♦ Math 409: Fall 2022 The little Questions Lectures:

• Lecture 01: 09/09/22: Introduction: https://youtu.be/FXLv9yhxA20
• Lecture 02: 09/12/22: Five Multiple Choice Questions: https://youtu.be/tax8BkrPB6A
• Lecture 03: 9/14/22: Induction (and sums of powers), Inequalities: https://youtu.be/gUvX8r-nnbc

• Lecture 04: 9/16/22: Coding: https://youtu.be/e8I5alerkOw  (code)  and Recurrences, Arithmetic Mean - Geometric Mean: https://youtu.be/_mhb_6S96OQ (no physical class, from 2018)

• Lecture 05: 9/19/22: AM-GM, Power sum, sum-product problem: https://youtu.be/FcqWSFz6mA4
• Lecture 06: 9/21/22: AM-GM inequality, Triangle Game: https://youtu.be/k1XF420-8QY (lecture from 2018)
• Lecture 07: 9/23/22: Discussing maximizing product a_1 * ... * a_n given a_i non-neg and sum to S.... https://youtu.be/PW4HPLJp_8U

• Lecture 08: 9/26/22: Why I love Monovariants: From Zombies and Conway's Soldiers to Fibonacci Games:  https://youtu.be/p2-QfjgitQ8  (slides here)

• Lecture 09: 9/28/22: From M&Ms to Mathematics, or, How I learned to answer questions and help my kids love math: https://youtu.be/UL73gGtu-aw   (slides here)

• Lecture 10: 9/30/22: (visitor): Egg drop mathematics: https://youtu.be/KYPFVdRuZU4

• Lecture 11: 10/3/22: Egg drop mathematics, Catalan numbers and generating functions: https://youtu.be/oVxqO1tzrOY

• Lecture 12: 10/5/22: Riemann Zeta Function, Generating Functions and the Circle Method, Fubini's Theorem: https://youtu.be/wHZ6sStCW3c

• Lecture 13: 10/7/22: Exam I (lowest non-Putnam exam dropped): No in-person class

• Lecture 14: 10/10/22: Reading Period: No Class

• Lecture 15: 10/12/22: Contour Integration: Complex Analysis in a Day: https://youtu.be/SapB24k6jl8

• Lecture 16: 10/14/22: Mountain Day

• Lecture 17: 10/17/22: Dirichlet Box Principle: https://youtu.be/g0pf8eqD2NE

• Lecture 18: 10/19/22: Fundamental Theorem of Calculus: https://youtu.be/kM6mfFfzlf0

• Lecture 19: 10/21/22: Class presentations

• Lecture 20: 10/24/22: Review day

• Lecture 21: 10/26/22: Class presentations

• Lecture 22: 10/28/22: Class presentations, Double Plus One: https://youtu.be/BZyj0F4axGA

• Lecture 23: 10/31/22: Double Plus One, Divisibility Rules: https://youtu.be/sEnpWmGV3i0

• Lecture 24: 11/2/22: Great American Shootout, Pirate Booty, Integral sin(x) / x: https://youtu.be/M0GR6Vu5bao

• Lecture 25: 11/4/22: No class: Midterm II

• Lecture 26: 11/7/22: Putnam A1 Problems: Basketball 80% Free Throw: https://youtu.be/BFwZR7uuBAI

• Lecture 27: 11/9/22:  Putnam 2005A1 and 2003A1 : https://youtu.be/5VuRk7GKrEU

• Lecture 28: 11/11/22: No class: spend 2+ hours straight doing Putnam problems

• Lecture 29: 11/14/22: More Putnam Problems: sums, special function, * operator: https://youtu.be/fN5dl9SGSY8

• Lecture 30: 11/16/22: Even More Putnam Problems: Conic Sections, Guessing Derivatives: https://youtu.be/4MCwy7EFw2U

• Lecture 31: 11/18/22: Even more even more Putnam problems: sums and Cauchy-Schwarz, ratio of areas of rectangles and triangles: https://youtu.be/GridGsQbtfU

• Lecture 32: 11/21/22: More even more even more Putnam problems: https://youtu.be/6Y1j9SizzXE

