Audio / Video of Classes

Math 341: Probability: Fall 2013

• Lecture 10: Monday, September 30: Basics of pdfs and random variables
  • YouTube link: http://youtu.be/Y4tqpC1pFo8
• Lecture 11: Wednesday, October 2: Taylor series and Expected Values
  • YouTube link: http://youtu.be/u_gFF8uD0PQ
• Lecture 13: Monday, October 7: Joint Densities, Expected number of heads (Friday's class was a guest speaker from Goldman Sachs)
  • YouTube link: http://youtu.be/YGa_ZL-uop4
• Lecture 14: Wednesday, October 9: Linearity of Expectation, Differentiating Identities.
  • YouTube lnk: http://youtu.be/4ivTf2cBAA4
• Lecture 15: Friday, October 11: Envelope Problem, Expected Value Products, Variances, Marriage / Secretary.
  • YouTube link: http://www.youtube.com/watch?v=Nqmu44s0_J8&feature=youtu.be
• Lecture 16: Wednesday, October 16: Convolutions, from Fibonaccis to Roulette.
  • YouTube link: http://www.youtube.com/watch?v=yqa2gohgUBY&feature=youtu.be
  • Here is the short video I made with OIT on this problem.
• Lecture 17: Monday, October 21: CDF Method, Monte Carlo Integration, Change of Variable Formula and Dimensional Analysis Proof of Pythagoras
  • YouTube link: http://youtu.be/ESzbCLnwQlg
• Lecture 18: Wednesday October 23: Standard Random Variables (Exponential, Poisson): Calculating Moments, Seeing Algebra
  • YouTube link: http://youtu.be/QJV3k7-jIcc
• Lecture 19: Friday October 25: Gaussian Density: Normalization factor, sums, moments.    part I    part II
  • YouTube link: part  I: http://youtu.be/LJPlcFF9Cjo
  • YouTube link: part II: http://youtu.be/-4xwhxrfFV8
• Lecture 20: Monday October 28: The Gamma Function, revisiting sums of normal random variables
  • YouTube link: http://youtu.be/Sjx-18FaNP4
• Lecture 21: Wednesday October 30: Chi-square random variables
  • YouTube link: http://youtu.be/JRCL9cjn9n0
• Lecture 22: Friday November 1: Markov and Chebyshev's inequalities
  • YouTube link:  http://youtu.be/VmB21uQTW1E
• Lecture 23: Monday, November 4: Weak law of large numbers, elementary approaches to Stirling's formula
  • YouTube Link: http://youtu.be/-DjoagA4lFg
• Lecture 24: Wednesday, November 6: Integral test and Stirling's formula, CLT for Poisson and Stirling's formula
  • YouTube Link: http://youtu.be/PlcV15Mu8Iw
• Lecture 25: Friday, November 8: Stirling's formula and Binomial to CLT
  • YouTube Link: http://youtu.be/VadIQZDyYL8
• Lecture 26: Monday, November 11: German Tank Problem, Generating Functions: part I    part II
  • YouTube Link:    part 1: http://youtu.be/CcVRiUToMlI      part 2: http://www.youtube.com/watch?v=-7kJu9Hy13o
• Lecture 27: Wednesday, November 13: Generating Functions, Fibonacci Numbers, MGF: part I    part II
  • YouTube Link: part 1: http://youtu.be/uUnOK8Z8rao         part 2: http://youtu.be/Z7YPe2Nmzxs
• Lecture 28: Friday, November 15: Moment Generating Functions (Theory, Examples); Standardization
  • YouTube Link: http://youtu.be/FcXxBk2nmoU
• Lecture 29: Monday, November 18: Complex Results for CLT, CLT for Sums of Poisson RVs
  • YouTube link: http://youtu.be/3IP7s1SLtwo
• Lecture 30: Monday, November 20: Proof of the CLT, the Bug Problem
  • YouTube link: http://youtu.be/P40DrGvHWEQ
• Lecture 31: Monday, November 22: Random Walk Problem, Method of Least Squares
  • YouTube link: http://youtu.be/ZE1EPsDeFO4
• Lecture 32: Monday, November : Sabeetrics Lecture: Pythagorean Won-Loss Formula
  • YouTube link: http://youtu.be/35kBJZQ3h18
• Lecture 33: Monday, December 2: Benford's law
  • YouTube link: http://youtu.be/rCsavxidCZ4
• Lecture 34: Wednesday, December 4: Zeckendorf Decompositions
  • YouTube link: http://youtu.be/65NU-JA_WYY
• Lecture 35: Friday, December 6: MSTD set
  • YouTube link: http://youtu.be/af-93zuW8kw

