Derangement: https://youtu.be/giH2MTZIU0E
• Lecture 06: 9/21/16: Trump splits, derangements, generating functions: https://youtu.be/MrvXpJJikEA
• Lecture 07: 9/23/16: Coding: Video: https://youtu.be/JMhkq_bczKk     Click here for the Mathematica code                Click here for a pdf       
• Lecture 08: 9/26/16: Conditional Probability and Independence: https://youtu.be/SVhyQiITN1c
• Lecture 09: 9/28/16: Bayes Rule, Simpson's Paradox and Inclusion-Exclusion: https://youtu.be/jPCkKyDbbpY
• Lecture 10: 9/30/16: ABBA, Cookie Problem, Multinomials, Binomial Identities, Circular Orderings: https://youtu.be/FEZFoli4Rs4
• Lecture 11: 10/3/16: Introduction to Random Variables: https://youtu.be/TV3o8QNZiFQ.
• Lecture 12: 10/5/16: Introduction to expectation, moments, Taylor series, Moments: https://youtu.be/QYm0BeFd4LY
• Lecture 13: 10/7/16: No class: Mountain Day
• Lecture 14: 10/10/16: No class: Reading Period
• Lecture 15: 10/12/16: No class: Yom Kippur: From years earlier: Josh McNutt '99 on analytics in the NBA: http://youtu.be/osTQa4Utd_g
• Lecture 16: 10/14/16: Joint Probability Density Functions, Marginal Distributions, Convolutions, Linearity of Expectation (10/14/15):  http://youtu.be/gQzorseWuVc
• Lecture 17: 10/17/16: Linearity of Expectation, Differentiating Identities: https://youtu.be/JnvVO0yymJs (video from '15 with additional examples: https://youtu.be/YF0v4O9dwyc).
• Lecture 18: 10/19/16: Marriage Problem, Poisson Random Variables: https://youtu.be/dafvzF66vzY  (code here)
• Lecture 19a: 10/21/16: Coding Practice: Card Game, Marriage Problem: https://youtu.be/7QgjEnytnFc (given in class)
• Lecture 19b: 10/21/16: Envelope Problem, Expected Value of a Product, Multiplicative Convolution, Variances, CDF Method: https://youtu.be/_hm1gOJT2WQ (Video from 2015).
• Lecture 20: 10/24/16: Normal Random Variables, Sums of Independent Normal Random Variables, Polar Trick: https://youtu.be/nxp3dvvG7MA
• Lecture 21: 10/26/16: Sums of Normal Random Variables, Gamma Function, Chi-square Random Variables: https://youtu.be/_psbkwFPd94
• Lecture 22: 10/28/16: Pythagoras at the Bat: https://youtu.be/PIQelk32SKQ  (Slides) (2015 version
• Lecture 23: 10/31/16: Distributions, Markov's Inequality, Chebyshev' Inequality: https://youtu.be/EV02Od8OVzE
• Lecture 24: 11/2/16: Markov's & Chebyshev's Inequalities, Divide and Conquer, Newton's Method, Stirling's Formula: https://youtu.be/cUD7PalcrXY  
• Lecture 25: 11/4/16: Stirling's Formula, Weak Law of Large Numbers, Poisson Random Variables: https://youtu.be/JSx7PTZzoiE
• Lecture 26: 11/7/16: Method of Least Squares: https://youtu.be/cgGSdVxp8N8
• Lecture 27: 11/9/16: CLT from Tossing Fair Coin: https://youtu.be/NlABhZo5OEA
• Lecture 28: 11/11/16: M&M Game: https://youtu.be/DFobthridWI
• Lecture 29: 11/14//16: Generating Functions I: https://youtu.be/DQNhhNNhwy8
• Lecture 30: 11/16/16: Generating and Moment Generating Functions: https://youtu.be/xzvOVQKo_Qo
• Lecture 31: 11/18/16: Poisson MGF, Proof of CLT for Poissons, Proof of CLT modulo results from Complex Analysis: https://youtu.be/qRR73ScAOOc
• Lecture 32: 11/21/16: Analysis in Probability: https://youtu.be/AGQWvtlGj30
• Lecture 33: 11/28/16: Monte Carlo Integration, Buffon's Needle: 2015 video: https://youtu.be/kVNQvzZKfQE; 2016 video: https://youtu.be/3CFnmkiteBs  (issues having simulation display).
  •  Computer program  here: http://web.williams.edu/Mathematics/sjmiller/public_html/341/mathematicaprograms/MonteCarloIntegration2.nb (right click and download)
• Lecture 34: 11/30/16: Benford's law of Digit Bias: 2015 version: https://youtu.be/ATqiJUUcWFg (slides here)
• Lecture 35: 12/02/16: Introduction to Random Matrix Theory: 2015 version:  https://youtu.be/qsalf_YH1qs  (slides here)
• Lecture 36: 12/05/16: No class due to exam
• Lecture 37: 12/07/16: Zeckendorf Decompositions: 2015 version: (slides here): Zeckendorf Decompositions: https://youtu.be/CjwDcsoigdE
• Lecture 38: 12/09/16: More Sum Than Difference Sets (Spring 2015): http://youtu.be/gub8TS11Fr4 and slides: slides for MSTD set lecture

