Department of Mathematical Sciences
Northern Illinois University

MATH 523, Summer 2008

June 16 - August 7

Professor John Beachy, Watson 355, 753-6753

Office Hours: 2:00 - 3:00 (in Watson 355), or by appointment

email: beachy@math.niu.edu | My faculty homepage | My personal homepage

SYLLABUS

COURSE: MODERN APPLIED ALGEBRA (3)
Concepts and techniques of modern algebra which are useful in applied mathematics. Topics include applications of group theory to coding, applications of latice theory to switching theory, and applications of ring theory to linear automata.

PREREQUISITE: MATH 420 or consent of department

TEXT: Introduction to Algebraic Coding Theory, by Sarah Adams
A local copy of the text (in .pdf format) is available here: coding_theory
The text is also available at Cornell University: eccbook2007

SYLLABUS: The topics covered will include linear codes and cyclic codes. I hope to finish all of the textbook. If time permits, there will be some material on codes based on elliptic curves from another text.

100 points for the midterm exam
200 points for homework
100 points for the final exam

MIDTERM: The midterm exam will be given on 7/10. It will cover Chapters 1 - 3 of the text by Spence, together with the lectures notes, and the notes given in class.

FINAL: The final exam will be given in class on Thursday, August 7. It will cover cyclic codes, Chapters 3 and 4 of the text by Spence, the lecture notes on finite fields, and the notes given in class (through to 7/31). Results will be posted on Blackboard, and you can pick up your final after it has been graded.

ASSIGNMENTS

```
DUE   CHAPTER    PROBLEMS

6/23    1        #1.10, 1.11, 1.12, 1.13

6/30    2        #2.4, 2.5, 2.6, 2.7

7/8     3        #3.1, 3.2, 3.3, 3.8

7/21  Notes      #2.1, 2.2, 2.4, 3.1, 3.2, 3.3

7/28  Notes      #4.1, 4.2, 4.3, 4.4
N.B.  4.4 was changed on 7/23

7/31    4        \$4.1, 4.2, 4.5
Notes      See the posted homework assignment

```
Printed copies of   Homework 4 ;   Homework 5 ;   Homework 6

CLASS NOTES

Lecture notes on finite fields: in pdf format; lecture notes on BCH and RS codes: in pdf format;

Lectures on the CDMA algorithm for cell phones: Lectures by A. Poon; Background

REFERENCES

Introduction to Cryptography, with Coding Theory, Trappe and Washington
Introduction to the Theory of Error-Correcting Codes, Pless
The Theory of Error-Correcting Codes, MacWilliams and Sloane
Introduction to Coding Theory, van Lint
Abstract Algebra, Beachy and Blair

RESOURCES ON THE WEB

Complete books online:
Papers on Coding Theory and Cryptography,
Notes on Coding Theory, Hall (Michigan State)
MIT Open Courseware contains a course called "Essential Coding Theory", in the Computer Science section (find it via Google)

Algebra: Abstract and Concrete, by F. Goodman (University of Iowa)

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