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CLASS VIDEOS: 2023 (for captioning you might try http://ncamftp.wgbh.org/cadet/ )

Lecture 01: 9/08/23: Introduction, Definition of Derivative: https://youtu.be/sljeScdiiR0 first day slides and notes from class

Lecture 02: 9/11/23: Definition of Derivatives, Experimental Math, Cauchy-Riemann Eqs: https://youtu.be/xYFwqGrs9mQ and notes from class

Lecture 03: 9/13/23: No class, do exam: Real Analysis Review (limsup/liminf, strange functions): https://youtu.be/DLyzZhJN58w (slides); watched at home: Differentiating Term By Term, Analytic Functions, Path Integrals: https://youtu.be/e60Dh8cAIhQ (2017). Green's Theorem in a day: https://youtu.be/Iq-Og1GAtOQ

Lecture 04: 9/15/23: Primitives, Goursat's Theorem: https://youtu.be/-hqBpme4Q2A

Lecture 05: 9/18/23: Primitives, Cauchy's Theorem: https://youtu.be/pTyXgBAGN7A

Lecture 06: 9/20/23: Cauchy's Theorem and Consequences: https://youtu.be/srLW0uLwVpk

Review of contour integrals a la multivariable calculus: https://www.youtube.com/watch?v=hle5zvG4ZrI (Lecture 06: 9/20/17)
Example of a contour integral: https://youtu.be/NgHIiZUYI6g?t=2655 (44:15) (Lecture 06: 9/20/17)

Lecture 07: 9/22/23: Evaluating Integrals: Cauchy Distribution, sin x / x: https://youtu.be/UVvYwP7_5Ww

Lecture 08: 9/25/23: Make sure you are comfortable with sequences and series.

Lecture 09: 9/27/23: Make sure you are comfortable with sequences and series.

Lecture 10: 9/29/23: Make sure you are comfortable with sequences and series.

Lectures from Math 150: Multivariable Calculus: Sequences and Series

Read multivariable calculus (Cain and Herod) and my lecture notes.

Read Intermediate and Mean Value Theorems and Taylor Series (you should know this material already; the main results are stated and

mostly proved, subject to some technical results from analysis which we need to rigorously prove the IVT).

•Twenty-third day lecture: http://youtu.be/aigdKmu-5ow   (April 28, 2014: Geometric and Harmonic Series, Memoryless Processes)

•Twenty-fourth day lecture:  http://youtu.be/6bf9fjwMs2o   (May 2, 2014: Comparison Test, Implications of Limits of Terms)

•Twenty-fifth lecture: https://youtu.be/fa4X1AcGFOA (May 2, 2014: Comparison Test, Implications of Limits of Terms: II)

•Twenty-sixth lecture: https://youtu.be/jFgCKfUTOQ8 (Comparison Test, Implications of Limits of Terms: III)

•Twenty-seventh day lecture:   http://youtu.be/ujJbUpCab6M     (May 7, 2014: Root Test, Integral Test)

•Twenty-eight day lecture:    http://youtu.be/yr01SLw9t4c    (May 12, 2014: Taylor Series)

•Twenty-ninth day lecture:    http://youtu.be/4OcxtpxuSJw (May 14, 2014: Special Series, Alternating Series, Pi formulas, Birthday Problem: Not doing 2018)

Lecture 11: 10/01/23: Holomorphic is Analytic, Accumulation Theorem, Liouville's Theorem, Fundamental Theorem of Algebra: https://youtu.be/3pgsv4hVrPs

Lecture 08: 9/27/21: Cauchy Formula, Accumulation Theorem, Cauchy-like Integrals: https://youtu.be/wSqTEQ4usno (slides)
Lecture 09: 9/29/21: Integration Examples: (see for other examples Lecture 09: 9/27/17: Integration Example, Types of Singularities: https://youtu.be/Jz76hM32C80) (slides)

