Syllabus 149B: Discrete Mathematics
Spring 2006


Office hours during finals week: Anne Monday June 12 11am-12pm; Wong Wednesday June 14 2-4pm
Lectures: MWF 3:10-4:00pm, CHEM 166
Instructor: Anne Schilling, MSB 3222, phone: 754-9371, anne@math.ucdavis.edu
Office hours: Mondays 2-3pm or by appointment
Discussion section: R 3:10-4:00pm, HUTCH 115
T.A.: Qiang Wang, MSB 3151, xqwang@math.ucdavis.edu
Office hours: Thursdays 2-3pm, 4-5pm
Text: N.L. Biggs, Discrete Mathematics, Oxford University Press, second edition, 2002, ISBN 0-19-850717-8
Pre-requisite: MAT 149A or permission by instructor
Problem Sets: There will be weekly homework assignments, handed out on Friday, due the following Friday.
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 10 in class, Final exam June 15 at 8:00 am
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/SQ2006/149B.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 11, 13 and 22-26 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 7, 2006 in class; ps or pdf
Solution: ps or pdf

Homework 2: due April 14, 2006 in class; ps or pdf
Solution: ps or pdf

Homework 3: due April 21, 2006 in class; ps or pdf
Solution: ps or pdf

Homework 4: due April 28, 2006 in class; ps or pdf
Solution: ps or pdf

Practice Problems: to be discussed in the discussion session on May 5; ps or pdf
Sample Solutions: pdf

Sections covered on midterm: 22.1-22.8, 23.1-23.8, 11.6, 11.7, 13.4, 13.5

Homework 5: due May 12, 2006 in class; ps or pdf
Solution: ps or pdf

Homework 6: due May 19, 2006 in class; ps or pdf
Solution: ps or pdf

Homework 7: due May 26, 2006 in class; ps or pdf
Solution: ps or pdf

Homework 8: due June 2, 2006 in class; ps or pdf
Solution: ps or pdf

Here are some notes on Rogers-Ramanujan identities: ps or pdf

Practice Problems: ps or pdf
Sample Solutions: pdf