# Math 20. Discrete Probability

Summer 2006

• Instructor:         Sergi Elizalde

• Lectures:           MWF 10:00-11:05 in Bradley 105

• X-period:           Th 12:00 - 12:50

• Office Hours:    MW 11:05-12:00 and by appointment

• Email:

• Phone:               646-8191

Announcements

Here is this week's homework assignment.

The take-home final has been scheduled to be given out on Wednesday, Aug 16, and due no later than Sunday, Aug 20, at 9 am.

Midterm 2 has been scheduled for Friday, Aug 4, in class. No books or notes allowed.

Midterm 1 has been scheduled for Friday, July 14, in class.

Textbook

Introduction to Probability (2nd revised edition) by Charles M. Grinstead and J. Laurie Snell

This book is available at Wheelock Books for \$50, and also may be downloaded from http://www.dartmouth.edu/~chance/teaching_aids/book_articles/probability_book/pdf.html

Tentative syllabus

This syllabus is subject to change, but it should give you an idea of the topics we will cover.

 Sections in the textbook Brief Description Week 1 1.2, 3.1 Basic probability. Combinatorics: permutations. Week 2 3.2, 4.1 Combinations. Conditional probability. Week 3 6.1, 6.2 Expected value. Variance. Week 4 5.1 Midterm 1. Important distributions. Week 5 8.1 Law of large numbers. Week 6 9.1 Central Limit Theorem: Bernoulli trials Week 7 9.2 Central Limit Theorem: Independent trials. Midterm 2. Week 8 11.1, 11.2 Introduction to Markov chains. Absorbing Markov chains. Week 9 11.3 Regular Markov chains, ergodic Markov chains

The course grade will be based on the homework (10%), two midterms (30% each), and a take-home final exam (30%).

Homework

There will be homework due roughly every week. It will consist typically of a reading assignment (of the part of the book covered in class) and some problems. Collaboration in the homework is permitted, but you are not allowed to copy someone else's work. The solutions must be written individually. You have to mention on your problem set the names of the students that you worked with.

Exams

On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams.

Students with disabilities: Students with learning, physical, or psychiatric disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see me before the end of the second week of the term. All discussions will remain confidential, although the Student Disability Services office may be consulted to discuss appropriate implementation of any accommodation requested.