Lecture 12: 10/04/23: Singularities, Probability, MGF/Characteristic Fns, Cauchy Integral, Trig Integrals: https://youtu.be/01xjCbFe8_Y

Lecture 13: 10/06/23: (lecture from 10/4/21): Meromorphic Functions, Log, Argument Principle, Rouche, Fund Thm Alg, Trig Integral: https://youtu.be/INRdLUT6ckQ (slides from 2021)

Lecture 14: 10/09/23: No Class, Columbus Day

Lecture Bonus: 10/10/23: Fresnel Integrals: https://youtu.be/R5lCHdPVESQ

Lecture 15: 10/11/23: Review of Argument Principle and Roche's, Open Mapping Theorem, Maximum Modulus Principle, Real Analysis Review: https://youtu.be/touNug0_fLw

Lecture 16: 10/13/23: No Class - Mountain Day

Lecture 17: 10/16/23:

Logarithm Review, Complex Logarithm, Exponential Function and Trigonometry: https://youtu.be/Uz42EoM6yLs

Watch the following videos before class / read the book (better both!):
- Another approach to proving open mapping theorem without using Rouche: watch from 28 minutes till end: https://youtu.be/-vuwc6irob4?t=1685
- Complex Logarithms, Earlier Material, Functions with Prescribed Zeros/Values: https://youtu.be/CR-sRChcID4 (slides)
- Writing functions as a product over zeros: https://youtu.be/AoiyKD17aKM
- Mathematica notebook on plotting zeros: https://web.williams.edu/Mathematics/sjmiller/public_html/383Fa23/mathematicaprograms/PlotZerosExpApprox.nb

Lecture 18: 10/18/23: Infinite Products I: https://youtu.be/WzJhBEwPwpA

Watch the following videos before class / read the book (better both!):
- Weierstrass Products, Conformal Maps: https://youtu.be/clP3ZO5HpV4
- Introduction to Conformal Maps: https://youtu.be/kzPm-0X_HW8 (slides)

Lecture 19: 10/20/23: No Class - Take-home Exam

Lecture 20: 10/23/23: Prescribed Values and Zeros, Conformal Maps Introduction: https://youtu.be/ahgjEjJkZks

Lecture 21: 10/25/23: Conformal Maps: https://youtu.be/C9JCkmjVrEg

Lecture 22: 10/27/23:

Conformal Maps, Sniffing out Automorphisms, Schwarz Lemma: https://youtu.be/n43JVHQigBE

Lecture 23: 10/30/23: Bijections on the boundary, Geometric Series to the Riemann Zeta Function: https://youtu.be/uMyZ5mgy3sQ

Lecture 24: 11/01/23: Stirling's Formula, Estimating Sums: https://youtu.be/0XjpgP9F5uw

Lecture 25: 11/03/23: No Class

Lecture 26: 11/06/23: Analytic Continuation of Zeta(s): https://youtu.be/mio4O-DpD2U

Lecture 27: 11/08/23: Class on Wednesday will be asynchronous. Please watch the following two videos (we may have covered a good amount of the first in class on Monday)

2021: Lecture 24: 11/12/21: Gregory-Leibniz Formula, Dirichlet L-functions, proof of RH (not!), Duality: https://youtu.be/K8RhtDyts7s (slides)
2021: Lecture 25: 11/15/21: Introduction to Fourier Analysis, Approximations to the Identity: https://youtu.be/YiFtCBbYe_I (slides)

Lecture 28: 11/10/23: Complex Analysis and Number Theory I: https://youtu.be/gfFtYYb4xPQ

