Mathematics 488 (Seminar in Contemporary Mathematics)

Digital Codes

Fall, 2008

(Prerequisite: Math 122; or Permission of the instructor)

1 hours, 1 credits


The purpose of this course is to introduce students to basic ideas in the involving various kinds of codes. Examples of how codes which track information (zipcodes, UPC, ISBN, etc.), correct errors (Hamming code and Hamming distance), compress information (Huffman codes, and other data compression methods), as well as other digital codes will be given


1. Introduction to codes and what goals they can accomplish

a. codes to hide information

b. codes to track information

c. codes to correct information

d. codes to compress information

2. Primer of modular arithmetic

3. Check digit systems such as zipcodes, UPC code, and ISBN numbers.

(different types of barcode systems).

4. Error correction codes and Hamming distance

5. Data compression codes (Huffman codes and Huffman trees).

6. Mathematical aspects of the genetic code.


There will be no text. Unfortunately, there is no text which treats the desired topics at the level this course will be taught at. Some notes I have written will be distributed in class and be made available on the web.

Homework will be assigned regularly and to save class time students can hand in their work (on a volunary basis) to be corrected if they so choose. I will answer questions related to homework in class but not specifically go over the problems.

Grading based on:

One Midterm Examination; attendance, writing project and classwork. There will also be a final examination which will cover the whole semester's work.

The examinations will be announced in advance.

Prepared by:

Joseph Malkevitch (Department of Mathematics)


web page:

Date: Fall, 2008