Probability Theory (Calculus-Based)

Often referred to as the "higher Probability & Statistics course", our Probability Theory course is actually an introduction to the study of statistics and probability, but based upon the usage of Calculus to study both discrete and continuous aspects of the subject. Accordingly, there is no prerequisite of a previous study of statistics, but rather a prerequisite of having completed (or being concurrently enrolled in) Multivariable Calculus.


The curriculum for the course, Prob/Stat&Mathematica by Carpenter/Davis/Raschke/Uhl, is a thorough and advanced investigation of the subject matter, fascinating and challenging at the same time. The usage of the powerful computer algebra and graphing system Mathematicaâ„¢ allows for a unique exploration of distributions - both discrete and continuous - and their application to the cornerstone of the subject - the data set from a real-world situation.

Probability Theory differs from the "lower" Statistics course significantly in both approach and difficulty level. Compare the prerequisites:

Course: Statistics Probability Theory
Prerequisite: Algebra II from high school Multivariable Calculus
Intended for Majors: Humanities, Social Studies, Biological Sciences Math, Engineering, Physics, Economics, etc.

Examples of the Curriculum

Below are some PDF "print outs" of a few of the Mathematicaâ„¢ notebooks from Prob/Stat&Mathematica by Carpenter/Davis/Raschke/Uhl. Included as well is an example homework notebook completed by a student in the course, demonstrating how the homework notebooks become the "common blackboards" that the students and instructor both write on in their "conversation" about the notebook.

Course Catalog Listing

MAT 4180: Probability Theory [4 credit hours]

Course Description: An introduction to Calculus-based Probability theory and statistics. Topics include distributions, Monte-Carlo methods, probabilities, Markov's Inequality, Chebyshev Theorem; discrete and continuous random variables, Central Limit Theorem.

Prerequisite: Multivariable Calculus
Detailed Course Syllabus in PDF