L-Functions and Random Matrix Theory:
- Introductory lectures on Random Matrix Theory and L-functions:
  - Part I (Classical RMT, Intro L-fns, Dirichlet): http://youtu.be/2PuUbk6gUMM (slides: part 1)
  - Part II (Convolving families, cusp forms: slides here): http://youtu.be/vJz6W24tDik (slides part 2)
- From the Manhattan Project to Elliptic Curves: MASON IV (3/7/20). pdf (video here: https://youtu.be/p15X3ERNvLs)
- Introduction to L-functions for SMALL students: 2021: https://web.williams.edu/Mathematics/sjmiller/public_html/math/talks/intronumbertheory/

Lecture 29: 11/13/23: Number Theory and Complex, Introduction to Fourier Analysis: https://youtu.be/8TIW3bFr6XE

Lecture 30: 11/15/23: Fourier Analysis: Convergence of Series: https://youtu.be/sGUVKUYhEY0

Lecture 31: 11/17/23: Fourier Analysis: Poisson Summation, Probability: https://youtu.be/d4QZPmR_LXA

Lecture 32: 11/20/23: Fourier Analysis IV: Probability, Laplace Transforms: https://youtu.be/fwDbGhG1fRw

Monday: From Complex Analysis to the CLT: 1-2pm in Wachenheim 114 (I will record): https://youtu.be/YwDJh6V8C3Y

Laplace Inversion, Trig Integrals: https://youtu.be/YLe4Wl1T-jo

Lecture 33: 11/27/23: Stirling I: Analysis arguments, Probability proof: https://youtu.be/65b0Jh1DIns

Lecture 34: 11/29/23: Stationary Phase II: https://youtu.be/NCalCkFs2a0

Lecture 35: 12/01/23: no class:

Lecture 36: 12/04/23: Uncertainty Principle: https://youtu.be/D8onKzVK9G4

Lecture 37: 12/06/23: Eigenvalues: https://youtu.be/47xCLUs12lk

See for a longer introduction (or happy to meet and chat):
- Lecture 31: 12/03/21: Eigenvalues and Random Matrix Theory: Part I: https://youtu.be/On9hT2ZFpdw (slides)
- Lecture 32: 12/06/21: Random Matrix Theory to L-Functions: Part II: https://youtu.be/FoKKIMs9wV8 (slides)

Lecture 38: 12/08/23: Several Complex Variables: https://youtu.be/tvKfVNy72SY

CLASS VIDEOS: 2021 (for captioning you might try http://ncamftp.wgbh.org/cadet/ )

Lecture 01: 9/10/21: Introduction, Definition of Derivative: https://youtu.be/8mrJvqbCqB8 first day slides and notes from class

Lecture 02: 9/13/21: Cauchy-Riemann Equations, Green's Theorem: https://youtu.be/IRcxF34gSPU (slides)

Lecture 03: 9/15/21: Real Analysis Review (limsup/liminf, strange functions): https://youtu.be/DLyzZhJN58w (slides); watched at home: Differentiating Term By Term, Analytic Functions, Path Integrals: https://youtu.be/e60Dh8cAIhQ (2017)

Lecture 04: 9/17/21: Primitives, Goursat's Theorem: https://youtu.be/6cJjM8PoTzU (slides)

Lecture 05: 9/20/21: Primitives, Cauchy's Theorem, Integration Exercise: https://youtu.be/xw_7-gQxkRg (slides)

Lecture 06: 9/22/21: Cauchy's Formula, Integration Example, Inverse Functions: https://youtu.be/m2O3nen0u4I (slides)

Review of contour integrals a la multivariable calculus: https://www.youtube.com/watch?v=hle5zvG4ZrI (Lecture 06: 9/20/17)
Example of a contour integral: https://youtu.be/NgHIiZUYI6g?t=2655 (44:15) (Lecture 06: 9/20/17)

Lecture 07: 9/24/21: Holomorphic is Analytic, Liouville's Theorem, Fundamental Theorem of Algebra, Cauchy Integral: https://youtu.be/girhkgCQpGw (slides)

Lecture 08: 9/27/21: Cauchy Formula, Accumulation Theorem, Cauchy-like Integrals: https://youtu.be/wSqTEQ4usno (slides)

