Syllabus 149B: Discrete Mathematics
Spring 2003


Lectures: MWF 3:10-4:00pm, Wellman 7
Instructor: Anne Schilling, Kerr Hall 578, phone: 754-9371, anne@math.ucdavis.edu
Office hours: Friday 4-5pm or by appointment
Discussion section: T 3:10-4:00pm, Wellman 7
T.A.: Maya Ahmed, Kerr 577, maya@math.ucdavis.edu
Office hours: Monday 2-3pm, Tuesday 4-5pm
Text: N.L. Biggs, Discrete Mathematics, Oxford University Press, revised edition, 1999, ISBN 0-19-853427-2
Pre-requisite: MAT 149A or permission by instructor
Problem Sets: There will be weekly homework assignments, handed out on Wednesday, due the following Wednesday.
You are encouraged to discuss the homework problems with other students. However, the homeworks that you hand in should reflect your own understanding of the material. You are NOT allowed to copy solutions from other students or other sources. No late homeworks will be accepted. Solutions to the problems will be discussed in the discussion section. This is also a good forum to get help with problems and to ask questions!
Exams: Midterm May 7 in class, Final exam June 10 at 1:30 pm
There will be no make-up exams!
Grading: The final grade will be based on: Problem sets 20%, Midterm 30%, Final 50%
Web: http://www.math.ucdavis.edu/~anne/SQ2003/149B.html

Course description

This course is an introduction to Discrete Mathematics via the study of classical algebraic techniques (groups, rings and fields). The second part (149B) focuses on finite rings and fields. We will explore the applications of rings and fields to partition theory, design theory, finite geometry, coding theory, and enumerative combinatorics. The class is primarily based on Chapters 4,6 and 15-19 of Biggs' book.

1. Rings and fields
polynomial factorization, polynomial algorithms, construction and characterization of finite fields

2. Designs and applications
latin squares, t-designs, finite geometries and projective planes

3. Error-correcting codes
linear codes, cyclic codes and generalizations

4. Ring of formal power series
formal power series, generating functions, recursions, theory of partitions

Problem sets

Homework 1: due April 9, 2003 in class: ps or pdf
Solutions: ps or pdf

Homework 2: due April 16, 2003 in class: ps or pdf
Solutions: ps or pdf

Homework 3: due April 23, 2003 in class: ps or pdf
Solutions: ps or pdf

Homework 4: due April 30, 2003 in class: ps or pdf
Solutions: ps or pdf

Practice Problems: not to be handed in; will be discussed in the discussion session May 6: ps or pdf

Homework 5: due May 14, 2003 in class: ps or pdf
Solutions: ps or pdf

Homework 6: due May 21, 2003 in class: ps or pdf
Solutions: ps or pdf

Homework 7: due May 28, 2003 in class: ps or pdf
Solutions: ps or pdf

Homework 8: due June 4, 2003 in class: ps or pdf
Solutions: ps or pdf

Practice Problems: ps or pdf
anne@math.ucdavis.edu