Department of Mathematics 203 Avery Hall University of Nebraska Lincoln Lincoln, NE 68588-0323 402-472-3731 (voice) 402-472-8466 (fax)

# Lessons

Note: In all notes, lessons, tests, quizzes and homework assignments, unless specifically noted otherwise

1. Because the lessons use MathML/xml/xhtml, and because Firefox is the only common browser with MathML enabled, use Firefox to view the following lessons.
2. Interest is assumed to be compounded continuously.
3. The mathematical function log(x) means the natural logarithm, that is, logarithms to the base e.

## Real Analysis Background

1. Asymptotic Limits and Series
Updated Monday, 03-Oct-2011 06:02:34 CDT

## Stirling's Formula

1. Wallis Formula
Updated [an error occurred while processing this directive]
2. Evaluation of the Gaussian Density Integral
Updated Saturday, 22-Oct-2011 05:49:19 CDT
3. Stirling's Formula Derived from Elementary Sequences and Series
Updated Tuesday, 20-Sep-2011 06:06:46 CDT
4. Stirling's Formula by Using Euler-Maclaurin Summation
Updated Monday, 10-Oct-2011 06:00:47 CDT
5. Stirling's Formula from Wallis' Formula and the Trapezoidal Approximation
Updated Monday, 10-Oct-2011 06:00:00 CDT
6. Stirling's Formula Derived from the Gamma Function
Updated Monday, 26-Nov-2012 05:56:59 CST
7. Stirling's Formula in Real and Complex Variables
Updated Monday, 23-May-2011 05:55:15 CDT
8. Stirling's Formula Derived from the Poisson Distribution
Updated [an error occurred while processing this directive]

## Bernoulli Trials

1. Binomial Distribution
Updated [an error occurred while processing this directive]
2. Weak Law of Large Numbers
Updated Wednesday, 25-May-2011 06:16:28 CDT
3. Large Deviations
Updated Saturday, 04-Jun-2011 09:38:07 CDT

## Normal Random Variables, Gaussian Distributions

1. The Sum of Independent Normal Random Variables is Normal
2. Updated [an error occurred while processing this directive]

## Brownian Motion

1. Introduction to Bernstein Polynomials and Brownian Motion
2. Bernstein Polynomials and the Weierstrass Approximation Theorem
3. Bernstein Motions and the convergence to Wiener measure

## Markov Process Variants

Eigenvalues, Eigenvectors, and Normal Forms of Matrices
Updated Friday, 28-May-2010 05:47:02 CDT

Fastest Mixing Markov Chain
Updated Friday, 16-Apr-2010 06:03:37 CDT

## Applications, especially with Markov Chains

Worst Case and Average Case Behavior of the Simplex Algorithm
Updated Thursday, 20-Jan-2011 21:01:31 CST

Smoothed Analysis for Linear Optimization Algorithm
Updated Thursday, 27-Jan-2011 20:52:43 CST

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## Online Tables for Probability and Cumulative Distributions

Here are some links to Online Distribution Tables:
1. Statsoft This site has several different distributions in a nice back-of-the-book-looking HTML format.
2. David Lane, Rice University, Hyperstat This links to a Java applet that will compute the percentages for the normal distribution when given the Z values

## Annotated Bibliography

A personal, eclectic and biased annotated bibliography of books and articles about probability, stochastic processes and mathematical finance.