♦ Videos of Advanced Analysis (Math 389) lectures from Fall 2014.

• Class 01: Sept 5, 2014: Class Mechanics: http://youtu.be/7b-6F4qJ4Ls
• Class 02: Sept 8, 2014: Taylor Series, Continuity, Series Convergence, Geometric Series: http://youtu.be/MonfQXBshnI
• Class 03: Sept 10, 2014: Geometric series and differentiation, exponential function: http://youtu.be/vVjOYrsHGqM
• Class 04 Sept 12, 2014: Fourth Class (via YouTube): https://www.youtube.com/watch?v=XwnzWOc3_-0&feature=youtu.be
• Class 05: Sept 15, 2014: L^p Spaces: http://youtu.be/Utf4esln9e0
• Class 06: Sept 17, 2014: Fejer and Dirichlet's Theorem: http://youtu.be/XuqIurfW_fs
• Class 07: Sept 19, 2014: Bessel's (In)Equality, Fourier Transform, Poisson Summation: http://youtu.be/v9eoWGQkoeM
• Class 08: Sept 22, 2014: Interchanging derivative and sum, Benford's law: http://youtu.be/8dPhdo98Gk8
• Class 09: Sept 24, 2014: Bounding integrals, proving Benfordness in Geometric Brownian Motions: http://youtu.be/AA_GHlM6sU4
• Class 10: Sept 26, 2014: Dirichlet's Theorem on Denseness, Generating Research Problems: http://youtu.be/tg47OJkNkcQ
• Class 11: Sept 29, 2014: Equidistribution: Discussion of ideas behind proof, continuous cutoff functions: http://youtu.be/BFVuimP8ZLE
• Class 12: Oct 1, 2014: Poissonian Behavior: http://youtu.be/I_10ADutXD8.
  • Video issues: Unfortunately the first 17 minutes is missing audio. NO idea why, no idea why it jumps in. Briefly what we did was look at Mathematica code (available in the additional comments) that showed that if we took n alpha mod 1 there were only 2 or 3 possible differences, but n^2 alpha mod 1 had what looked like a continuum. Thus, while n alpha mod 1 is equidistributed, it does have different behavior. We talked about applications to Monte Carlo Integration, and the advantage of not necessarily taking points completely at random but rather using some structure.
• Oct 3, 2014: No class: Mountain Day
• Class 13: Oct 6, 2014: Arithmetic Functions, Estimating sums/integrals: http://youtu.be/EJ4Ijxwfi5Q
• Class 14: Oct 8, 2014: Size of divisor function: http://youtu.be/C4gw6cYxmEo
• Class 15: Oct 10, 2014: Chebyshev's Theorem, Estimating Sums and Integrals: http://youtu.be/ejbZw-tIN9w
• Class 16: Oct 15, 2014: Splitting integrals, Riemann Zeta Function, Special Values and Infinite Products: http://youtu.be/XhVHeawbLPc
• Class 17: Oct 17, 2014: Riemann Zeta Function and Analytic Continuation: http://youtu.be/z8WstIYV3Xc
• Class 18: Oct 20, 2014: Basics of Complex Analysis: http://youtu.be/zCbm7hZUY9Q
  • Green's theorem in a day: https://www.youtube.com/watch?v=Iq-Og1GAtOQ
• Class 19: Oct 22, 2014: Cauchy Residue Theorem Example, Prime Number Theorem: http://youtu.be/EGDPdOuK3Jg
• Class 20: Oct 24, 2014: Mertens Proof that \(\zeta(1+it) \neq 0\), Dirichlet Characters: http://youtu.be/DfSCUElVr6s
• Class 21: Oct 27, 2014: Dirichlet L-Functions, Primes in Arithmetic Progression: http://youtu.be/hg1xKs7WMQQ
• Class 22: Oct 29, 2014: Dirichlet: There are infinitely many primes congruent to a modulo m: http://youtu.be/Wavl_-DsdWw
• Class 23: Oct 31, 2014: Introduction to the Circle Method, The Cookie Problem (Waring(1)): http://youtu.be/jzSt1Uepv-c
• Class 24: Nov 3, 2014: Size of functions for the Circle Method, Estimating Sums: http://youtu.be/sF9gBL85lrc
• Class 25: Nov 5, 2014: Circle Method: Major arc definition, singular series: http://youtu.be/5iROetdSRVY
• Class 26: Nov 12, 2014: Applications of the Circle Method: http://youtu.be/3n2BTQKdFfo
• Class 27: Nov 14, 2014: Circle Method for Various Problems, Heuristics: http://youtu.be/_9xI2tmhjHs
• Class 28: Nov 17, 2014: Introduction to Random Matrix Theory: http://youtu.be/kiswyjwDirg
• Class 29: Nov 19, 2014: RMT: Eigenvalue Trace Lemma, Method of Moments: http://youtu.be/-3wk-wqNFJw
• Class 30: Nov 21, 2014: RMT: Calculating Moments: http://youtu.be/Ij-t_KHt9KU
• Class 31: Nov 24, 2014: RMT: Calculating Moments II: http://youtu.be/Pz43bbE_sPE
• Class 32: Dec 5, 2014: From RMT to L-functions: http://youtu.be/JV4KtPuLWT0

♦ 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
• In computers we trust: http://www.simonsfoundation.org/quanta/20130222-in-computers-we-trust/
• Mathematicians shed light on a minimalist conjecture: http://www.simonsfoundation.org/quanta/20130709-mathematicians-shed-light-on-minimalist-conjecture/

♦ 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