Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 148: Discrete Mathematics
Approved: 2006-05-18, Eric Rains & Jesus DeLoera

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Introduction to the Theory of Error-Correcting Codes, Pless ($99)
Search by ISBN on Amazon: 0471190470

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

Week 1

1.1, Appendix

Motivation; review of modular arithmetic and linear algebra over finite fields.

Week 2

1.2, 1.3

Basic definitions (code, weight, minimum distance). Main theorem of multiple-error correction.

Week 3

2.1, 2.2

Syndrome decoding; sphere packing bound; Hamming codes; perfect codes.

Week 4

2.3

Packing and covering; more bounds.

Week 5

2.4

Self-dual codes, Golay codes.

Week 6

3.1, 3.2

Definition of a field. Polynomials; factorization.

Week 7

3.3, 3.4

F16; applications.

Week 8

4.1-4.3

Abelian groups, structure and classification of finite fields.

Week 9

5.1, 5.2, 4.4

Cyclic codes, factorization of xn-1

Week 10

5.3, 5.4

Cyclic codes continued

Additional Notes:

Further topics (time permitting): Chapter 6 (QR codes) and chapter 9 (designs) would both be suitable.