• Lecture 33: 11/28/22: Sum of Factorials Putnam Problem: https://youtu.be/hZBoxP3w47I

• Lecture 34: 11/30/22: Volumes, Factorials: https://youtu.be/SNNeDUvLK1k

• Lecture 35: 12/02/22: No class, prepare for the Putnam

• Lecture 36: 12/05/22: Rubik's Cube I

• Lecture 37: 12/07/22: Rubik's Cube II and Putnam Problems:

• Lecture 38: 12/09/22: Putnam 2022: https://youtu.be/qTlJD0001C0 (note: some errors in last problem, corrected a bit in slides)

♦ Math 331: Fall 2018: The little Questions Lectures:

• Lecture 01: 09/07/18: Introduction: https://youtu.be/zpxb9Kyn3b4

• Lecture 02: 09/10/18: Analyzing inequalities, induction, power sums, tiling and Fibonacci numbers: https://youtu.be/gkwZZknl9gU
• Lecture 03: 09/12/18: Coding: https://youtu.be/e8I5alerkOw  (code)
• Lecture 04: 09/14/18: Recurrences, Arithmetic Mean - Geometric Mean: https://youtu.be/_mhb_6S96OQ
• Lecture 05: 09/17/18: AM-GM inequality, Triangle Game: https://youtu.be/k1XF420-8QY
• Lecture 06: 09/19/18: Applications of the AM-GM Inequality, Chess Problem: https://youtu.be/wAzB4vbUUSY 
• Lecture 07: 09/21/18: Games: Rectangle, Dots, Fibonacci, Zombie (prospectives visiting): https://youtu.be/40iiOyG8GDw  (moved out of order in 2022)
• Lecture 08: 09/24/18: Catalan numbers, Generating Functions: https://youtu.be/Q6JtprSOa70
• Lecture 09: 09/26/18: Generating Functions, Sum of Squares, Exponential Function, Trigonometry Relations: https://youtu.be/auIW46iXwTA
• Lecture 10: 09/28/18: Commando, Generating Functions and the Circle Method, Fubini's Theorem: https://youtu.be/11LCG4B8E_g
• Lecture 11: 10/01/18: Pythagorean Formula, Asking Questions: https://youtu.be/UC32VpkY1Pw (click here for slides)
• Lecture 12: 10/03/18: Estimating sums: https://youtu.be/DuI81e-o5Fc
• Lecture 13: 10/10/18: Fundamental Theorem of Calculus: https://youtu.be/hDini6X5UY4
• Lecture 14: 10/12/18: Geometry Problems, Points on Spheres and Hemispheres: https://youtu.be/vi1utgfeQHU
• Lecture 15: 10/15/18: Monovariants, Linear Programming, Convergence Tests, Zeckendorf Decompositions: https://youtu.be/cRRZY5hwoQ8
• Lecture 16: 10/17/18: Dirichlet Box Principle, Approximating Irrationals, 3 Hat Problem, Quadratic Code: https://youtu.be/qP1xdM3WQdU
• Lecture 17: 10/19/18: Monoinvariants, 3 Hats, Checksum, Tell me three times, Misleading statistics: https://youtu.be/geVgAJ3RrYI
• Lecture 18: 10/22/18: Coding Linear Programming Problems, Discrete vs Continuous Optimization: https://youtu.be/rCyq3HLbKT8
• Lecture 19: 10/24/18: Discrete vs Continuous Optimization, Hamming Codes, Chess Queen-Pawn Problem: https://youtu.be/NX_YUXKsPho
• Lecture 20: 10/29/18: Divisibility Rules, 3x+1: https://youtu.be/rsfsP4bvI_0
• Lecture 21: 10/31/18: Monovariants: Tournament, Cards, Conway's Checker Problem: https://youtu.be/iKqhjKmI5x4
• Lecture 22: 11/2/18: Coding lecture: Amicable Numbers, Fibonacci Numbers, Sudoku: https://youtu.be/_D7M1eGyRTQ
• Lecture 23: 11/5/18: The Egg Drop Problem: https://youtu.be/0cSaTRrp2LQ
• Lecture 24: 11/7/18: Notation, Magic Wand and Rationals: https://youtu.be/DoeMwljbLZE

