The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man’s mind. James Clerk Maxwell (1850).

Probability is a field of mathematics that studies random events. It began ignominiously when mathematically minded people turned their attention to gambling (“games of chance”). It has developed into a deep body of mathematics that serves as the primary engine of statistical inference and much of modern science.

This course serves well as an elective within the math major, particularly when paired with Mathematical Statistics (MATH 392) in the spring. It will also be useful for majors in the sciences who utilize probability and statistical reasoning in their work.

The course begins with first principles, builds notions of independence, conditioning, random variables, and explores the properties of the fundamental discrete and continuous distributions. There will be a strong problem-solving focus throughout, with intuition developed by composing analytical solutions alongside computational ones (in R). Towards the end of the course, we’ll look at the major theoretical results in limits then explore a series of special topics.

Contact

Andrew Bray

  • Office: Library 304
  • Office Hours: Tu: 1:45 - 3 PM, Th: 3 - 4:30 PM, and by appointment

Textbook

Probability with Applications and R (2014), by Robert P. Dobrow. The textbook is backordered from the publisher, but you can access it by:

  • Purchasing one of the copies in the bookstore.
  • Finding one online for purchase/rent.
  • Checking out the copy on reserve at the library.
  • Refering to the digital copy via the library website.

Class components

This course has three components: Problem Sets, Quizzes/Exams, and a Project. For details on the problem sets, please see the tab at the top of the page.

Exams

We’ll have three examinations and quizzes throughout the semester in order to challenge your understanding and provide us with a sense of where you’re at. Some will be more traditional pen and paper and others are to be done with the computer using R. These dates are tentative so stay tuned for updates.

Exam I
Wednesday, September 28, 2016

Exam II
Take home, distributed Monday, November 7, 2016

Final
Finals Week