♦ Lectures from Math/Stat 341: Spring 2025: (slides)   (click here for comments / solutions to the HW)

• Lecture 01: 2/05/25: Introduction, Birthday Problem, Hoops Game: https://youtu.be/bSdLy3-BVvQ (slides)

• Lecture 02: 2/11/25: Combinatorics, Institutionalization, Efficiency, Die Problem:   (slides)

• Lecture *2: 2/11/25: Supplement: Watched at home: Set Theory, Probability Wish List, Coding: https://youtu.be/2agUkFQJtnU  (2019 lecture)

• Lecture 03: 2/13/25: Binomial Coefficients, Poker, Coding Efficiently, Generating Functions, Laws of Probability. https://youtu.be/aByMKJ8NPEE  (slides)

• Lecture 04: 2/18/25: No physical class, watch at least two of the videos (the double plus one is part of mathematical modeling)

• Lecture 05: 2/20/25: No physical class, watch at least two of the videos (the double plus one is part of mathematical modeling)

  • Roulette: Double Plus Ungood: https://youtu.be/Esa2TYwDmwA
  • German Tank Problem:  pdf (video: https://youtu.be/1N2IhpifwAk).
  • Probability and Mathematical Modeling: I: (slides online here): https://youtu.be/T-35mhZioeo)
  • Probability and Mathematical Modeling: II:  (slides online here): https://youtu.be/ZGM6be90XqA) 

• Lecture 06: 2/25/25: Trump Splits, Conditional Probability, Bayes' Theorem, Method of  Exhaustion, Inclusion/Exclusion, Independence: https://youtu.be/xMAzWda4yZU    (slides)

• Lecture 07: 2/27/25: Inclusion-Exclusion Bounds, Derangements, Multinomial Coefficients, Combinatorics: https://youtu.be/e5H3XxPxdJk    (slides)

• Lecture 08: 3/04/25: Induction, PDF/CDF, Moments: https://youtu.be/N5jLFMOyW8A      (slides)

• Lecture 09: 3/06/25: CDF Method, Cauchy Distribution, Joint Distributions, Marginal Distributions, Convolutions, Linearity of Expectation: https://youtu.be/gXubfwC0vJw             (slides)

• Lecture 10: 3/11/25:Buffon's needle, Simpson's Paradox, Crackerjack Problem: https://youtu.be/iXmE8jvOYAQ (slides)

• Lecture 11: 3/13/25: Review, Variance/Covariance, Portfolios, Coding: https://youtu.be/mGQb4ZTTu0c           (slides)

• Lecture 12: 3/18/25: Coding, Differentiating Identities: https://youtu.be/E6o3AUEbGxM           (slides)

• Lecture 13: 3/20/25: Differentiating Identities (Geometric), Darth Vader, Double Six, Marriage/Secretary Problems: https://youtu.be/BRTWawmZJLs           (slides)

• Lecture 14: 4/08/25: Differentiating Identities: Negative Binomial (also Lin Exp, Recurrence); Sums of Uniform and Gaussian; Cauchy and Gregory-Leibnitz:  https://youtu.be/FjfRqQnJlLo   (slides)

• Lecture 15: 4/10/25: Pythagorean Won-Loss and Introduction to Modeling: https://youtu.be/EZq9XKLSzPA     (slides)

  (slides for the lecture here  and here)

• Lecture 16: 4/15/25: Pythagoras, Gamma Function, Chi-Square Distribution, Markov Inequality:  https://youtu.be/0IqoNdzPI84       (slides)

• Lecture 17: 4/17/25: Markov and Chebyshev's inequalities, Divide and Conquer vs Newton's Method, Exponential Function, Stirling's Formula, Dyadic Decomposition, Poisson Random Variables, CLT to Stirling: https://youtu.be/e17FtuD-qJk       (slides)

• Lecture 18: 4/22/25: CLT to Stirling, CLT for Fair Coins, Introduction to Generating Functions: https://youtu.be/PAgTajBx5ak        (slides)

• Lecture 19: 4/24/25: Generating Functions and Moment Generating Functions, Properties of MGF, Poisson and Normal Example, Poisson to CLT:  https://youtu.be/x-RNxpyi_4I        (slides)

• Lecture 20: 4/29/25:         (slides)

• Lecture 21: 5/01/25:         (slides)

♦ 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 03: 9/15/21: Die Problem, Coding, Integration: https://youtu.be/ZhPypMaQWhc (slides); watched at home: Set Theory, Probability Wish List, Coding: https://youtu.be/2agUkFQJtnU  (2019 lecture)
• Lecture 04: 9/17/21:
Axioms, Sniffing out Equations (Product Rule), Generating Functions: https://youtu.be/h6UrtHrwdbw (slides)
• Lecture 05: 9/20/21: Pascal's Triangle, Binomial Theorem, Poker Hands, Coding: https://youtu.be/AV02q6VnSa0  (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 08: 9/27/21: German Tank Problem II: Statistical Inference: https://youtu.be/JnaVkeO9qtc (slides) (Lecture 08: 9/23/19: Card Shuffling (Guest Lecturer Francis Su): https://youtu.be/L_VTwdyyzUU)
• Lecture 09: 9/29/21: Trump Splits, Conditional Probability, Bayes' Theorem, Method of  Exhaustion, Inclusion/Exclusion: https://youtu.be/jbXlsYsqH34  (slides)

• 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:

Differentiating Identities:  (Gaussian, Exponential, Geometric, Negative Binomial): https://youtu.be/oYRoyqV2jAI  (slides)

• 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 03: 9/11/19: Set Theory, Probability Wish List, Coding: https://youtu.be/2agUkFQJtnU  
• Lecture 04: 9/13/19: Axioms of Probability, Consequences, Sniffing out Formulas: https://youtu.be/qiek1ZM_KLE (2018 version)

• Lecture 04': 9/13/19: Supplemental: Infinities, Generating Functions, Differentiating Identities: https://youtu.be/TQ20q4yZsho

• Lecture 05: 9/16/19: Factorial Function, Binomial Coefficients, Poker Hands, Pascal's Triangle Mod 2: https://youtu.be/pEoW_hX4-oo (2018 version)

• 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 09: 9/25/19: Trump Splits, Conditional Probability, Bayes' Theorem: https://youtu.be/Id0h1Nawh9Q

• 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

• 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:
  • 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