Math 180a course syllabus and references

Math 180a is a one quarter upper division course in probability for students who have a good background in calculus. The topics covered will be taken from the first eight chapters of the text: A First Course in Probability, 7^th Edition, by Sheldon Ross. Major topics will include the following: Basics of counting and axioms of probability, conditional probability and Bayes’ Formula, discrete random variables and expectation, continuous random variables and distribution functions, the Central Limit Theorem and Law of Large Numbers.

Although students will not be expected to write proofs in this course, a certain amount of “mathematical maturity” will be expected. There will be an emphasis on understanding theories and formulae and in knowing how to apply them in new situations. Almost all the exercises given will be “story problems.” Each chapter in the text includes a section called “Self-Test Problems and Exercises,” for which complete answers are given in the back of the book. Numerical answers for some of the exercises in the section “Problems” are also given in the back.

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 5-7 hours per week outside of class for this course.) There will also be exams:

Midterm 1: Monday, October 20 in class

Midterm 2: Monday, November 17 in class

Final: Friday, December 12, 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.

Other references that may be useful are the following.

Online:

Downloadable probability book by Grinstead and Snell This book has more theory, but also includes many interesting examples.

Online introductory statistics course by Philip Stark Parts of chapters 7,8,9, 10, 11, 12, and 13 are relevant to Math 180a. This is a very useful self-study guide to statistics.

Online probability book for junior high by Yours Truly A childish approach to probability, but at least it’s free.

Books:

R. Durrett, “The Essentials of Probability.” This is a briefer introductory text.

W. Feller, “An Introduction to Probability Theory and its Applications. This is a great classic text, written more than 50 years ago.

P. Hoel, S. Port, and C. Stone, “Introduction to Probability Theory.” This is a briefer introductory text, written in 1970 for a one-quarter course at UCLA.

J. Pitman, “Probability. ” This is a big fat modern introductory textbook often used for this course. Its emphasis is more on applications to problems in statistics.