V63.0235:Probability and Statistics
Term: | Spring 2011 |
Meeting times: | Tu Th 3:30pm–4:45pm - 101 WWH |
Recitation: |
F 2:00 - 3:15 pm - Classroom TBD |
Course Website: | Probability & Statistics - Spring 2011 (and Blackboard) |
Instructor: | Dr. Tom LaGatta |
Office: | 927 WWH |
Office hours: | Mondays at 11am and Wednesdays at 10am |
Phone: | 212-992-9920 |
Email: | lagatta@cims.nyu.edu |
Prerequisites
Students who wish to enroll in V63.0235 must meet the following prerequisites:
- V63.0122 Calculus II with a grade of C or better and/or the equivalent.
Goals and Topics
The primary goals of this course are to understand the laws of theoretical probability, and to apply them to real-world problems. The course will be full of hands-on examples, but we will not shy away from theory. In particular, this course is structured around the two major themes of the Law of Large Numbers and the Central Limit Theorem. The most important application of these ideas is statistics.
Course Details
Textbook and Materials
The Pleasures of Probability, Richard Isaac. Springer-Verlag, ISBN 0-387-94415
The Drunkard’s Walk, Leonard Mlodinow. Pantheon, ISBN 0-375-42404-0
Homework
Homework will be due every Friday by 2pm, and must be submitted in my mailbox in Warren Weaver Hall (not in class). Each week's assignment will be posted on the course website. Late homework will not be accepted for any reason; however, when I compute your final grade I will drop your lowest homework score. Homework is worth 20% of your final grade.
Programming Assignments: Probability should not be studied in a vacuum; your intuition must be honed by working with examples. The laws of probability are strongest in situations with large numbers of independent trials, such as flipping a coin 10,000 times or polling 1,500 people. Instead of doing this by hand, we will make use of the computing power available to us. As part of your homework grade, you will be expected to write a number of simple computer programs. We will be using the open-source software package, which is available to download for free from http://www.r-project.org
Reading and Writing: Probability touches on many areas of modern life, from science to finance. To place the subject matter in a broader context, there will be assigned readings each week, from the popular mathematics book The Drunkard's Walk as well as other articles. As part of your homework grade, you will be expected to write some short essays on what you read.
Exams
Quizzes
There will be a number of quizzes throughout the semester, each announced at least one week in advance. Quizzes will start at the beginning of class. These will be counted as part of your homework grade.
Midterms
There will be in-class midterm examinations on Thursday, March 3 and Thursday, April 14. I will give make-up exams only in exceptional circumstances (e.g., death in the family, outbreak of mono). Please notify me far in advance. Each midterm exam is worth 25% of your final grade.
Final
The cumulative final examination for this course is scheduled for Thursday, May 12 from 4:00pm to 5:50pm. The location will be announced in advance. The department will not be able to accommodate early finals for non-academic, non-emergency reasons. Plan your travel schedule accordingly. The final exam is worth 30% of your final grade.
Grading policy
Grades will be computed by a weighted average:
Homework 20%
Midterm 25%
Final 30%
Other 20%
Calendar
Week | Topic |
---|---|
1 | Introduction: The Law of Large Numbers and the Central
Limit Theorem |
2 | Chapter 1 - Cars, Goats, and Sample Spaces |
3 | Chapter 2 - How to Count: Birthdays and Lotteries |
4 | Chapter 3 - Conditional Probability: From Kings to Prisoners |
5 | Chapter 4 - The Formula of Thomas Bayes and Other Matters |
6 | Chapter 5 - The Idea of Independence, with Applications |
7 | Chapter 7 - Random Variables, Expectations, and More About
Games |
8 | Chapter 8 - Baseball Cards, The Law of Large Numbers, and Bad
News for Gamblers |
9 | Chapter 9 - From Traffic to Chocolate Chip Cookies with the
Poisson Distribution |
10 | Chapter 10 - The Desperate Case of the Gambler’s Ruin |
11 | Chapter 11 - Breaking Sticks, Tossing Needles, and More:
Probability on Continuous Sample Spaces |
12 | Chapter 12 - Normal Distributions, and Order from Diversity
via the Central Limit Theorem |
13 | Chapter 15 - Statistics: Applying Probability to Make
Decisions |