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 will be earned through homework assignments, midterms, and a final.

homework assignments

there will be 6 homework assignments, submitted via canvas

homework # problems due date
1 PG 1.28, 1.31, 1.33, 2.03, 3.02,
additional problems
 
2 PG 2.04, 3.05, 4.01, 4.02, 4.04, 4.05, 4.06, 4.11
clarification on 4.05
 
3 PG 5.01-5.05, 5.08, 6.01, 6.03, 6.07, 6.22, 6.37, 6.49, 6.50, 6.57, 6.52, 6.80, 6.81, 8.17  
4 PG 6.30, 6.31, 9.11, 9.12, 10.04, 10.08, 10.11, 11.11, 12.06, 12.10, 12.12,  
5 PG 12.01, 12.02, 12.04, 12.14, 12.15, 12.17, 12.19, 12.20, 13.02, 13.05, 13.07, 13.09, 13.10  
6 PG 11.04, 11.05, 14.02, 14.05, 15.03, 15.13  

exams

exams will be administered in-class during the weeks of february 18, april 1, and may 5. exact dates tbd. sample exams will be available below.

exam # pdf of sample exam
1  
2  
final  

additional resources

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

lecture content

this reflects what was actually covered on the given date.

date rough content
1/22 Intro + PG 3.1

questions

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