Lecture 09: 9/29/21: Integration Examples: (see for other examples Lecture 09: 9/27/17: Integration Example, Types of Singularities: https://youtu.be/Jz76hM32C80) (slides)

Lecture 10: 10/01/21: Mountain Day: No Class: Riemann's Removable Singularity Theorem, Casorati-Weierstrass, Examples, Infinities: https://youtu.be/dPvAMy64p1k

Lecture 10: 10/04/21:Singularities, Probability Integrals (Moment Generating / Characteristic functions), Trig Integrals: https://youtu.be/9zSVjGpwbBc (slides) (see also the lecture above)

Lecture 11: 10/06/21: Meromorphic Functions, Log, Argument Principle, Rouche, Fund Thm Alg, Trig Integral: https://youtu.be/INRdLUT6ckQ (slides)

Lecture 12: 10/08/21: Rouche, Open Mapping and Maximum Modulus: 10/4/17 lecture: https://youtu.be/-vuwc6irob4 (lighting issues; see also lecture from 2015: https://youtu.be/gQwK2CIEa1M)

Lecture --: 10/11/21: No class: Reading period

Lecture 13: 10/13/21: Complex Logarithms, Earlier Material, Functions with Prescribed Zeros/Values: https://youtu.be/CR-sRChcID4 (slides)

Lecture --: 10/15/21: No class: Take home exam

Lecture 14: 10/18/21: Sick: Lecture 14: 10/11/17: Writing functions as a product over zeros: https://youtu.be/AoiyKD17aKM (Video from 2015: Products with Zeros of Functions: https://youtu.be/QYseyAB_Sx0)

Lecture 15: 10/20/21: Sick: Lecture 15: 10/16/17: Weierstrass Products, Conformal Maps: https://youtu.be/clP3ZO5HpV4 (Video from 2015: Weierstrass Products, Automorphisms, Unit Disk: https://youtu.be/Az78Kof-1OA)

Lecture 16: 10/22/21: Introduction to Conformal Maps: https://youtu.be/kzPm-0X_HW8 (slides)

Lecture 17: 10/25/21: Schwarz Lemma, Automorphisms of the Disk: https://youtu.be/q4eZRrVPGA0 (slides)

Lecture 18: 10/27/21: Montel's Theorem and Results from Analysis: https://youtu.be/YAWP7TXRGJA (fix on error here: https://youtu.be/A2E5fVKyKXw) (slides)

Lecture 19: 10/29/21: Analysis and the Fundamental Theorem of Calculus: https://youtu.be/SxiE0e4pg-M (slides) (also watch Lecture 20: 10/30/17: Riemann Mapping Theorem (Overview): https://youtu.be/FhphhYFxIP0 (slides)

Lecture 20: 11/01/21: Riemann Mapping Theorem (Proof), Differences between Real and Complex: https://youtu.be/yivEV2yhxgA (slides) (Lecture 19: 10/27/17: Riemann Mapping Theorem (Proof) https://youtu.be/x0Yy1Ivn1c4 (2015 Lecture))

Lecture 21: 11/03/21: Finishing Proof of the Riemann Mapping Theorem, Introduction to the Riemann Zeta Function, Partial Summation: https://youtu.be/-TpU7PdIEf0 (slides)

Lecture --: 11/05/21: No class

Lecture 22: 11/08/21: Approximating Solutions, Perturbing Equations: Sums of powers, Stirling's formula: https://youtu.be/gsW8VnoZSjk (slides)

Lecture 23: 11/10/21: Continuation of Zeta(s), Theta Functions: https://youtu.be/2pNLlEy40Ug (slides)

Lecture 24: 11/12/21: Gregory-Leibniz Formula, Dirichlet L-functions, proof of RH (not!), Duality: https://youtu.be/K8RhtDyts7s (slides)

