Kirjahaku

These Lecture Slide Notes have been used for a two-quarter graduate level sequence in probability covering discrete and continuous probability in two separate volumes. Although reasonably self-contained, they do not constitute a formal exposition on the subject; rather the intent is to provide a concise and accessible format for reference and self-study. In this regard, each slide stands alone to encapsulate a complete concept, algorithm, or theorem, using a combination of equations, graphs, diagrams, and comparison tables. The explanatory notes are placed directly below each slide in order to reinforce key concepts and give additional insights. A Table of Contents serves to organize the slides by topic and gives a complete list of slide titles and their page numbers. An index is also provided in order to link related aspects of topics and also to cross-reference key concepts, specific applications, and the abundant visual aids.This book constitutes the first volume on discrete probability; a second volume will cover continuous probability. Part 1 covers counting with and without replacement, axiomatic probability models, computation techniques, conditional, joint, marginal, and Bayesian update probabilities. The concept of a random variable (RV) is fully characterized by a discrete probability mass function (PMF) and a quasi-continuous cumulative distribution function (CDF). A numerical characterization of a RV is given by the mean, variance, and expectation value. Pairs of RVs give way to new concepts such as independence, covariance, and the effects of linear and bi-linear transformations. Common discrete probability mass functions (PMFs) are discussed in terms of related pairs, tree diagrams, and algebraic representations.

These Lecture Slide Notes have been used over the past several years for a two-quarter graduate level sequence in numerical analysis. Part 1 covers introductory material on the Nature of Numerical Analysis, Root Finding Techniques, Polynomial Interpolation, Derivatives, and Integrals. Part 2 covers Ordinary Differential Equations and Numerical solutions to Linear Systems of Equations. Each slide stands alone to encapsulate a complete concept, algorithm, or theorem using a combination of equations, graphs, diagrams, illustrative tableaus, and comparison tables. The explanatory notes are placed directly below each slide in order to reinforce and give additional insight into the particular numerical technique or concept illustrated in the slide. Students have found this "Lecture Slide Note" format to be extremely useful in reviewing the concepts in preparation for an exam. This format is convenient for self-study; it covers the subject matter in a concise and easily accessible form using many visualizations. The Table of Contents serves to organize the slides in terms of the main numerical analysis topics covered and gives a complete list of slide Titles and their page numbers. A selection of Illustrative MatLab scripts is given in Appendix A. Finally, references to a number of standard text books are given, but there has been no attempt to make an exhaustive bibliography.