State University College at Buffalo
Department of Mathematics
Request for Course
I. Number and title of
course
MAT 309 ‑ Discrete
Mathematics II
II. Reasons for addition
to the present curriculum
A. To provide an alternative to the
more traditional approach to algebra for those students interested in
computational mathematics.
B. To provide an elective
mathematics course for students interested in the mathematics of
computation.
C. To continue the study of discrete
mathematics begun in Mathematics 301‑Introduction to Modern Algebra I.
III. Major
objectives of the course
A. To introduce the student to
discrete mathematical structures.
B. To provide the student with a
foundation in algebraic theory relating to the mathematics of computation.
C. To extend the results and
techniques begun in Mathematics 301‑Introduction to Modern Algebra I.
IV. Behavioral
Objectives
The following is a partial list of behavioral
objectives.
The student will be expected to know how to:
A. recognize and perform basic
operations with discrete
mathematical
structures, and
B. apply the principles of
discrete mathematics in
designing systems for
computation.
V. Topical
Outline
A. Automata
1. Building Automata with
specified behavior.
2. Direct
products and machine decomposition.
B. Linear Machines and Codes
1. Modules
2. Group codes
3. Linear
machines and shift registers
4. Building
linear machines with specified behavior
C. Algebraic Coding Theory
1. Polynomial rings over a field
2. Introduction to Cyclic codes
3. Minimum polynomials and
maximum length codes
D. Language
Theory
1.
Context-free grammars
2.
Tree Automata
3.
Polish notation
4.
Pushdown automata
VI. Bibliography, texts and references
1. Birkoff, 0. and Bartee, T.C.,
Modern Applied Algebra
McGraw Hill, 1970..
2. Bobrow, L.S. and Arbib, M.A.,
Discrete Mathematics
W.B. Saunders, 1974.
3. Stone, L.S.,
Discrete Mathematical Structures, SRA
1973.
VII. Presentation and Evaluation
A. Presentation will be by lectures
and class discussions.
B. Evaluation will be by
examinations, homework and c
class
participation
VIII. Prerequisites
MAT
30l and MAT 207
IX. Credit
3 Semester hours
X. Catalog Description
MAT 309 ‑ Discrete
Mathematics II
Automata, modules, group codes,
linear machines, polynomial rings, cyclic codes, minimum polynomials, context‑free
grammers, tree automata, polish notation, pushdown automata. Prerequisites:
MAT 301 and MAT 270
XI. Statement
of qualifications of faculty who will teach this course
A master's degree in
mathematics is a minimum formal education. All members of this Department
meet this requirement. Current staff and facilities are adequate for the
offering of this course.
The following faculty have
experience in the area of discrete mathematics:
M.W. Boyd, Assistant
Professor of Mathematics, Ph.D., SUNY at Binghamton
A.C. Green, Assistant
Professor of Mathematics, Ph.D., Syracuse University
XII. Statement of Approval
This course was examined in
accordance with recommended procedures and approved by the Department of
Mathematics.