Math 180b course syllabus and references

Main text: An Introduction to Stochastic Modeling, 3^rd Edition, by Howard M. Taylor and Samuel Karlin

Math 180b is the first quarter of a two quarter course in stochastic processes. A stochastic process is a family of random variables indexed by time, (either discrete or continuous). Topics this quarter will include random walks and more general Markov processes, including classification of states and long term behavior, and Poisson processes. These topics will be taken mainly from chapters III to V, inclusive, of the text. The emphasis of the course will be the application of stochastic processes to modeling phenomena in the physical and biological sciences, as well as in economics and engineering. The same text will be used for Math 180c this spring, beginning with Chapter VI.

Prerequisites: The formal prerequisites are Math 20a-d, Math 20f, and a calculus-based introductory probability course, such as Math 180a. In practical terms, students are expected to know calculus (one and several variable), and to have some experience with differential equations (first order) and linear algebra. While you will not be expected to write formal proofs in this course, you should be able to work through the examples, calculations, and theorems given in the text. Typically, students find this course considerably harder than Math 180a.

Course Organization: As in any math course, “No pain, no gain,” so there will be weekly problems sets (linked below) that will be collected. (According to self-reported past data, students typically spend 5.5-7.5 hours per week outside of class for this course.) There will also be exams:

Two midterms given in class (dates to be set)

Final: Friday, March 20, 8:00 am to 10:50 am

Grading is based on the following. Homework: 15%, Midterms (2): 40%, Final: 45%

Here is a link to the weekly problem sets currently due. They should be put in VP’s homework box (6^th floor, AP&M) by 3:00 pm of due date.

Other references that may be useful are the following.

P. Hoel, S. Port, and C. Stone, “Introduction to Probability Theory,.” Chapter 9 will be very useful for discussion of random walks.

S. Ross, “A first course in Probability.” Sections 9.1 and 9.2 provide a brief introduction to Poisson processes and Markov chains.

C. M. Grinstead and J. L.Snell, “Introduction to Probability, 2^nd Edition” (Click here for free download.) Chapter 11 is particularly useful for Markov processes.

Some other texts on stochastic processes:

G. Lawler, “Introduction to Stochastic Processes.” This is a shorter book, more mathematically sophisticated, but very useful.

S. Karlin and H. Taylor, “A First Course in Stochastic Processes.” This book is by the same authors as the required text, but follows a more theoretical and systematic approach. Considerably more mathematically sophisticated than our text.

S. Resnick, “Adventures in Stochastic Processes.” This book, which is aimed at graduate students, contains many interesting examples sparkling with the author’s serious attempt at humor.