MATH 530, 531 Discrete Mathematics with Applications I, II

Undergoing Reorganization:

Advanced mathematical methods of discrete mathematics with applications. Topics will include probability theory with generating functions, difference equations and number theory. Additional topics to be drawn from the theory of algorithms, coding theory, set theory, and the relation of discrete mathematics to complex analysis. 4 lectures.

Prerequisite: MATH 481, MATH 306 and

graduate standing, or consent of the instructor.

Required Background or Experience

MATH 306, MATH 481 and graduate standing, or consent of the instructor. MATH 336 strongly recommended.

Learning Objectives:

The student should be able to:

a) use the techniques of discrete mathematics, especially the idea of recurrence, to solve problems in probability theory, counting, and number theory.

b) formulate and model the problems in discrete mathematics and present either complete or partial solutions to these problems using oral or written expression.

Text and References:

Our Class text will be Combinatorics: Topics, Techniques, Algorithms by Peter Cameron.

Other useful references are:

Combinatorics: Topics, Techniques, Algorithms by Peter Cameron
Concrete mathematics : a foundation for computer science / Ronald L. Graham, Donald E. Knuth, Oren Patashnik.
Eunmerative Combinatorics Vols I, II, Stanley
GeneratingFunctionology, Herb Wilf
Combinatorial Species and Tree-Like Structures (Encyclopedia of Mathematics and Its Applications, Vol 67) by F. Bergeron, P. Leroux, Gilbert Labelle (not in library)
Notes on introductory combinatorics / George Polya, Robert E. Tarjan, Donald R. Woods
Graphical Enumeration by Frank Harary, Edgar M. Palmer (not in library)

Content to be covered:

Probability and related topics

1. Basic set theory/foundations

2. Discrete probability

3. Generating functions

4. Binomial coefficients

5. Difference equations

B. Number theory

1. Primes

2. Congruence

3. Prime number theorem

4. Coding theory

5. Algorithms

C. Additional topics

1. Euler phi function

2. Riemann zeta function

3. Hypergeometric function

4. Asymptotics

5. Methods of Assessment

You grade will be based on take on home assignments and class participation.

Open problems from the West Coast Number Theory Conference for possible extra credit or independent research projects. See me if you're interested.

Reference List

Combinatorics: Topics, Techniques, Algorithms by Peter Cameron

Concrete mathematics : a foundation for computer science / Ronald L. Graham, Donald E. Knuth, Oren Patashnik.

Eunmerative Combinatorics Vols I, II, Stanley

GeneratingFunctionology, Herb Wilf

Combinatorial Species and Tree-Like Structures (Encyclopedia of Mathematics and Its Applications, Vol 67) by F. Bergeron, P. Leroux, Gilbert Labelle (not in library)

Notes on introductory combinatorics / George Polya, Robert E. Tarjan, Donald R. Woods

Graphical Enumeration by Frank Harary, Edgar M. Palmer (not in library)

Notes:

3core maple file (text version)

reference_list.htm

l_functions.pdf

NormContRevision.pdf