# Mathematics Courses Graduate

### MATHEMATICS DEPARTMENT COURSE DESCRIPTIONS

The Department offers three types of courses. "Professionalized subject matter" courses generally approach mathematics in a way which enhances the depth of understanding and teaching, of mathematics in the secondary school. "Pure mathematics" courses encourage the student to strengthen the knowledge of mathematics with a possible goal of pursuing an additional advanced degree. "Computer related" courses provide students with a mathematical approach to computational processes.

MATH 502 Concepts of Computer Science (3) view syllabus-pdf

This course provides an historic overview and survey of equipment and other elements to be found in computer systems. The operations and management of computer resources, use of math software, and an overview of computer programming languages are other topics covered.

MATH 503 Computers in Mathematics (3) view syllabus-pdf

This course provides students, who have basic computer literacy and some elementary knowledge of computer programming, specific skills in using mathematical software. Problems and projects are taken from a variety of mathematical subjects including: precalculus, calculus, number theory, geometry, linear algebra, abstract algebra, and statistics. Explanations and introductions to these subjects are provided. Prerequisite: MATH 502 Concepts of Computer Science or by permission of department chair.

MATH 508 Professionalized Subject Matter in Arithmetic (3) view syllabus-pdf

This course offers a study of procedures in arithmetic. Attention is given to concepts in manipulative and problem solving areas. Various services for diagnostic and remedial measures are introduced and evaluated.

MATH 510 Professionalized Subject Matter in Algebra (3) view syllabus-pdf

This course provides the student with a reappraisal of the fundamental concepts of algebra. Emphasis is placed on the manner in which these concepts can be used to teach algebra more effectively. This course demands evidence of effective use of these concepts in the student's own classroom. Topics include: number, set, relations, functions, operation structure, and problem solving.

MATH 511 Professionalized Subject Matter in Junior High School and General Mathematics (3) view syllabus-pdf

This course stresses mathematical concepts and skills required of children entering the junior high school curriculum in recent years, as well as those which are appropriate for students with less interest and ability in mathematics. The student is required to show evidence of use of some of these in the student's own classroom. Topics include: modular arithmetic, numeration, geometry, descriptive statistics, algebra, and mathematical games.

MATH 512 Professionalized Subject Matter in Geometry (3) view syllabus-pdf

This course provides a review of fundamental concepts of geometry and an investigation of their significance in the teaching of secondary school mathematics. Concepts to be analyzed include: logic, proof, and axiomatic systems; physical and geometric models; sets, relations, and transformation; non-metric and metric concepts, duality and dimensionality; and coordination of spaces. Attention is given to: historical considerations bearing on the teaching of geometry; integration of geometry with algebra and science; and significant literature on the subject. This course requires evidence that the stu dent is making effective use of these concepts in the student's own classroom.

MATH 514 Professionalized Subject Matter in Precalculus Mathematics (3) view syllabus-pdf

This course presents pre-calculus topics, particularly trigonometry and matrix operations. Attention is given to historical considerations and to current trends in teaching this content. This course requires evidence that the student is making effective use of these concepts in the student's own classroom.

MATH 515 Math Manipulatives 1 (3) view syllabus-pdf

This course explores the use of manipulatives such as geoboards, Cuisenaire rods, number lines, software and CD ROM materials in the teaching of mathematics in elementary and middle schools. Both commercial and teacher-made manipulatives are utilized.

MATH 516 Math Manipulatives 2 (3) view syllabus-pdf

This course continues the exploration of using manipulatives to teach mathematics. Students are expected to demonstrate and use these manipulatives in their own classrooms.

MATH 517 Calculators in the Classroom 1 (3)

This course explores the use of calculators in the teaching of mathematics K-8. Topics include using calculators to reinforce the elementary and middle school mathematics curriculum and constructing student projects which make use of the calculator.

MATH 518 Calculators in the Classroom 2 (3)

This course explores the use of graphing calculators in the teaching of secondary school mathematics. The use of calculators is demonstrated for algebra, geometry, trigonometry, and calculus. Student projects are constructed which make use of the calculator. Calculators in the Classroom I is not a prerequisite.

MATH 526 Algorithmic Number Theory (3) view syllabus-pdf

This course presents number theory from an historical point of view and emphasizes significant discoveries from ancient to modern times, as well as presenting unsolved problems and areas of current interest. Topics include: prime numbers and related theorems; Euclidean algorithm and quadratic reciprocity; Pythagorean numbers and continued fractions.

MATH 527 Probability and Statistics (3) view syllabus-pdf

Prefaced by a study of the foundations of probability and statistics, this course is an extension of the elements of probability and statistics introduced in an undergraduate course. Topics include: unlimited sequences, random variables, expectation, law of large numbers, and generating functions.

MATH 529 Selected Topics in Topology (3) view syllabus-pdf

This course stresses the merging of fundamental ideas of analysis, algebra, and geometry. Topics include: continuous transformation, invariants, compactness, local compactness, and open and closed sets.

MATH 531 Numerical Analysis (3) view syllabus-pdf

Topics include iterative methods of solving equations; interpolation and polynomial approximation; numerical differentiation and integration; numerical solution of differential equations; solution of linear systems by direct and iterative methods; matrix inversion and calculation of eigenvalues and eigenvectors of matrices. Selected algorithms may be programmed.

MATH 536 Mathematical Modeling (3) view syllabus-pdf

The main objectives of this course are: to explore mathematical models of real world situations, to set up such models, and to review the mathematics needed to treat such models. Analysis of computer simulations of the models plays a major role in this course.

MATH 540 Graph Theory (3) view syllabus-pdf

Topics studied in this course include paths, walks, networks, trees, connected graphs, subgroups and related applications.

MATH 598 Computer Programming and Applications Graphics (3) view syllabus-pdf

Topics include: two dimensional algorithms; transformations, scaling, translations, rotations, matrix notation, line clipping, b-spline curve fitting, and recursion. Geometric tools for three dimensional algorithms, and affine and projective geometry are included. Viewing and perspective transformations, wire frame models, algorithms for the triangle decomposition of polygons and hidden-line elimination are included. Object-oriented programming using C++ is included. MATH 599 Structured Programming in C Language This course includes: fractal geometry, basic definitions, metric spaces, classification of subsets, and the space of fractals. Other topics covered are: transformations on metric spaces; contraction mappings; construction of fractals; recursion and fractals; Sierpinski triangle; Hilbert curve; dragon curves; trees; chaotic dynamics on fractals; and fractal dimension. Object-oriented programming principles using C++ are included.

MATH 602 Elements of Modern Mathematics (3) view syllabus-pdf

This course includes an introduction to sets; elementary work with unordered fields, finite fields, and ordered fields; elements of number theory; systems of numeration; introduction to logic; nonmetric and informal geometry; and growth of the number system.

MATH 604 Math in the Urban Schools (3) view syllabus-pdf

This course, designed primarily for in-service elementary urban school teachers, stresses the study of modern mathematics-its organization, its underlying psychological and philosophical principles, and creative teaching techniques important to the teacher of mathematics. Students are exposed to some of the significant research programs currently being undertaken by mathematics educators.

MATH 606 Survey of Modern Mathematics (3) view syllabus-pdf

This course offers a review of modern trends in mathematics, with emphasis given to experimental programs. Topics in discrete mathematics are also included. Analyses are made of recommendations for new mathematics curricula.

MATH 607 Mathematics in Secondary School (3) view syllabus-pdf

A presentation of objectives and techniques in major areas of junior and senior high mathematics is provided. Topics include: basic approaches to arithmetic; teaching of algebra; formal and informal geometry; status of general mathematics, senior (12th grade) mathematics; and current literature on the teaching of mathematics.

MATH 608 Seminar in Modern Elementary School Mathematics (3) view syllabus-pdf

This course includes classroom applications of the following ideas: distinction between number and numeral structure in arithmetics; the use of set ideas in understanding the fundamental operations in arithmetic; and a modern approach to the solution of verbal problems, open sentences, number families, patterns in arithmetic, geometry, and informal proofs.

MATH 609 Statistics for Classroom Teachers (3) view syllabus-pdf

This course is designed to develop an appreciation and general understanding of statistics. It offers an interpretation of fundamental statistical concepts as applied in the fields of education. A mathematics background (i.e., advanced mathematics courses) is not required.

MATH 614 Calculus for Teachers I (3) view syllabus-pdf

This course is designed for teachers to investigate the concepts, techniques, and applications of elementary calculus. Topics include: the foundations of calculus, differentiation, and integration of both algebraic functions and transcendental functions, and applications of calculus to the arts and sciences, professional studies and education.

MATH 615 Calculus for Teachers II (3) view syllabus-pdf

This course provides an intermediate level knowledge of mathematical concepts, techniques, and applications related to calculus and their application to the arts and sciences, professional studies and education. Prerequisite: MATH 614 Calculus for Teachers I

MATH 620 Selected Topics in Advanced Calculus I (3) view syllabus-pdf

Prefaced by a careful examination of the foundations of calculus, this course provides an extension of fundamental concepts of calculus that are taught in undergraduate calculus courses. Topics include: generalized mean value theorem, functions of several variables, partial differentiation, transformation, and mappings.

MATH 621 Selected Topics in Advanced Calculus II (3) view syllabus-pdf

This course studies: vector, multiple integrals, curves and surfaces, theory of integration, and infinite and power series. Prerequisite: MATH 620 Selected Topics in Advanced Calculus I.

MATH 622 Selected Topics in Modern Algebra I (3) view syllabus-pdf

This course extends the concepts that are taught in an undergraduate introduction to abstract algebra. Topics include: finite and infinite groups, rings, ideals, and integral domains and fields.

MATH 623 Modern Algebra II (3) view syllabus-pdf

This course studies: vector spaces, Euclidean space, sets of linear transformations and matrices, and bilinear and quadratic forms. Selected Topics in Modern Algebra I is not a prerequisite.

MATH 624 Selected Topics in Modern Geometry (3) view syllabus-pdf

This course is prefaced by a careful examination of the foundations of geometry. Major topics include: finite geometry, synthetic and coordinate-projected geometry, hyperbolic geometry, elliptic geometry, differential geometry, and topology. Considerable attention is given to the modern alliance of geometry with linear and abstract algebra.

MATH 626 Differential Equations (3) view syllabus-pdf

This is a course in ordinary and partial differential equations including topics such as separating variables, linear first and higher order differential equations and applications. In addition to many applications, the course includes an examination of the theory supporting various techniques for solution. Computer software is used as needed. Prerequisite: MATH 621 Selected Topics in Advanced Calculus II

MATH 630 Complex Variables (3) view syllabus-pdf

This course extends the concepts of elementary calculus to include the domain of complex numbers. Topics include: differentiation and integration of complex functions, analytic function, analytic continuation, and Cauchy's theorems.

MATH 660 Research Seminar in Mathematics (2) view syllabus-pdf

This seminar may involve the student in experimentation and research in mathematics. Emphasis is placed on skills and techniques appropriate for mathematics education. Each student may formulate and complete a classroom experiment involving the presentation of new material, analysis of student difficulties, or some other similar activity. Some initial work on a thesis may begin in this course. MATH 661 Research Credit in Mathematics (3) The candidate may elect to do independent research by enrolling in this course. Prerequisite: MATH 660 Research Seminar in Mathematics or permission of the chairperson