Lecture 25: 11/15/21: Introduction to Fourier Analysis, Approximations to the Identity: https://youtu.be/YiFtCBbYe_I (slides)

Lecture 26: 11/17/21: Fejer's Theorem: https://youtu.be/FLJFBKx_Hmg (slides)

Lecture 27: 11/19/21: Convolutions, Generating Functions, Introduction to the CLT: https://youtu.be/Z7V8fxFHUQc (slides)

Lecture 28: 11/22/21: Fourier Transforms and Differential Equations, Two Fun Problems: https://youtu.be/cXpqwRQIjfk (slides)

Lecture 29: 11/29/21: Laplace's Method, Stirling's Formula: https://youtu.be/1Ll8vw1M7Fs (slides)

Lecture 30: 12/01/21: Laplace's Method Part II, Discrete to Integer: https://youtu.be/_mjl93gXaY8 (slides)

Lecture 31: 12/03/21: Eigenvalues and Random Matrix Theory: Part I: https://youtu.be/On9hT2ZFpdw (slides)

Lecture 32: 12/06/21: Random Matrix Theory to L-Functions: Part II: https://youtu.be/FoKKIMs9wV8 (slides)

Lecture 33: 12/08/21: Dimension, Fractals, Divide and Conquer, Newton's Method: https://youtu.be/c1QOgbi21_c (slides)

Lecture 34: 12/10/21: Uncertainty Principle: https://youtu.be/iUkFrowVRng (slides)

♦ CLASS VIDEOS: 2017 (for captioning you might try http://ncamftp.wgbh.org/cadet/ )

Lecture 01: 9/08/17: Introduction, Difference b/w Real and Complex, Trigonometry: https://youtu.be/acSy7rJQTGY; first day slides and handout

Lecture 02: 9/11/17: Caucy-Riemann Equations, Green's Theorem: https://youtu.be/aJBDcKw7pfE

Lecture 03: 9/13/17: Differentiating Term By Term, Analytic Functions, Path Integrals: https://youtu.be/e60Dh8cAIhQ

/Lecture 04: 9/15/17: Primitives, Goursat's Theorem, Goldbach: https://youtu.be/xb9FDV1ldrE

Lecture 05: 9/18/17: Primitive Theorem, Cauchy's Formula, Example: https://youtu.be/RkZHw4fKHfE

Lecture 06: 9/20/17: Cauchy's Formula, Integration Example: https://youtu.be/NgHIiZUYI6g (bonus beginning on path integration)

Lecture 07: 9/22/17: Holomorphic is analytic, Cauchy's Inequalities, Liouville's Theorem, Fundamental Theorem of Algebra: https://youtu.be/hle5zvG4ZrI

Lecture 08: 9/24/17: Cauchy Residue Theorem, Points of Accumulation, Integrating 1/(1+x^3): https://youtu.be/6CdYqD_1Zwg

Lecture 09: 9/27/17: Integration Example, Types of Singularities: https://youtu.be/Jz76hM32C80

Lecture 10: 9/29/17: Riemann's Removable Singularity Theorem, Casorati-Weierstrass, Examples, Infinities: https://youtu.be/dPvAMy64p1k

Lecture 11: 10/02/17: Complex Logarithms, Argument Principle, Rouche's Theorem: https://youtu.be/iyt4EhHvy-s

Lecture 12: 10/04/17: Rouche, Open Mapping and Maximum Modulus: https://youtu.be/-vuwc6irob4 (lighting issues; see also lecture from 2015: https://youtu.be/gQwK2CIEa1M)

Lecture 13: 10/06/17: 2015 Lecture: Complex Logarithm: https://youtu.be/bnZOX0KXSmg (2017 Review Problem Lecture: https://youtu.be/zxziYCD5Jzc)

Lecture 14: 10/11/17: Writing functions as a product over zeros: https://youtu.be/AoiyKD17aKM (Video from 2015: Products with Zeros of Functions: https://youtu.be/QYseyAB_Sx0)

