♦ CLASS VIDEOS

• Lecture 01: 9/11/15: Introduction: https://youtu.be/bfrIk13rAJ4
• Lecture 02: 9/14/15: Complex differentiable, Cauchy-Riemann equations, Stokes' theorem, preview of Cauchy's formula: https://youtu.be/kOZyCqVoRVk
• Lecture 03: 9/16/15: Series, Differentiation, Primitives: https://youtu.be/HqRbop2TVPo
• Lecture 04: 9/18/15: Primitives of analytic functions, Goursat's Theorem, Example, Goldbach: https://youtu.be/AyjB6L5DDMk
• Lecture 05: 9/21/15: Holomorphic means primitive, example of using contours to do real integrals, stating Cauchy's formula: https://youtu.be/5TNnZ7WietQ
• Lecture 06: 9/23/15: Cauchy's integral formula, holomorphic means analytic: https://youtu.be/lURAn41ipEw
• Lecture 07: 9/25/15: Liouville's Theorem, Fund Thm Alg, Accumulation Theorem: https://youtu.be/i3tB8uuYguo
• Lecture 08: 9/28/15: Residue Theorem, Finding Residues, Integrating 1/(1+x^2): https://youtu.be/0NT28MUmHUk
• Lecture 09: 9/30/15: Contour Integration Examples (sin(x)/x, 1/(1+x^3)): https://youtu.be/EbKKt-6eLP4
• Lecture 10: 10/2/15: Singularities, Riemann's Removable Theorem, Cassorati-Weierstrass: https://youtu.be/uitgg2QXcy4
• Lecture 11: 10/5/15: Classification of Functions, Argument Principle: https://youtu.be/XZt3C3ZIY1M
• Lecture 12: 10/7/15: Rouche's Theorem, Open Mapping Theorem, Maximum Modulus Principle, Homologous: https://youtu.be/gQwK2CIEa1M
• Lecture 13: 10/14/15: Complex Logarithm: https://youtu.be/bnZOX0KXSmg
• Lecture 14: 10/19/15: Products with Zeros of Functions: https://youtu.be/QYseyAB_Sx0
• Lecture 15: 10/21/15: Back to the Future Lecture: Weierstrass Products, Automorphisms, Unit Disk: https://youtu.be/Az78Kof-1OA
• Lecture 16: 10/23/15: Mappings, Inverse Map Holomorphic, Schwartz Lemma: https://youtu.be/zX2XKDJLkf8
• Lecture 17: 10/26/15: Montel's Theorem and Results from Analysis: https://youtu.be/JDtuMS38hhQ
• Lecture 18: 10/28/15: Riemann Mapping Theorem (Proof): https://youtu.be/x0Yy1Ivn1c4
• Lecture 19: 11/02/15: Introduction to Analytic Continuation, The Gamma Function, The Riemann Zeta Function: https://youtu.be/8Fg_1lP2H8c
• Lecture 21: 11/04/15: Analytic Continuation of Zeta(s), Preliminary Integral for PNT: https://youtu.be/2mdU3kIuI4I
• Lecture 22: 11/06/15: Riemann Zeta Function and the Prime Number Theorem: https://youtu.be/Rj8nLKuWaIE
• Lecture 23: 11/09/15: Laplace's Method: https://youtu.be/GvKI5I_cfDQ
• Lecture 24: 11/13/15: Laplace's Method and Stirling's Formula: https://youtu.be/_sRP7ovkgU0
• Lecture 25: 11/16/15: Introduction to Probability and Generating Functions: https://youtu.be/zw3yPh6oWOU
• Lecture 26: 11/18/15: Fourier Transform of Gaussian and Densities with same Integral Moments: https://youtu.be/62Eq8i--8_Q
• Lecture 27: 11/20/15: Fourier Transform of Gaussian, Proof of the CLT modulo Complex Analysis Results: https://youtu.be/IsKFhb7C_CQ
• Lecture 28: 11/23/15: Complex Analysis and the Central Limit Theorem: https://youtu.be/pf3sbVA_T-E
• Lecture 28b:11/23/15: The Uncertainty Principle (in Mathematics): https://youtu.be/l-N7bMLJNaA
• Lecture 29: 11/30/15: Laplace Transform and Fractals: https://youtu.be/ZrLeIC9SBbw (with Cam and Kayla)
  • Newton fractal: https://www.youtube.com/watch?v=VXu-BYfk36I
  • Mandelbrot zoom: https://www.youtube.com/watch?v=0jGaio87u3A
  • Star Trek: Wrath of Khan: https://www.youtube.com/watch?v=Tsr-XtuKuSw&feature=related
• Lecture 30: 12/02/15: WCMA: Power of Perspective: https://youtu.be/U04C2TSGb5k
• Lecture 31: 12/04/15:
Introduction to Random Matrix Theory: https://youtu.be/qsalf_YH1qs (slides here)
• Lecture 32: 12/07/15: Introduction to Several Complex Variables: https://youtu.be/6wy_b96W4g4
• Lecture 33: 12/09/15: Laplace Inversion, Trig Integrals: https://youtu.be/YLe4Wl1T-jo
• Lecture 34: 12/11/15: Branch cut method: https://youtu.be/WiqYZD0vIPw

♦ 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