# Graduate Catalog 2010-12

### Mathematics

Note: Additional work will be required for graduate credit in 400-level courses.

**MATH 421 History of Mathematics 3**

Prereq.: MATH 221 or for graduate students, admission to M.A., Mathematics or the M.S., Mathematics (for certified secondary teachers). Development of mathematics is traced from arithmetic of commerce, astronomy, geometry, and trigonometry in Babylonia, Egypt, Greece, and Rome to the later accomplishments in algebra, geometry, and calculus. Spring. (O)

**MATH 440 Selected Topics in Mathematics 1 TO 3**

Prereq.: Permission of instructor. Selected topics in mathematics covering specialized areas not covered in regular offerings or that go beyond that provided for in the standard curriculum. May be repeated with different topics for a maximum of 6 credits. Irregular.

**MATH 449 Mathematics Laboratory for Elementary School 3**

Prereq.: MATH 412, 414 or 327 or equivalent and student teaching. Provides teachers in elementary school with the opportunity to make mathematical materials useful in teaching elementary mathematics. Each participant constructs mathematical models and manipulatives appropriate to his/her teaching level and interest. Mathematical projects and educational implications are discussed. Can be used to meet the requirements for a major or minor in mathematics only for students seeking elementary, early childhood or middle level certification. Not recommended for use in meeting requirements for secondary school mathematics. Summer.

**MATH 455 Introduction to Partial Differential Equations with Applications 4**

Prereq.: MATH 355 (C- or higher) or permission of department chair. Introduction to analytical, geometric, and numerical methods for solving partial differential equations. Basic models of physical systems using partial differential equations. Introduction to software used for solving partial differential equations. Fall. (O)

**MATH 468 Symbolic Logic 3**

Prereq.: MATH 366 or equivalent. Introduction to truth, validity and argument. Methods of deduction, propositional functions and quantifiers, logic of relations, deductive systems, and propositional calculus. Spring. (E)

**MATH 469 Number Theory 3**

Prereq.: MATH 366 or equivalent. Elementary theory of numbers. Divisibility, prime numbers, Fundamental Theorem of Arithmetic, congruences, Diophantine equations, quadratic residues and continued fractions are among topics considered. Fall. (O)

**MATH 470 Mathematical Methods in Operations Research 3**

Prereq.: STAT 215 or 315, and MATH 110 or 228 or permission of instructor. Selected topics chosen from the areas of linear programming, decision analysis, and network analysis. Summer. (E)

**MATH 477 Numerical Analysis 3**

Prereq.: MATH 221 and CS 151 or permission of instructor. Selected topics including difference operators, iterative methods of finding zeros of functions, interpolation and polynomial approximation, numerical integration and differentiation, matrices, and systems of linear equations. No credit given to students with credit for CS 254. Summer. (O)

**MATH 491 Advanced Calculus 3**

Prereq.: MATH 222 or permission of instructor. Topics from continuity and differentiability of functions of several variables, exterior differential forms, multiple and iterated integration, line integrals, Gauss', Green's, and Stokes' theorems. Fall. (E)

**MATH 500 Mathematics Practicum **3

Prereq.: Admission to the M.A. program in mathematics and permission of the department. Supervised application of academic knowledge to an employment environment related to their field of study. On demand.

**MATH 504 Topics in Mathematics 1 TO 3**

Prereq.: Permission of instructor. Topics in mathematics appropriate for in-service and pre-service graduate certification students who are not covered in regular course offerings. May be repeated under different topics for a maximum of 6 credits. Irregular.

**MATH 506 Teaching Number Concepts in the Elementary Grades 3**

Prereq.: Admission to M.S. in mathematics for certified elementary teachers. NCTM Standards-based instructional practices that promote the development of number sense; operations with whole numbers, decimal numbers and common fractions; problem solving; and graphical representations in the elementary grades. Fall. (O)

**MATH 507 Teaching Geometry & Measurement in the Elementary Grades 3**

Prereq.: Admission to M.S. in Mathematics for certified elementary teachers. NCTM Standards-based instructional practices that promote understanding of key concepts in geometry and measurement in the elementary grades. Fall. (E)

**MATH 508 Teaching Probability & Statistics in the Elementary Grades 3**

Prereq.: Admission to M.S. in Mathematics for certified elementary teachers. NCTM Standards-based instructional practices that promote understanding of key concepts in probability and statistics in the elementary grades. Spring. (O)

**MATH 509 Teaching Algebraic Thinking in the Elementary Grades 3**

Prereq.: Admission to M.S. in Mathematics for certified elementary teachers. NCTM Standards-based instructional practices that promote algebraic thinking in the elementary grades. Spring. (E)

**MATH 515 Abstract Algebra I 3**

Prereq.: MATH 366 or permission of instructor. Extension of basic group theory introduced in MATH 366, including normal subgroups, quotient groups, cyclic groups, permutation groups, classical isomorphism theorems, and Sylow theorems. Fall. (E)

**MATH 516 Abstract Algebra II 3**

Prereq.: MATH 515. Selected topics from advanced polynomial ring theory, Galois and extension field theory, homological algebra. Spring. (E)

**MATH 519 Principles of Real Analysis I 3**

Prereq.: MATH 377 or permission of instructor. Introduction to functions of a real variable and their properties. Rigorous study of the real number system, topological properties of real line, Cauchy sequences, limit and continuity properties of a real variable, metric spaces. Fall. (O)

**MATH 520 Principles of Real Analysis II 3**

Prereq.: MATH 519. Topics include Riemann-Stieltjes integrals, functions of bounded variation, sequences and series of real numbers, power series. Spring. (O)

**MATH 523 General Topology 3**

Prereq.: MATH 377 or permission of instructor. Rigorous study of point-set topology. Topics include set theory, definition and basic properties of topological spaces, continuous functions, and homeomorphisms. Spring. (O)

**MATH 525 Higher Geometry 3**

Prereq.: MATH 221 or permission of instructor. Topics from higher-dimensional geometry. Foundations of several geometries and relationship of Euclidean geometry to other geometries. Projective properties in a Euclidean (metric) setting. Selected topics from synthetic and analytic projective geometry. Fall.

