♦ Math 313: Spring 2017: Number Theory Lectures:

1. Lecture 01: 2/3/17: Introduction, Euclid's proof of infinitude of primes, power sums: https://youtu.be/-swSmjLqlfE
2. Lecture 02: 2/6/17: Algorithms, notation, Babylonian math, Gregory-Leibniz formula: https://youtu.be/4ku0APonNxc
3. Lecture 03: 2/8/17: Coding Lecture:
   • 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: Axioms, Division and Euclidean Algorithms: https://youtu.be/BZwacoCYU4Y
5. Lecture 05: 2/13/17: Divisibility tests, clock arithmetic, unique factorization of primes, Riemann zeta function: https://youtu.be/Qmz9BAk8SrM
6. Lecture 06: 2/15/17: Clock Arithmetic, Binomial Coefficients, Morley's theorem, Fermat's little Theorem: https://youtu.be/46m_kBnrzeo
7. Lecture 07: 2/20/17: Euler's generalization of FlT, Solving polynomial equations, Chinese Remainder Theorem: https://youtu.be/WxpNtlsYbzM
8. Lecture 08: 2/22/17: Solving the 2x2x2 Rubik's Cube: https://youtu.be/AteP1iFbVmo
   • 2x2x2: https://www.youtube.com/watch?v=PKZ7pxFyYu0
   • 3x3x3: https://www.youtube.com/watch?v=FO1kOU-3Blw
   • 4x4x4: parity issue: https://www.youtube.com/watch?v=nC4jsBD1L1w
9. Lecture 09: 2/24/17: Dirichlet's Theorem for Primes in Arithmetic Progression, Number Theory Motivation: https://youtu.be/zG185Ef1gPM
10. Lecture 10: 2/27/17: Legendre Symbols, Elliptic Curve Motivation, Law of Quadratic Reciprocity, Euler's Criterion: https://youtu.be/cBxqW2OkpWM
11. Lecture 11: 3/1/17: Introduction to Cryptography, Caesar Cipher, Affine Cipher, Permutation Cipher, Vigenere Cipher, Midway: https://youtu.be/0kKow_0HHHQ
12. Lecture 12: 3/3/17: Diffie-Hellman, UPC codes, RSA, Euler Totient: https://youtu.be/LW3R1V7GTtM
13. Lecture 13: 3/8/17: Mobius function, Mobius Inversion, Dirichlet Convolution, Totient Function: https://youtu.be/dvGxcVfyUdY
14. Lecture 14: 3/10/17: Euler Totient Function: https://youtu.be/tFnemsbV5xw
15. Lecture 15: 3/13/17: Gregory-Leibniz Formula, Average Order, Prime Number Theorem: https://youtu.be/EMmZvRLlDl8
16. Lecture 16: 3/15/17: Perfect Numbers, Mersenne Primes, Fermat Primes: https://youtu.be/5CtFP-5dxyU
17. Lecture 17: 3/17/17: Introduction to Generating Functions: Fibonaccis and Cookie Problem: https://youtu.be/lJIwL2tsCXE
18. Lecture 18: 4/3/17: Irrationality I: Sqrt(2), Dirichlet's Theorem, Pigeonhole Principle: https://youtu.be/JJJSNHhtMSg
19. Lecture 19: 4/5/17: Liouville's Theorem: https://youtu.be/h4IJNV_mjEA
20. Lecture 20: 4/7/17: Transcendental Numbers and Continued Fractions: https://youtu.be/kPDSyW6CL9Q
21. Lecture 21: 4/10/17: Computing Continued Fraction Expansions: https://youtu.be/eKFrbmIOlq8
22. Lecture 22: 4/12/17: Introduction to Diophantine Equations, the Pythagorean Theorem and Pythagorean Triples: https://youtu.be/GW3zoVUZ4Xs
23. Lecture 23: 4/14/17: Method of Descent for Fermat and Introduction to p-adics: https://youtu.be/DIwYrmIxQpg
24. Lecture 24: 4/17/17: Sniffing out eqns, Series Expansions for DiffEQs, Pascal's Triangle, Steganography, Solving mod prime powers https://youtu.be/eRuKhHYJpTg
    1. https://www.youtube.com/watch?v=tt4_4YajqRM (my movie constructing table mod 2)
    2. https://www.youtube.com/watch?v=QBTiqiIiRpQ (mod different primes)
25. Lecture 25: 4/19/17: Hensel's lemma: https://youtu.be/zlsAbRTxmWQ
26. Lecture 26: 4/26/17: 3x+1 Problem: https://youtu.be/RcHmAbtfL7g (mathematica code and pdf) (unfortunately video did not project, have to look at code)
27. Lecture 27: 4/28/17: Coding and Conjecturing for 3x+1: https://youtu.be/nwEdbWXc8AQ
28. Lecture 28: 5/1/17: Introduction to Elliptic Curves, Roots of Polynomials, Discriminants: https://youtu.be/KerQfFu4WEY  (code and pdf of code)
29. Lecture 29: 5/3/17: Discriminants, Elliptic Curve, Points at Infinity: https://youtu.be/MPDxH0Qor4M
30. Lecture 30: 5/5/17: Elliptic Curve Group Law and the Congruent Number Problem: https://youtu.be/RqJfLqyWMFM
31. Lecture 31: 5/8/17: Elliptic Curve Cryptography and Integer Points: https://youtu.be/M-bRTl4H_KQ
32. Lecture 32: 5/10/17: Polynomial Fermat's Last Theorem: https://youtu.be/2jzReEvf7eA
33. Lecture 33: 5/12/17: Dr Seuss' Circle Method: https://youtu.be/vDxCIkCg2ik

♦ 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