• Lecture 25: 11/9/18: Geometry proof of cuberoot(2), Prime Divides a Product: https://youtu.be/b0otIw7B6Wk

• Lecture 26: 11/12/18: Solving the Rubik's cube:
  • 2x2x2: https://www.youtube.com/watch?v=PKZ7pxFyYu0
  • 3x3x3: https://www.youtube.com/watch?v=FO1kOU-3Blw
• Lecture 27: 11/14/18: Rubik's Cube Math: https://youtu.be/kgrIXWcTs_U
• Lecture 28: 11/16/18: Harmonic Sums, Teller Problem, Grid Game: https://youtu.be/uYr8polXE-M
• Lecture 29: 11/19/18: Putnam Problems I: https://youtu.be/47KfJlOqgmA
• Lecture 30: 11/26/18: Putnam Problems II: https://youtu.be/sqzIn6AxpfY
• Lecture 31: 11/28/18: Putnam Problems III: https://youtu.be/Q26M197Cy-E
• Lecture 32: 11/30/18: Putnam Problems IV: https://youtu.be/Y4vGVVbw8es
• Lecture 33: 12/3/2018: Putnam 2018 A1: https://youtu.be/nOZwi3_b0rM
• Lecture 34: 12/5/2018: Differentiating Identities: https://youtu.be/Z3lgxbp2_yA

♦ Math 331: Spring 2017: The little Questions Lectures:

1. Lecture 01: 2/3/17: Introduction, Queens Problem, Tic-Tac-Toe and Symmetry: https://youtu.be/VZhnU2OSWAY
2. Lecture 02: 2/6/17: Analyzing inequalities, power sums, tiling and Fibonacci numbers: https://youtu.be/5grmPRBBbaE
3. Lecture 03: 2/8/17: Coding Lecture: https://youtu.be/e8I5alerkOw
   • 2017 Problem Solving (331) / Number Theory (313): Mathematica code   (the pdf)      Video: 313: https://youtu.be/khMJuFXOhFE   Video 331: https://youtu.be/vPGjly_7QVw
   • 2016 Probability Iteration: Click here for the Mathematica code                Click here for a pdf        Video: https://youtu.be/JMhkq_bczKk
   • 2015 Probability Iteration: Click here for the Mathematica code                Click here for a pdf        Video:  https://youtu.be/wUC-iUsZL6M
   • some suggested coding problems you should try (click here for Mathematica notebook, and click here for a pdf).
4. Lecture 04: 2/10/17: Recurrences and Arithmetic Mean - Geometric Mean inequality: https://youtu.be/caL16-pST5A
5. Lecture 05: 2/13/17: AM-GM inequality, Games (Triangle, Rectangle, SpotIt): https://youtu.be/fW28E5ruG3E
6. Lecture 06: 2/15/17: Applications of the AM-GM Inequality, Zeckendorf and kilometers: https://youtu.be/MxZIk-Y0_U4
7. Lecture 07: 2/20/17: Generating Functions, Binet's Formula, Waring's Problem, Catalan Numbers: https://youtu.be/nFDLwoTanDc
8. Lecture 08: 2/22/17: Catalan numbers, Generating Functions, Circle Method: https://youtu.be/KfEig_0kckQ
9. Lecture 09: 2/24/17: Pythagorean Formula, Asking Questions: https://youtu.be/6HxVSoOR-zc (click here for slides)
10. Lecture 10: 2/27/17: Geometry Problems, Points on Spheres and Hemispheres: https://youtu.be/8jRZjc9Q8PU
11. Lecture 11: 3/1/17: Irrationality Proofs, Morley's Theorem, Pigeon Hole Problems: https://youtu.be/xx8f8z8zzfQ
12. Lecture 12: 3/3/17: 12a: Monovariants, Zeckendorf Decomposition: https://youtu.be/kC7GVWEaVYI (slides HERE, start at 16minutes, then go to start); 12b: Pigeon Hole Problem, Dirichlet's Approximation Theorem: https://youtu.be/AA0ajr-foUw
13. Lecture 13: 3/8/17: Chessboard Tiling, Room Movement, Reversing Cards: https://youtu.be/QYNBKXFfVmA
14. Lecture 14: 3/10/17: Monovariants: Tournament, Cards, Conway's Checker Problem: https://youtu.be/iKqhjKmI5x4
15. Lecture 15: 3/13/17: Conway Checker Problem, \(e^\pi\) vs \(\pi^e\): https://youtu.be/PcK3HKXc4-A
16. Lecture 16: 3/15/17: Maximizing Product, Babylonian Math, Jug Problem: https://youtu.be/VEdhSgdf82c
17. Lecture 17: 3/17/17: Integration Techniques: https://youtu.be/MH3tDaarOas
18. Lecture 18: 4/3/17: Pythgoras at the Bat: Introduction to Modeling: https://youtu.be/mJrSzYmCAlI (paper here, slides here)
19. Lecture 19: 4/5/17: Integration by Differentiating: https://youtu.be/yvfKdI9K-JU
20. Lecture 20: 4/7/17: Differentiating Identities and Probability: https://youtu.be/CU_UIS-4xFI
21. Lecture 21: 4/10/17: Complex Analysis in a day: The Path to Cauchy's Residue Formula: https://youtu.be/TGJtH7K-mXs
22. Lecture 21b: 4/11/17: Bonus Lecture in Swarthmore: Sperner's Lemma and Fixed Point Theorems: https://youtu.be/D0WC20F9NXQ
23. Lecture 22: 4/12/17: Contour Integration II: https://youtu.be/bRH-K-yatBU
24. Lecture 23: 4/14/17: Contour Integration III: https://youtu.be/unZCcqeD4KY
25. Lecture 24: 4/17/17: Solving Rubik's cube: https://youtu.be/naSm9dt84b8  (Math 313: Solving the 2x2x2 Rubik's Cube: https://youtu.be/AteP1iFbVmo)
    1. 2x2x2: https://www.youtube.com/watch?v=PKZ7pxFyYu0
    2. 3x3x3: https://www.youtube.com/watch?v=FO1kOU-3Blw
    3. 4x4x4: parity issue: https://www.youtube.com/watch?v=nC4jsBD1L1w
26. Lecture 25: 4/19/17: Video: Student Presentations: Power Sums, Integrals, Squares: https://youtu.be/OgaYlA-l-ZU
27. Lecture 26: 4/26/17: Game Theory: Rectangle Game and Bidding Tic-Tac-Toe: https://youtu.be/DRBmLlrztvI (Game Theory: Screen Capture: https://youtu.be/Nwf5jVviVLU)
    1. Slides: powerpoint        pdf
28. Lecture 27: 4/28/17: Theory of Bidding Tic-Tac-Toe: https://youtu.be/9620-9VMKDA
29. Lecture 28: 5/1/17: Bridge and Egg Riddles: https://youtu.be/mlsGd1zkrKs
30. Lecture 29: 5/3/17: Egg Drop Problem and Combining Algorithms: https://youtu.be/50UOA42WzfA
31. Lecture 30: 5/5/17: Egg Problem Resolution: https://youtu.be/iAs76Yjbpr0
32. Lecture 31: 5/8/17: Dominoes and the Harmonic Series: https://youtu.be/LG-pPUYFhnE
33. Lecture 32: 5/10/17: Egg Drop Recurrence: https://youtu.be/z9tYmZXDe6Y
34. Lecture 33: 5/12/17: Harmonic Sums, Teller Problem, Grid Game: https://youtu.be/uYr8polXE-M

♦ Videos of The little Questions (Math 331) lectures from Fall 2014.

• Lecture 01 (9/5/14): First class: Mechanics: http://youtu.be/tVLPZgRt9ug

• Lecture 02 (9/8/14): Second class: Induction: http://youtu.be/ow8nGYDYbzE

• Lecture 03 (9/10/14): Third class: AM-GM: http://youtu.be/QgxP7l3BRuY

• Lecture 04 (9/12/14): Fourth Class (via YouTube): https://www.youtube.com/watch?v=XwnzWOc3_-0&feature=youtu.be

• Lecture 04: Supplement: Go here for Mathematica / LaTeX tutorials: http://web.williams.edu/Mathematics/sjmiller/public_html/math/handouts/latex.htm