♦ Lectures from Math/Stat 341: Fall 2015:

• Lecture 01: 9/11/15:  Introduction: click here for first day slides                click here for first day's handout        first day's video: https://youtu.be/URenWxlXHBQ
• Lecture 02: 9/14/14: Click here for slides, Day the music died, HW, birthday problem, basketball game: https://youtu.be/VSOAXnBaDws
• Lecture 03: 9/16/15: Basics of Set Theory, Russell's Paradox, Countable/Uncountable, Basic Probability, Wish List for Probability, Sniffing out Formulas: https://youtu.be/bkGZ62RNQSA
• Lecture 04: 9/18/15: Kolmogorov Axioms of Probability, Implications of Axioms, Factorial Function, Binomial Coefficients, Proofs by Story: https://youtu.be/5a75Ta-0f3o
• Lecture 05: 9/21/15: Counting and probability (tic-tac-toe, poker hands, bridge), binomial theorem: https://youtu.be/pJ7RXimgBBo
• Lecture 06: 9/23/15: Basic coding in Mathematica: https://youtu.be/wUC-iUsZL6M
• Lecture 07: 9/25/15: Fibonacci Numbers, Binet's Formula, Double Plus 1: https://youtu.be/ltR19jRU8wA
  • Mathematical Modeling Lectures: From Spring 2015
    • 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: 9/28/15: Conditional Probability, Independence and Bayes Theorem: https://youtu.be/7tYdnrMmMd4
• Lecture 09: 9/30/15: ABBA and Combinations, Partitions, Inclusion-Exclusion: https://youtu.be/V0jgvAVj-Lw
• Lecture 10: 10/2/15: Inc-Exc Example, Circular Orderings, Mississippi Words, Cookie Problem: https://youtu.be/esi25VbpKms
• Lecture 11: 10/5/15: Introduction to Discrete and Continuous Random Variables: https://youtu.be/hfhPh14ExMA
• Lecture 12: 10/7/15: Taylor Series and Applications, Moments: https://youtu.be/w_lTjpY4I3s
• Lecture 13: 10/14/15: Joint Probability Density Functions, Marginal Distributions, Convolutions, Linearity of Expectation:  http://youtu.be/gQzorseWuVc
• Lecture 14: 10/19/15: Prizes in a Box Problem, Differentiating Identities, Geometric Random Variable, Linearity of Expectation: https://youtu.be/YF0v4O9dwyc
• Lecture 15: 10/21/15: Back to the Future Lecture: Marriage Problem, Differentiating Identities, Binomial Random Variables, Bernoulli Random Variables: https://youtu.be/QgmZpp5Ztyw
• Lecture 16: 10/23/15: Envelope Problem, Expected Value of a Product, Multiplicative Convolution, Variances, CDF Method: https://youtu.be/_hm1gOJT2WQ
• Lecture 17: 10/26/15: The Normal Distribution and Integration without Integrating: https://youtu.be/9zIvJahTp-I
• Lecture 18: 10/28/15: Gamma Function, Normal Distribution and Chi-Square Random Variables: https://youtu.be/pLK9omzuH04
• Lecture 19: 10/30/15: No class
, please watch one of the following and answer: State anything you learned or enjoyed in whatever video you watched. One or two sentences suffice.
• Probability and Mathematical Modelling  I (slides online here): http://youtu.be/VwiX36gkDVI
• Probability and Mathematical Modeling II (slides online here): http://youtu.be/Jnqud_IcfAs
• William Arms: The Early Years of Academic Computing: http://youtu.be/JoGFR4cDRu0
• Josh McNutt '99 on analytics in the NBA: http://youtu.be/osTQa4Utd_g
