MATHEMATICS FOR TEACHERS: ALGEBRA
MATHEMATICS FOR TEACHERS: GEOMETRY
Formal and informal geometry; non-metric geometry; congruence;
measurement; constructions; similarity; coordinate geometry;
trigonometric functions, constructions.
MATHEMATICS FOR TEACHERS: NUMBER THEORY
A study of the structure of the integers, divisiblity, primes, congruence classes, linear congruences, diophantine equations. Fibonacci numbers and selected topics. Some topics will be developed and adapted by the students for the elementary classroom.
MATHEMATICS FOR TEACHERS: PROBABILITY AND STATISTICS
Probability, probability distributions, sampling, design of experiments, hypothesis testing, regression, analysis of variance, nonparametric statistics.MATHEMATICS FOR TEACHERS: FINITE MATHEMATICS
Prerequisites: MAT 121 and 122 or equivalents.
Partitions; permutations; probability measure; conditional probability; vectors; matrices, operations, and properties; linear programming applications.
Prerequisites: The successful completions of the course work usually required for an undergraduate major in mathematics. This is necessary to provide a foundation for the understanding of the course content. An introductory course in modern algebra is recommended.
Groups, semigroups, and monoids. Hemomorphisms. Subgroups and cosets. Abelian groups. The symmetric group. Actions and the Sylow theorems. Rings, subrings and ideals. Ring homomorphisms. Integral domains. Division ring and fields. Ring and field extensions. Galois theory.
The algebra of matrices and determinants; equivalence, similarity and congruence relations on matrices; vector space, linear transformations; characteristic roots and vectors; application.
Prerequisites: Three semesters of an undergraduate calculus sequence.
Introduction to Real Functions-The real numbers, basic topology, sequences, continuous functions, differentiation, the Reimann-Stieltje's integral, sequence and series of functions, some special functions, the Lebesque theory.
MODERN GEOMETRY: SELECTED TOPICS
Prerequisites: MAT 322 or equivalent.
The topics will be selected from teh following list. Foundations, Axiomatic Projective Geometry, Real Projective Geometry, Linear Projective Geometry, Finite Geometries, Non-Euclidean Geometries.
The axiomatic method; theory of sets and infinite sets; real number system and linear continuum; the complex number system; groups and their significance for the foundations; development of various viewpoints on foundations.
Counting and recording of numbers; properties of numbers; Euclid's algorithm; prime numbers; the aliquot parts, indeterminate problems and their theory; Diophantine problems; congruences; analysis of congruences; Wilson's theorem; Euler's theorem; theory of decimal expanisons; the converse of Fermat's theorem; the classical construction problems.
DISCRETE MATHEMATICS AND FOUNDATIONS OF COMPUTER SCIENCE
Prerequisites: At least 24 semester hours of undergraduate mathematics.
Problems and theorems from discrete mathematics and computer science. Discrete structures commonly used in computer science and mathematics, including sets, relations, graphs and trees. Counting, permutations, combinations, and recursion. Topics from theoretical computer sciences include: algorithms on discrete structures, measures of algorithms on discrete structures, measures of alogrithm complexity, the polynomial classes P and NP, complete problems, models of computation, non-computable functions.
Prerequisite: MAT 381 Probability or equivalent.
Selected topics which are more advanced than the introductory treatment of probability theory such as problems of combinatorial analysis, the laws of large numbers, and the theory of stochastic processes.
Prerequisite: MAT 381 Probability or equivalent.
Probability, estimation, confidence sets, tests of hypotheses, decision theory. Bayesian methods, linear models, and non-parametric methods.
Chronological study of the development of mathematics; contributions of nation, age, or periods; selected biographies; appraisals and critiques; problem studies.
ADVANCED SPECIAL TOPICS
Prerequisite: Permission of the instructor.
Selected Advanced Topics: Seminar will consider an advanced branch of contemporary mathematics such as Combinatorics, Game Theory, Automata Theory, or intensive study of an advanced topic in mathematical research.
Prerequisite: MAT 301 or equivalent.
Cyclic groups, transformation groups; factor groups; groups with operators; isomorphism theorems; composition series; direct products of groups; Sylow theorems; residue clas rings; operations on ideals, extensions of rings.
Prerequisite: MAT 417 Introduction to Real Analysis I.
Introduction to graduate functions of several variables, topology
of Euclidean spaces, continuity and uniform continuity, convergence
and uniform convergence of sequences of functions, theorems.
Riemann-Stieltjes integration, multiple integrals. Fubini's theorem.
Line integrals.
Graduate Math Education Course Descriptions
Back to Math Department Home Page
Back to Buffalo State College Home Page