• Lecture 05 (9/15/14): Fifth Class: Sphere / disk problem: subset of a cover: http://youtu.be/R5gNdjEyODA

• Lecture 06 (9/17/14): Sixth Class: Method of Descent, irrationality, 2n points on circle: http://youtu.be/nKatBilIhmw

• Lecture 07 (9/19/14): Eighth Class: Recurrence Relations: http://youtu.be/AKb4FdeNbPk

• Lecture 08 (9/22/14): Ninth Class: Recurrences, Bring it Over, Generating Functions: http://youtu.be/VSPLrTT85nE

• Lecture 09 (9/24/14): Tenth Class: Basic Probability and Combinatorics, The Cookie Problem: http://youtu.be/uwA65Mrn7vw

• Lecture 10 (9/26/14): Eleventh Class: Coding for Project Euler, Miscellaneous Problems: http://youtu.be/yktBY8Wi6BA

• Lecture 11a (9/29/14): Pigeonhole Principle: Part 1: http://youtu.be/b_7Gam3o_eA

• Lecture 11b (9/29/14): Pigeonhole Principle: Part 2: http://youtu.be/jHomcvVEf2w

• Lecture 12 (10/1/14): Countable and Uncountable: http://youtu.be/2_DeAX_rDZY

• (10/3/14): No class b/c of Mountain day

• Lecture 13 (10/6/14): Monoinvariants, Part I:  http://youtu.be/4xJ4GW11AcQ

• Lecture 14 (10/8/14): Mononinvariants, Part II:  http://youtu.be/t6D3Iu49pQo

• Lecture 15 (10/10/14): Parity and Monoinvariants: http://youtu.be/XZQKWIHZq18

• Lecture 16 (10/15/14): Integration (Symmetry, Missing Pieces), Exp Fn to Trig Identities: http://youtu.be/hnJIq48q5zo

• Lecture 17 (10/17/14): Monoinvariant card problem, \(e^\pi\) vs \(\pi^e\), maximizing  restricted product: http://youtu.be/bYIYuWbFSg0

• Lecture 18 (10/20/14): Integration, Differentiating  Integrals: http://youtu.be/nFhv2FdTxY4

• Lecture 19 (10/22/14): Differentiating Identities, Gaussian, Combinatorics: http://youtu.be/kydIrofUmuo

• Lecture 20 (10/24/14): Diophantine Equations  and Induction / Attacking Problems, The Egg Problem: http://youtu.be/3bklAXEbJvo

• Lecture 21 (10/27/14): Logic Problems: Part I: http://youtu.be/Gg6-RdVK2XE    and Part II: http://youtu.be/gwZCLO1lj-I

• Lecture 22 (10/29/14): Coins and the Devil, Solving n(n+1)(n+2) = m^r, Chessboard: http://youtu.be/xaMSbRJDzco

• Lecture 23 (10/31/14): Class work: no video

• Lecture 24 (11/3/14): Class work: no video

• Lecture 25 (11/4/14): Two person games: Chomp, Coins in a line: http://youtu.be/yurWIzJWW1A

• Lecture 26 (11/10/14): JosEPHus Problem, Basketball Problem: http://youtu.be/lItHw6CfjIo

• Lecture 27 (11/12/14): Problems from the 2008 Green Chicken: f(x+y) = f(xy), dot configurations, digit sums: http://youtu.be/WabH2AhjBlY

• Lecture 28 (11/14/14): Problems from the 2008 Green Chicken: sum of factorials, double sum, logarithm: http://youtu.be/e4P6W2U9RUw

• Lecture 29 (11/17/14): Green Chicken Problems 2014, Project Euler: http://youtu.be/1yDfY7jQYus

• Lecture 30 (11/19/14): Green Chicken 2014 finished, Project Euler: Part  I chicken:   http://youtu.be/23Jj6uWaBPo     Part II Euler: : http://youtu.be/0epsqX0kxkA

• Lecture 31 (11/21/14): Class work: no video (same for next few)

• Lecture 32 (12/04/14): Sum and integral problems: http://youtu.be/KCTl8yRIzfk (slowly uploading, might not make it till Saturday!)

♦ 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