Mathematical Computation, Math 9171A, Fall 2025

This course will cover the interplay between mathematics and computation. This includes the use of computers to study problems in mathematics, as well as the use of mathematics to better understand computation.

It is aimed at MSc and PhD students in Mathematics, and will assume standard undergraduate mathematical background, such as familiarity with linear algebra, groups and rings. No programming background is required, but an interest in learning about computers is a necessity.

• Instructor: Dan Christensen
• Time/location: See OWL site.
• E-mail: jdc@uwo.ca
• Office: Middlesex 130
• Office Hours: After class.
• Prerequisites: Permission of instructor. See the statement above.

Outline:

Here are the topics that may be covered. Additional topics will be covered in presentations.

• Basic ideas of programming, using python 3.
• Calculus and plotting.
• Group theory.
• Linear algebra and homology computations.
• Various rings and fields, and floating point arithmetic.
• Galois theory (to be decided).
• Computability, Turing machines, lambda calculus.
• Complexity theory, P vs NP.
• The Rocq proof assistant.
• An introduction to version control with git.
• Software that will be used: Sage, python, Rocq, git and more.
• Software development topics: efficiency, data structures, numerical stability, common pitfalls, version control.

Here is the official course outline.

Text: There is no textbook for the course. During the second part, I will base some material on: Michael Sipser, Introduction to the Theory of Computation, 3rd ed. But this book is not required.

Homework: Problem sets will be due roughly every 2 weeks, and will often involve software. Doing problems and talking about the material are both essential for learning the material in this course, so you are encouraged to discuss the problems with classmates and with me. But you must write up the solutions on your own and must not look at other students' written solutions nor should you attempt to find solutions to problems online or in textbooks. You should not use an AI assistant in any way for this course. Your solutions should be clear and carefully written and you should give credit to those who helped you and to any references you used. Homework will be graded based on both correctness and clarity. Late problem sets will not be accepted unless arranged in advance for a good reason.

Presentations: In the second half of the semester, each student will give a 50 minute presentation on a topic related to the course. Here is a list of potential topics.

Lecture 1: Here is some information about snakify and other python resources.

Evaluation: Evaluation will be based upon homework (60%) and presentations (40%).

Technical requirements: Completion of this course will require you to have a reliable internet connection and a device that can be used to complete the assessments described above.