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 2023-06-01, J. Gravner and A. Soshnikov)
Suggested Textbook: (actual textbook varies by instructor; check your
instructor)
Lecture Notes for Introductory Probability by Janko Gravner, freely available at https://www.math.ucdavis.edu/~gravner/MAT135A/resources/lecturenotes.pdf
Prerequisites:
MAT 021C; (MAT 108 or MAT 067).
Suggested Schedule:
| Lecture(s) | Sections | Comments/Topics |
| 4 Lectures | 2 | Combinatorial probability |
| 3 Lectures | 3 | Axioms of probability and inclusion-exclusion formula |
| 4 Lectures | 4 | Conditional probability and independence |
| 3 Lectures | 5 | Discrete Random Variables |
| 3 Lectures | 6 | Continuous Random Variables |
| 3 Lectures | 7 | Joint distributions and independence |
| 3 Lectures | 8 |
Sums of random variables, Law of large numbers, and Central Limit Theorem |
Additional Notes:
Sample exams, homework problems, and some additional resources are
available at
https://www.math.ucdavis.edu/~gravner/MAT135A/resources
Learning Goals:
This is an introductory course in probability. Probability is
fundamental to such areas as statistics, data science, 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.