Professors: Bevelacqua, Collings, Dearden, Dunnigan, Gilsdorf, Halcrow, J. Iiams, M. Iiams, Khavanin, Metzger, Millspaugh (Chair and Graduate Director), Peterson, Richards, Takahashi and Zerr
Program Description
The Department offers courses leading to the M.S. (thesis and non-thesis) and M.Ed. degrees with a major in mathematics.
Admission Requirements
- The equivalent of a bachelor’s degree with a major in mathematics. Students who have not completed the equivalent of Math 431 and Math 432, Advanced Calculus, as undergraduates will be required to do so as part of their graduate program. Students without the required degree, or equivalent, may be admitted but will be required to satisfactorily complete undergraduate courses to make up their deficiency before advancement to Approved status.
Degree
Requirements
Master of Science
- A major of 30 (thesis) or 32 (non-thesis) credits or a major with a minor or cognate.
- Two full graduate sequences of the five available: 512-513, 515-516, 518-519, 520-521 and 541-542.
- At least one additional mathematics
graduate course.
The remainder of the program will be determined in consultation with an advisor based on the student’s mathematical aims, interests and background.
Master of Education
- A minimum of 32 semester credits is required for the M.Ed. degree of which 16 credit hours of graduate work must be completed in mathematics, with at least 8 credits of mathematics being at the 500 level or above, including 2 hours of 997, Independent Study. (See Degree Requirements for Master of Education.)
- Must have completed, in undergraduate or graduate school, courses in algebra equivalent to Mathematics 441 and 442, a course in analysis equivalent to Mathematics 431, a course in geometry equivalent to Mathematics 409, and a course in probability and statistics equivalent to Mathematics 421.
Graduate
Minor in Statistics
The requirements consist of 9 hours of which Math 421 and Math 422 are required if they were not taken as an undergraduate. The remaining credits may be selected from various probability and statistics-oriented courses in mathematics and other disciplines. For further information about this option, contact the chair of the Mathematics Department.
Courses
505. Seminar in Mathematics. 1 to 3 credits.
512. Modern Analysis I. 3 credits. Prerequisite: Math 432. Algebras and ó - algebras, Borel sets, measures, measurable sets and Lebesgue measure, non-measurable sets, measurable functions, the definition and basic properties of the Lebesgue integral, Fatou’s lemma, the monotone convergence theorem, and Lebesgue’s dominated convergence theorem.
513. Modern Analysis II. 3 credits. Prerequisite: Math 512. Product measures, Fubini’s theorem, the Radon Nikodym theorem, inequalities of Hölder and Minkowski, definitions and basic properties of normed spaces and Banach spaces, some classical Banach spaces such as Lp and lp, bounded linear operators, and dual spaces.
515, 516. Applied Mathematics. 3 credits each. Prerequisite: Math 266 or consent of instructor. The content of the course varies but includes current topics in applied mathematics such as: (1) ordinary or partial differential equations, (2) approximation theory and perturbation techniques, (3) modeling and computer simulation, (4) special functions, (5) numerical analysis, (6) variational methods, (7) transforms, (8) integral equations.
518, 519. Algebra I, II. 3 credits each. Prerequisite: Math 441 and 442. Group theory, rings and fields, vector spaces, Galois theory and finite fields.
520, 521. Topology I, II. 3 credits each. Prerequisite: Math 431. Point set topology, including metric spaces and such topics as homeomorphisms, separation axioms, compactness, connectedness, general convergence, compactification and metrizability.
541. Linear Statistical Models. 3 credits. Prerequisite: Math 422 or consent of instructor. Distributions of quadratic forms, general linear hypotheses of full rank, least squares, Gauss-Markoff theorem, estimability, parametric transformations, Cochran’s theorem, projection operators and conditional inverses in generalized least squares, applications to ANOVA and experimental design models.
542. Advanced Topics in Statistics and Probability. 3 credits. Prerequisite: Math 541 or consent of instructor. The content of the course varies but may include (but is not restricted to) current topics in statistics and probability such as (1) time series, (2) sampling, (3) nonparametric statistics, (4) experimental design, (5) probability theory, (6) statistical theory, (7) multivariate statistical analysis.
576. Algebra and Geometry for Middle School Teachers. 3 credits. Prerequisites: Must be a licensed K-12 teacher; college Algebra; instructor consent. Algebra and Geometry course intended for middle school teachers: a) planning to qualify to teach middle school mathematics; or b) teachers looking to enrich their content knowledge in mathematics. Topics may include: rational number system, introduction to number theory, algebraic thinking, spatial reasoning and representation, introduction to Euclidean and non-Euclidean geometry, problem solving and pedagogical issues. May not be used in Ph.D. or Master’s programs.
577. Calculus Concepts for Middle School Teachers. 3 credits. Prerequisites: Must be a licensed K-12 teacher; college Algebra; instructor consent. Calculus course intended for middle school teachers: a) planning to qualify to teach middle school mathematics; or b) teachers looking to enrich their content knowledge in mathematics. Topics may include: analysis of functions, mathematical modeling, limits, continuity, differentiation, integration, and pedagogical issues. May not be used in Ph.D. or Master’s programs.
578. Probability and Statistics for Middle School Teachers. 3 credits. Prerequisites: Must be a licensed K-12 teacher; college Algebra; instructor consent. Probability and statistics course intended for middle school teachers: a) planning to qualify to teach middle school mathematics; or b) teachers looking to enrich their content knowledge in mathematics. Topics may include: counting, empirical and theoretical probabilities, simulation of probabilistic events, conditional probability, expected value, data and variables, random sampling, measures of central tendency and spread, least squares regression, and pedagogical issues. May not be used in Ph.D. or Master’s programs.
579. Practicum in Middle School Mathematics. 2 credits. Prerequisites: Must be a licensed K-12 teacher; Math 576, 577 or 578; instructor consent. Teachers will use their content and pedagogical knowledge to plan lesson(s) and develop and implement an action research project in their school. May be repeated for up to 6 credits. May not be used in Ph.D. or Master’s programs.
403. Theory of Probability. 3 credits.
405. Selected Topics in Mathematics. 1 to 3 credits.
408. Combinaturics. 3 credits.
409. Geometry. 3 credits.
412. Differential Equations. 3 credits.
415. Topics in Applied Mathematics. 1 to 3 credits.
416. Topics in Statistics. 1 to 3 credits.
421, 422. Statistical Theory. 6 credits.
431, 432. Advanced Calculus. 6 credits.
435. Theory of Numbers. 3 credits.
441. Abstract Algebra. 3 credits.
442. Linear Algebra. 3 credits.
450. Elements of Topology. 3 credits.
460. Mathematical Modeling. 3 credits.
461, 462. Numerical Analysis. 6 credits.
465. Topics in Operational Research. 3 credits.
471. Introduction to Complex Variables. 3 credits.
494, 495. Reading Course in Mathematics. Credit not to exceed 1 hour a semester and total credit not to exceed 3 hours.
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