Math/Stat 431 Introduction to the Theory of Probability

Fall 2014 Lecture 2 MWF

Meetings: MWF, Lecture 2 8:50-9:40, Van Vleck B139
Instructor: Timo Seppäläinen
Office: 425 Van Vleck. Office Hours: Mondays and Wednesdays 11-12, other times by appointment.
Phone: 263-3624
E-mail: seppalai and then at math dot wisc dot edu (I may be able to answer questions by email.)

This is the course homepage that also serves as the syllabus for the course. Here you will find our weekly schedule and updates on scheduling matters. The Mathematics Department also has a general information page on this course.

Course description

Math 431 is an introduction to probability theory, the part of mathematics that studies random phenomena. We model simple random experiments mathematically and learn techniques for studying these models. Topics covered include methods of counting (combinatorics), axioms of probability, random variables, the most important discrete and continuous probability distributions, expectations, moment generating functions, conditional probability and conditional expectations, multivariate distributions, Markov's and Chebyshev's inequalities, laws of large numbers, and the central limit theorem.

Probability theory is ubiquitous in natural science, social science and engineering, so this course can be valuable in conjunction with many different majors. 431 is not a course in statistics. Statistics is a discipline mainly concerned with analyzing and representing data. Probability theory forms the mathematical foundation of statistics, but the two disciplines are separate.

From a broad intellectual perspective, probability is one of the core areas of mathematics with its own distinct style of reasoning. Among the other core areas are analysis, algebra, geometry/topology, logic and computation.

To go beyond 431 in probability you should take next 521 Analysis, and after that one or both of these: 632 Introduction to Stochastic Processes and 635 Introduction to Brownian Motion and Stochastic Calculus.


To be technically prepared for Math 431 one needs to be comfortable with the language of sets and calculus, including multivariable calculus, and be ready for abstract reasoning. Formally Math 234 (Calculus of several variables) is a prerequisite. Probability theory can seem very hard in the beginning, even after success in past math courses.


The course follows lecture notes authored by David Anderson, Timo Seppäläinen, and Benedek Valkó. These will be provided to the students at no cost.


We will use Learn@UW to post homework assignments, solutions to homework, and lecture notes. The lecture notes may evolve during the semester so if you print, do not print a large number of pages at one time.

Library reserves

Four books are on reserve in the library for you to see how other authors develop the material. You can also find old 431 exams in the Math Library Course Reserves. But note that these exams might not necessarily be a perfect fit for this year's course.


Course grades will be based on homework and quizzes, midterm exams, and a comprehensive final exam. No calculators, cell phones, or other gadgets will be permitted in exams and quizzes, only pencil and paper. Here are grade lines that can be guaranteed in advance. A percentage score in the indicated range guarantees at least the letter grade next to it.
[100,89) A, [89,87) AB, [87,76) B, [76,74) BC, [74,62) C, [62,50) D, [50,0] F.

Weekly schedule

Here is a tentative weekly schedule, to be adjusted as we go. Section numbers refer to the lecture notes.

Instructions for homework

The Math Club provides interesting lectures and other math-related events. Everybody is welcome.