# 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:**

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

**Prerequisites:**

**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:**

**Assessment:**