Math 372: Complex Analysis: Fall 2013

• Green's theorem in a day (click link for YouTube video, 50 minutes)
• Lecture 2: Monday, September 9, 2013 (missing first few minutes: audio).
• Lecture 3: Wednesday, September 11, 2013. (audio)
• Lecture 4: Didn't record (malfunction).
• Lecture 5: Monday, September 16, 2013. (audio)
• Lecture 6: Friday, September 20, 2013 (missing first few minutes: audio).
• Lecture 7: Monday, September 23, 2013: Didn't record (malfunction).
• Lecture 8: Wednesday, September 25: Residue Theorem (with video)
  •     YouTube link: http://youtu.be/pbwJILJiWKI
• Lecture 9: Friday, September 27: Accumulation Theorem, Integrals of (sin x / x)^m for m in {1, 2}.
  •     YouTube link: http://youtu.be/rcypKcC_huw
• Lecture 10: Monday, September 30: Singularities (Riemann's Removable Theorem, Casorati-Weirestrass and denseness near essential singularity)
  •     YouTube link: http://youtu.be/FEAPeT0-3EY
• Lecture 11: Wednesday, October 2: Compactification of C, functions on extended complex plane, argument principle and stating consequences
  •     YouTube link: http://youtu.be/yg_F3TfDT6o
• Lecture 12: Friday, October 4: Proofs of Rouche's Theorem, the Open Mapping Theorem and the Maximum Modulus Principle.
  •     YouTube link: http://www.youtube.com/watch?v=pzgxbyXs3Js
• Lecture 13: Monday, October 7: Simply Connected Regions, Homotopic Curves, the Complex Logarithm.
  • YouTube link: http://www.youtube.com/watch?v=Fizv--FMmcY
• Lecture 14: Wednesday, October 9: What does knowing the zeros tell you of a function? Part I.
  • YouTube link: http://www.youtube.com/watch?v=GiHtRAJawlw&feature=youtu.be
• Lecture 15: Friday, October 11: Products and Functions with Prescribed Zeros.
  • YouTube link: http://youtu.be/v1TMFC3JHQk
• Lecture 16: Wednesday, October 16: Weierstrass products, formulas for \(\pi\).
  • YouTube link: http://youtu.be/7JPAlvyBA3M
• Lecture 17: Monday, October 21: Conformal Maps, Automorphism Groups, \({\rm SL}(2,\mathbb{Z})\)
  • YouTube link: http://youtu.be/1XXm0korIcg
• Lecture 18: Wednesday October 23: Conformal maps, figuring out region of definition
  • YouTube link: http://youtu.be/oezw4haqlAU
• Lecture 19: Friday October 25: Schwartz Lemma, Real vs Complex Analogues
  • YouTube link: http://youtu.be/ajvW8cK1p3o
• Lecture 20: Monday October 28: The Proof of the Riemann Mapping Theorem (Steps I and III)
  • YouTube link: https://www.youtube.com/watch?v=Leethyz6-hE
• Lecture 21: Wednesday October 30: Definitions for Montel's Theorem, Examples, Statement of Montel 1.
  • YouTube link: http://youtu.be/oBaDjBdAgGE
• Lecture 22: Friday November 1: Proof of Montel's Theorem
  • YouTube link: http://youtu.be/y39SMGvnceE
• Lecture 23: Monday, November 4: Finishing proof of Riemann mapping, introduction to Riemann zeta function: part 1    part 2
  • YouTube Link: part 1: http://youtu.be/sAaOvU1oKeo        part 2: http://youtu.be/WWS7usazcZ4
• Lecture 24: Wednesday, November 6: Analytic Continuation of Geometric Series, Zeta(s), and the Prime Number Theorem
  • YouTube Link: http://youtu.be/L4y-Z7VgR8E
• Lecture 25: Friday, November 8: Introduction to Fourier Analysis: Basis vectors, inner products, convergence issues, approximations to the identity
  • YouTube Link: http://youtu.be/VafWOrtv7bA
• Lecture 26: Monday, November 11: Midway, Fejer's Theorem
  •  YouTube Link: http://youtu.be/-FA4_DjYRqo

• Lecture 27: Wednesday, November 13: Bessel's inequality and Plancherel's Theorem

  • YouTube Link: http://youtu.be/TFYqB44x-Yw
• Lecture 28: Friday, November 15: Using Fourier Analysis to Evaluate Sums, Poisson Summation:   part 1    part 2
  • YouTube Link: part 1: http://youtu.be/_Mgfhac-X3o         part 2: http://youtu.be/7GN1mRnVUEE
• Lecture 29: Monday, November 18:  Uncertainty Principle in a day!
  • YouTube link: http://youtu.be/y_AXASHUHE8
• Lecture 30: Monday, November 20: Fourier transform of the Gaussian, Gamma Function, Analytic continuation of zeta(s)
  • YouTube link: http://youtu.be/VgaUoo_ceRc
• Lecture 31: Monday, November 22: Sketch of the Proof of the PNT
  • YouTube link: http://youtu.be/wIDO0DSdkwg
• Lecture 32: Monday, November 25: Weierstrass' Continuous but Nowhere Differentiable Function, Laplace's Method / Method of Stationary Phase
  • YouTube link: http://youtu.be/wlRMu_gS_Ig
• Lecture 33: Monday, December 2 : Several Complex Variables, Branch Cuts
  • YouTube link: http://youtu.be/qZVGVYxpOqc
• Lecture 34: Wednesday, December 4: Chaos and Fractals
  • YouTube link: