math 5251 - error correcting codes, finite fields, algebraic curves - spring 2025

this is a course about the mathematics of transmitting information. it is not a course about encoding/decoding messages for secrecy (cryptology).

we will primarily use Paul Garrett’s book on the subject. here is an unofficial errata for the book. the book is legally available for free on Garrett’s website. here are some more resources from Garrett. we will also follow Vic Reiner’s notes on the subject, which can be found on his website. additional textbooks are available through the UMN library. i have provided links to the ones i find most interesting on Canvas.

here is information about coding theory using SageMath, a free open-source mathematics software system.

course logistics

grades are earned using a mastery-based learning framework with 20 specifications, including 10 “core” specifications and 10 “advanced” specifications.

assignments

each week there is a homework and two quizzes. one quiz focuses on definitions relevant to upcoming course material. the other provides an opportunity for students to demonstrate mastery on specifications recently addressed in class.

additional resources

some of the following resources may only be available with UMN library access.

questions

my students ask great questions. here are the answers to some of them.