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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)
- 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!)
♦
Interesting videos
♦
Course disclaimer
- I may occasionally say things such as
`Probability is one of the most useful courses you can take' or 'If you know
probability, stats and a programming language then you'll always be able to
find employment'. I really should write `you should always be able to find
employment', as nothing is certain. Thus, please consider yourself warned
and while you may savor the thought of suing me and/or Williams College, be
advised against this! I'm saying this because of the recent lawsuit of a
graduate who was upset that she didn't have a job, and sued her school!