**MATH 526 Complex Variables 3**

Prereq.: MATH 222 or permission of instructor. An introduction to the theory of functions of a complex variable. Topics include the field of complex numbers, complex analytic functions, elementary functions and their mapping properties, integration theory, and power series expansion of analytic functions. Spring. (E)

**MATH 531 Basic Concepts of Elementary School Mathematics 3**

Analysis of concepts underlying contemporary mathematics program in elementary school. Emphasis is placed on both structure of mathematical content and procedures used in developing pupil understanding of concepts and processes. Open only to post-baccalaureate certification students. Fall.

**MATH 534 Techniques in Diagnosis and Remediation for the Teaching of Mathematics - K-12 3**

Prereq.: Admission to M.S. in Mathematics for certified elementary or certified secondary teachers. This course will train early childhood, elementary, middle and secondary teachers in diagnosis and remediation. The course will use a clinical case study approach so that each student will get practical, as well as theoretical experience. Topics include identifying the factors related to learning difficulties in mathematics in the cognitive and affective domains, diagnostic tests, identification of the underachiever, and case studies. Spring.

**MATH 536 Teaching Number Concepts in the Middle Grades 3**

Prereq.: Admission to M.S. in Mathematics for Certified Elementary School Teachers. NCTM Standards-based instructional practices that promote the development of number sense; operations with whole numbers, rational numbers, integers; problem solving; and graphical representations in the middle grades. Fall. (O)

**MATH 537 Teaching Geometry & Measurement in the Middle Grades 3**

Prereq.: Admission to M.S. Mathematics for certified elementary teachers. NCTM Standards-based instructional practices that promote understanding of key concepts in geometry and measurement in the middle grades. Fall. (E)

**MATH 538 Teaching Probability & Statistics in the Middle Grades 3**

Prereq.: Admission to M.S. in mathematics for certified elementary teachers. NCTM Standards-based instructional practices that promote understanding of key concepts in probability and statistics in the middle grades. Spring. (O)

**MATH 539 Teaching Algebraic Thinking in the Middle Grades 3**

Prereq.: Admission to M.S. in mathematics for elementary teachers. NCTM Standards-based instructional practices that promote algebraic thinking in the middle grades. Spring. (E)

**MATH 540 Curriculum Problems in School Mathematics 3**

Prereq.: Admission to M.S. in Mathematics for certified elementary or certified secondary teachers. Current issues in mathematics education. Study of some current major curriculum projects. Content basic to these programs is studied with emphasis on mathematical structure. Opportunity is provided for special investigation into topics of student's interest. Spring. (O)

**MATH 543 Secondary School Algebra with Technology from Advanced Viewpoint 3**

Prereq.: Admission to graduate certification program in mathematics or M.S. in Mathematics for certified secondary teachers. Intended for in-service secondary school teachers and pre-service graduate certification students. Major objective is to broaden and deepen teacher's knowledge of the algebra topics encountered in secondary schools with particular emphasis on topics new to the curriculum and the uses of technology in teaching them. Opportunities will be provided to discuss the NCTM standards and their implications for teachers. Summer. (E)

**MATH 544 Secondary School Geometry with Technology from an Advanced Viewpoint 3**

Prereq.: Admission to graduate certification program in mathematics or M.S. in Mathematics for certified secondary teachers. For in-service mathematics teachers and graduate certification students in mathematics. Major objective is to expand teachers' knowledge of new topics and technology for teaching geometry. NCTM standards for geometry will be included. Summer. (O)

**MATH 547 Reflective Practice in Teaching Mathematics 3**

Designed to help in-service teachers develop as reflective practitioners through the use of lesson logs, narrative commentary, analysis of videotaped lessons, and examination of student work. Emphasis on relating instruction to the big ideas of mathematics, designing appropriate assessments, and determining meaningful feedback for students. Particularly helpful to beginning teachers who will be compiling their BEST portfolios. Open only to certified in-service teachers of mathematics, grades 7-12. Fall.

**MATH 580 Directed Study in Mathematics 1 TO 3**

Prereq.: Permission of the instructor. A study of selected topics in mathematics. The area of study will depend on the instructor and the interests and needs of the student(s). May be repeated with different topics to a maximum of 6 credits. Irregular.

**MATH 590 Special Project in Mathematics 3**

Prereq.: Completion of at least 21 credits in the student's planned program of graduate study and a 3.00 overall GPA. The study of an advanced topic in mathematics/mathematics education, approved by the student's graduate advisor and supervised by a faculty member. Requirements include preparation and oral presentation of a paper on the topic. Irregular.

**MATH 598 Research in Mathematics Education 3**

Prereq.: STAT 453 and permission of advisor. Course designed to familiarize graduate student with techniques and resources associated with research in mathematics and mathematics education. Opportunity for practical application will be provided. Fall.

**MATH 599 Thesis (Plan A) 3 OR 6**

Prereq.: Permission of the advisor, and a 3.00 overall GPA. Preparation of thesis under guidance of thesis advisor for students completing master's requirements under M.S. and M.A. Plan A.