Math 60850 - Probability - University of Notre Dame.
Rick's Ramblings Blue Ridge Parkway. I am a Professor in the Mathematics Department at Duke University. My favorite research topics are stochastic spatial models that arise from questions in ecology, and use of probability problems that arise from genetics.
R. Durrett Probability: Theory and Examples (4th edition) is the required text, and the single most relevant text for the whole year's course. The style is deliberately concise. Quite a few of the homework problems are from there, P. Billingsley Probability and Measure (3rd Edition). Chapters 1-30 contain a more careful and detailed treatment.
Probability and Measure by Billingsley, A Course in Probability Theory by Chung, A First Look at Rigorous Probability Theory by Rosenthal for the main subject material of the course. Lecture notes: These notes were written by John Pike for last year's version of this class.
Homework is the most important part of a graduate mathematics course, and I encourage you to take it very seriously. Homework solutions will be posted on Friday after the homework is turned in. Grading Policy: The final grade is weighted in the following way: homework (40%), midterm (30%), final (30%). Te grade for the semester will be curved.
Course description: This is the first semester of a year-long introduction to probability theory. This semester will focus on basic definitions and results such as the strong law of large numbers, central limit theorem and weak convergence, and discrete time martingales.
About the course. Probability theory in the discrete setting (finite or countable outcome spaces) does not require much technical machinery --- once a probability is assigned to each possible outcome, the probability of landing inside some arbitrary subset of outcomes can be unambiguously declared to be the sum of the probabilities of the outcomes in that subset, and everything goes through.
Probability theory material needed throughout this course includes joint probability laws, probability mass functions and densities, conditional expectations, moment generating functions, and an understanding of the various kinds of probabilistic convergence, including the Law of Large Numbers.
This is the web page for the Math 235 (a.k.a. Stat 235) yearly graduate course at the UC Davis math department. The course comprises three quarter-long classes: 235A (fall), 235B (winter) and 235C (spring). Below you will find some useful general information about the course.
Note on Homework: This is a demanding course. The homework exercises are difficult, and the problem sets are long. The only way to learn this material is to solve problems, and for most students this will take a substantial amount of time outside class— six to ten hours per week is common.
Required Text: Probability: Theory and Examples, by Rick Durrett. We will use the fourth edition, but earlier editions should be fine. Just make sure you are completing the correct homework assignments.
Assignments Download Course Materials; The problem numbers reference specific problems in Durrett, Rick. Probability: Theory and Examples. 4th ed. Cambridge University Press, 2010. ISBN: 9780521765398. (Preview with Google Books) Each assignment encourages you to write a few sentences of notes about your readings. (Hand them in, but they won't be graded. This is just to give you an excuse to.
This lively introduction to measure-theoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference.
R. Durrett, Probability: Theory and Examples, 4th edition, 2010. P. Billingsley, Probability and Measure, 3rd edition, 1995. D. Williams, Probability with Martingales, 1990. Grading: The homework and midterm will each count for 20% of the final grade, and the final exam will count for the remaining 60%.
