HANDOUTS: click here for class notes and lecture slides

• REVIEW MATERIAL: Over 50 worked out calculus problems (differentiation, integration, partial derivatives, multiple integrals)
• Review sheet (significantly more extensive one by Ville Satopaa)
• Write-up of solutions to HW problems
• paper summaries by the class
• takeaways for the course
• Free textbooks:
  • Free probability textbook (Grinstead and Snell)
  • Free real analysis textbook (from William Trench)
• Terry Tao:
  • blog post on unified way to view the mean, median and mode
  • blog post on a review of probability theory
  • blog post on Stirling's formula
• Convergence rates in the Central Limit Theorem: The Berry-Esseen Theorem
  • preprint by Korolev and Shevtsova
  • preprint by Tyurin
• Uniqueness / non-uniqueness of moments: Lin and Stoyanov (logarithmic skew-normal distributions are moment-indeterminate)
• Burgin: Negative probabilities
• Bridge: 8 ever, 9 never?     see also this webpage with the calculations
• Schwarzenegger veto:  veto text         sponsor's reply        article on probability
• Actuarial exams
  • Probability:      exam    solution
  • Financial math: exam    solution
• Clinton and Obama tied in Syracuse primary
• World record at an Atlantic City casino in craps (Ethier and Hoppe)
• Blackjack: Thorpe's original article    Thorpe's book     Baldwin et al's article on the optimal strategy in blackjack.
• Three hats, a strange probability and error correcting codes (slides from a talk by M. Bernstein)
• Markov chains and cryptography: Persi Diaconis, The Markov Chain Monte Carlo Revolution. (2008). Bull. Amer. Math. Soc. Nov. 2008
  • RSA reading: Notes on abstract algebra and group theory and RSA cryptography (from my book An Invitation to Modern Number Theory) as well as some history of RSA.
• Isaac Asimov: The Relativity of Wrong
• On Buffon machines and numbers: Flajolet, Pelletier and Soria.
• Probability and the Maxwell-Boltzman Distribution (Frank W. K. Firk)
• Differentiating identities handout.
• The power of expectation
• Video on how to interchange summation (the method generalizes to interchanging a derivative and a sum).