Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 135A: Probability
Approved: 2006-05-01 (revised 2013-01-01, B. Morris)

ATTENTION:

This course has two approved syllabi, provided below, for separate primary textbooks.

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
See information below.

Prerequisites:

Completion of course MAT 125A.

Suggested Schedule:

Approved Version #1

Textbook: Probability and Stochastic Processes, 1st Edition by Frederick Solomon; Pearson Publishing; ISBN-13 #978-0137119615; $42.00-78.00 via Amazon Books.

Lecture(s) Sections Comments/Topics
1.5 Lectures 1.1–1.4 The Language and Axioms of Probability.
2.5 Lectures 2.1–2.4 Combinatorics.
3 Lectures 3.1–3.4 Conditional Probability and Independence.
3 Lectures 4.1-4.3, 4.5, 4.6, and 4.8 Discrete Random Variables
3 Lectures 5.1-5.5 and 5.7 Continuous Random Variables
4 Lectures 8.1-8.4 and 8.6 Joint Probability Distributions
5 Lectures 9.1-9.3 and 9.5 Variances, Covariances, etc.
4 Lectures 10.1-10.4 The Normal Distribution, CLT, and Law of Large Numbers

Additional NoteS

Optional sections are: 3.3, 4.4, 4.7, 5.8, 8.5, 9.4, and 10.6. The core sections should be doable without additional lectures. One or more optional sections may be covered, depending on the time schedule and instructor’s taste.

Approved Version #2

Textbook: Probability and Random Processes, 3rd Edition by Geoffrey R. Grimmett and David R. Stirzaker; Oxford University Press; ISBN-13 #978-0198572220; $34.00-67.00 via Amazon Books.

Lecture(s) Sections Comments/Topics
Chapter 1 1.1-1.5 Events and their probabilities.
Chapter 2 2.1-2.3 Random variables and their distributions.
Chapter 3 3.1-3.8 with a little of 3.9 Discrete random variables.
Chapter 4 4.1-4.8 Continuous random variables.
Chapter 5 5.7-5.10 Generating Functions and their applications.

Learning Goals:

This is an introductory course in probability. Probability is fundamental to such areas as statistics, finance and operations research. The problems require a type of thinking that is unique in mathematics. The main emphasis of the course is problem solving and "thinking probabilistically". Students will solve problems involving gambling, medicine and crime. They will do computations with random variables such as finding mean and variance.

Assessment:

The grade is decided by homework, quizzes, midterms and a final exam.