Department of Mathematics, Spring 2006

Math 275: Living in a Random World

MWF 2:30-3:30, 205 Malott Hall

 
Instructor: Lea Popovic
email: popovic@math.cornell.edu 

Office Hours: TW 3:30-4:30 (or by appointment), 580 Malott Hall

Course Outline

The course will cover basic topics in probability and illustrating their use in applications in the physical, biological and social sciences. We will discuss how to do answer mathematical questions in many examples, such as:games,lotteries, option pricing, opinion polls, etc.

List of topics:
  • Basic notions, definition of probability, counting of events
  • Conditional probability, independence, Bayes formula
  • Discrete probability distributions, expected value, variance
  • Joint distributions, sums of independent random variables, covariance
  • Limit theorems, law of large numbers, central limit theorems
  • Hypothesis testing, confidence intervals
  • Markov chains, stationary distributions, limiting behavior

Prerequisites

Semester of calculus, such as Math 106..

Text

"Elementary Probability for Applications" by R.Durrett, available online at pi.math.cornell.edu/~durrett/ep4a/ep4a.html
(For more advanced material see: "The Essentials of Probability" R.Durrett, Duxbury, 1994.)

Grading

  • Homework 30% - approximately 7 homework sets, once every other week
  • Two mid-terms 20% each - in class exams, dates: Feb 24, Apr 10
  • Final 30% - May 15
There will be no make-up times for the mid-terms. If a serious reason prevents you from attending any of the mid-terms, you need to consult with me before the date of the exam. Homeworks are due approximately a week after they have been handed out (exact dates are on the Homeworks site). Hand in your homeworks in class. Late homeworks can not be accepted.

Homeworks      Lecture Schedule      Final Exam: May 15 7PM in 207 Malott Hall

Feb 24: Test 1 Solution      Apr 10: Test 2 Solution      May 15: Final Pratice questions     Final Practice Solutions