• Lecture 20: 11/02/15: Sums of chi-square random variables, Markov's Inequality: https://youtu.be/SJ1jJMKhSUc
• Lecture 21: 11/04/15: Markov and Chebyshev Inequalities, Divide and Conquer and Newton's Method, Stirling's Formula: https://youtu.be/5-LIXIi_QYg
• Lecture 22: 11/06/15: Stirling's Formula, Poisson Random Variables and the CLT: https://youtu.be/9Po84qqfnzk
• Lecture 23: 11/09/15: Method of Least Squares: https://youtu.be/XdfieGTbhoI
  • Unfortunately the video is a bit dark and hard to see; here is the video from last spring: https://www.youtube.com/watch?v=_L72XJXxGCc&feature=youtu.be
• Lecture 24: 11/13/15: CLT from Tossing Fair Coin: https://youtu.be/NlABhZo5OEA
• Lecture 25: 11/16/15: Introduction to Generating Functions: https://youtu.be/4wbai2-EdFU
• Lecture 26: 11/18/15: Generating Functions, Moment Generating Functions and Examples: https://youtu.be/UM7GnOLVRTg
• Lecture 27: 11/20/15: Poisson MGF, Proof of CLT for Poissons, Proof of CLT modulo results from Complex Analysis: https://youtu.be/f620wNdxyQQ
• Lecture 28: 11/23/15: Monte Carlo Integration, Buffon's Needle: https://youtu.be/kVNQvzZKfQE
• Lecture 29: 11/30/15: Pythagoras at the Bat: https://youtu.be/PIQelk32SKQ  (Slides)
• Lecture 30: 12/02/15:
Introduction to Random Matrix Theory: https://youtu.be/qsalf_YH1qs (slides here)
• Lecture 31: 12/04/15: No class
, please watch one of the following and answer: State anything you learned or enjoyed in whatever video you watched. One or two sentences suffice. Obviously don't do one you've already watched (if you did two earlier that counts, just let me know).
• Probability and Mathematical Modelling  I (slides online here): http://youtu.be/VwiX36gkDVI
• Probability and Mathematical Modeling II (slides online here): http://youtu.be/Jnqud_IcfAs
• William Arms: The Early Years of Academic Computing: http://youtu.be/JoGFR4cDRu0
• Josh McNutt '99 on analytics in the NBA: http://youtu.be/osTQa4Utd_g
• Lecture 32: 12/07/15: Zeckendorf Decompositions: https://youtu.be/CjwDcsoigdE  (slides here)
• Lecture 33: 12/09/15: Benford's law of Digit Bias: https://youtu.be/ATqiJUUcWFg (slides here)
• Lecture 34: 12/11/15: M&M Game: Memoryless Processes, Geometric Series, Double Recurrences, Hypergeometric, ...:   https://youtu.be/CZGj5hV84Ok  (slides)  (paper)

♦ 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
• 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:
  • Rise and fall of internet election-fraud hunters (Carl Bialik, Wall Street Journal)
  • Statistical sleuthing on the Iran elections (Carl Bialik, Wall Street Journal Blog)
  • Statistical test suggestive of fraud in Iranian elections
• When precision is only 92.11567% accurate (Charles Forelle, Wall Street Journal)
• World record in craps (the casino game!) (S. N. Ethier and Fred M. Hople)
• http://www.sciencenews.org/view/authored/id/43/name/Julie_Rehmeyer

♦ Interesting videos

• TED Lectures:
  • Malcolm Gladwell on spaghetti sauce
  • Dan Pink on Motivation
• Did You Know (2009 version)
• Yes, Prime Minister: Manipulation Polls (YouTube video)

♦ Course disclaimer