Lecture 15: 10/16/17: Weierstrass Products, Conformal Maps: https://youtu.be/clP3ZO5HpV4 (Video from 2015: Weierstrass Products, Automorphisms, Unit Disk: https://youtu.be/Az78Kof-1OA)

Lecture 16: 10/18/17: Introduction to Conformal Maps: https://youtu.be/5klb8gxnQTc (2015 Video: Mappings, Inverse Map Holomorphic, Schwartz Lemma: https://youtu.be/zX2XKDJLkf8)

Lecture 17: 10/23/17: Schwarz Lemma, Automorphisms of the Disk: https://youtu.be/eYtNzkwFf6c

Lecture 18: 10/25/17: Montel's Theorem and Results from Analysis: https://youtu.be/JDtuMS38hhQ (2015 lecture)

Lecture 19: 10/27/17: Riemann Mapping Theorem (Proof): https://youtu.be/x0Yy1Ivn1c4 (2015 Lecture)

Lecture 20: 10/30/17: Riemann Mapping Theorem (Overview): https://youtu.be/FhphhYFxIP0

Lecture 21: 11/01/17: Introduction to the Riemann Zeta Function, Partial Summation: https://youtu.be/7wuZQyd1nYc

Lecture 22: 11/03/17: Sketch of the Prime Number Theorem, Gamma Function and Stirling's Formula: https://youtu.be/I3YaoEw8z6s

Lecture 23: 11/06/17: Continuation of Zeta(s), Theta Functions, Gregory-Leibniz Formula, Intro to Fourier Series: https://youtu.be/XZdhwkrTMnA

Lecture 24: 11/08/17: Bessel's Inequality and Approximations to the Identity: https://youtu.be/G3JefXkxlEU

Lecture 25: 11/10/17: Dirichlet's Theorem and Poisson Summation: https://youtu.be/jtHKBW9ncYI

Lecture 26: 11/13/17: Basel Problem, Fourier Transforms of the Gaussian: https://youtu.be/UDKfNPnp560

Lecture 27: 11/15/17: Laplace's Method, Stirling's Formula: https://youtu.be/AycMlf4Mbyo (2015 lecture: https://youtu.be/GvKI5I_cfDQ)

Lecture 28: 11/17/17: Convolutions, Generating Functions, Introduction to the CLT: https://youtu.be/4u4aiHm3sPI

Lecture 29: 11/20/17: Generating Functions, Proof of the Central Limit Theorem, Integral Challenge: https://youtu.be/soTUjKTVQfo

Lecture 30: 11/25/17: Uniqueness of Inversions, Laplace Transform: https://youtu.be/C-6WGid4vBA

Lecture 31: 11/27/17: Dimensions and Fractals and Chaos: https://youtu.be/YnL-TYtRX-s (slides here: pdf)

Lecture 32: 11/29/17: Uncertainty Principle (from 2013): http://youtu.be/y_AXASHUHE8

Lecture 33: 12/04/17: Jordan Plane Curve Theorem: https://en.wikipedia.org/wiki/Jordan_curve_theorem

Lecture 34: 12/06 and 08/17: Choose two out of three (advantage of teaching and recording multiple times is that we have options):

Lecture Option I: Laplace Inversion, Trig Integrals: https://youtu.be/YLe4Wl1T-jo continued with Branch cut method: https://youtu.be/WiqYZD0vIPw (this counts as two videos)

Lecture Option II: Introduction to Several Complex Variables: https://youtu.be/6wy_b96W4g4

Lecture Option III: Introduction to Random Matrix Theory: https://youtu.be/qsalf_YH1qs (slides here) (talk given in probability course)

♦ CLASS VIDEOS: 2015

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:

♦ Interesting videos

TED Lectures:

Did You Know (2009 version)

Yes, Prime Minister: Manipulation Polls (YouTube video)

♦ 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!