Mathematics (MATH) Graduate Course Descriptions
MATH 521. Introduction to Real Analysis I.
The real number system, sequences and limits, continuity and differentiation. Upper and lower bounds, the completeness axiom for real numbers, Cauchy sequences, the Bolzano-Weierstrass property, the extreme value theorem, the intermediate value theorem, the mean value theorem, L'Hospital's rule and Taylor's theorem. Prereq.: 222, 253. 3 credits F, ALT.
MATH 522. Introduction to Real Analysis II.
Series, power series, uniform and pointwise convergence, Reimann integration, and applications. Prereq.: 421/521. 3 credits DEMAND.
MATH 523. Complex Variables I.
The complex field, the theory of analytic functions, power series. Fundamental theorem of algebra. Prereq.: 311 or 321. 3 credits DEMAND.
MATH 527. Partial Differential Equations.
Partial differential equations of mathematical physics, boundary value problems, classical solution methods, Bessel functions. Prereq.: (311 or 321), 325. 3 credits S, ALT.
MATH 531. Professional Subject Matter for Middle Grades Mathematics.
Number sense, patterns and functions, number theory, geometry, data analysis and probability, current curriculum and pedagogical developments, lesson planning, and microteaching. For teacher candidates only. Prereq.: for Elementary Ed.majors: MATH 171, 112, and 330. Prereq. For Secondary Ed. majors: ED 300, MATH 321 and 373, or permission of instructor. 3 credits F.
MATH 532. Professional Subject Matter for Secondary School Mathematics.
For teacher candidates only. Algebra, geometry, data analysis, and advanced topics; current curriculum and pedagogical developments, lesson planning, and macroteaching. Must be taken concurrently with ED 521 or ED 537, but not with MATH 531. 4 credits F.
MATH 533. Algebra for Elementary and Middle School Teachers.
Algebraic concepts, representations, structures and applications. Prereq.: 330 or permission of instructor. 3 credits F.
MATH 535. Teaching Problem Solving in Elementary School Mathematics.
Problem solving strategies, teaching problem solving, problem solving via concrete materials, cooperative learning. For elementary education majors only. Prereq.: 330 or permission of instructor. 3 credits F.
MATH 536. Data Analysis and Probability for K-8 Teachers.
Data collection and organization; measures of central tendency and variance; inferences and convincing arguments; subjective, theoretical, experimental, and conditional probability; simulation; counting principles; mathematical expectation. Techniques, technology, and current trends in the teaching and learning of data analysis and probability. Prereq.: 112, 171, and 330. 3 credits S.
MATH 537. Geometry for K-8 Teachers.
Geometric concepts, spatial visualization, spatial reasoning, justification, and proof. Techniques, technology, and current trends in the teaching and learning of geometry. Prereq.: 112, 171 or 211, and 330. 3 credits F.
MATH 539. Using Technology to Teach Science and Mathematics, K-8.
Demonstrating and exploring technology, such as computers and calculators, that enhances mathematics and science learning and instruction in the K-8 curriculum. Lab. Prereq.: 330 or permission of instructor. 3 credits S.
MATH 552. Numerical Analysis.
Round-off error and computer arithmetic. Solutions of equations in one variable. Interpolation and polynomial approximation. Numerical integration and differentiation. Error analysis. Prereq.: 222, 252 or permission of instructor. 3 credits F, ALT.
MATH 553. Numerical Linear Algebra.
Direct and iterative solutions in linear algebra. Orthogonal polynomials, splines and least squares approximations. Error analysis. Prereq.: 222, either 311 or 312, and either 252 or CSCI 201. 3 credits F, ALT.
MATH 561. Modern Algebra I.
Groups, subgroups, cyclic groups, permutation groups, isomorphisms, Cayley's theorem, cosets, LaGrange's theorem, normal subgroups, quotient groups, homomorphisms, the first isomorphism theorem construction of the integers and rational numbers from the natural numbers, rings, integral domains, and fields. Prereq.: 273, and either 311 or 312 or consent of instructor. 4 credits F, S.
MATH 562. Modern Algebra II.
Ideals, factor rings, ring homomorphisms, polynomial rings, factorization of polynomials, irreducible polynomials, Euclidean domains, introduction to fields, extension fields, splitting fields, algebraic and transcendental numbers, geometric construction. Prereq.: 561. 3 credits DEMAND.
MATH 565. Elements of Geometry
An analysis of axiomatic systems, a critique of Euclid, an axiomatic development of neutral, Euclidean, Llobachevskian and Riemannian geometrics, and an introduction to transformational geometry. Prereq.: high school geometry, 273 and 312. 3 credits S.
MATH 580. Topics in Mathematics.
Designed for intensive study in a special topic in pure or applied mathematics. Topic will be announced in class schedule. Approval of instructor required for enrollment. May be repeated to a maximum of six credits. 3 credits DEMAND.
MATH 582. Student Teaching Seminar.
Reflections of and extensions of the student teaching experience in a seminar format; individual classroom observations. Must be taken concurrently with student teaching. S/U grading option only. 2 credits F, S.
MATH 583. Topics in Elementary School Mathematics.
In depth study of a special topic in mathematics relevant to the elementary school curriculum. Prereq.: 330 or permission of instructor. 3 credits DEMAND.
Mathematics (MATH) Courses for Graduate Students Only
MATH 610. Advanced Engineering Mathematics.
Ordinary differential equations, series solutions, transforms, boundary value problems, vector calculus, partial differential equations. Prereq.: 311 or 321, 325. 3 credits F.
MATH 630. Topics in Mathematics Education.
In-depth study of a special topic in mathematics education: topic to be announced in class schedule. May be repeated to a maximum of six credits to be applied to M. S. in mathematics. Grading option: S/U or ABCD. Prereq.: approval of instructor. 1-3 credits DEMAND.
MATH 631. Teaching Mathematics in the Junior High School.
Selected topics including: current curriculum and pedagogical developments; mathematics content, materials, and approaches; assessment, remediation, research. 3 credits F, ALT.
MATH 632. Teaching Mathematics in the Secondary School.
Selected topics including: mathematical perspectives and processes; mathematics content, materials, and approaches; assessment and remediation; research. 3 credits F, SUM, ALT.
MATH 633. Research Implications for Mathematics Learning and Teaching.
Implications for classroom practice of current and past research on mathematics learning and teaching at the middle and secondary school levels. How students learn specific mathematical content within the context of mathematical learning theory. 3 credits DEMAND.
MATH 634. Teaching Geometry in the Secondary School.
Historical development, current issues and trends, curricular reform movements, experimental programs, research findings. 3 credits DEMAND.
MATH 635. Teaching Algebra in the Secondary School.
Historical development, current issues and trends, pedagogical issues, role of technology, special topics, experimental programs, assessment and research findings. 3 credits DEMAND.
MATH 636. Calculus for Secondary Teachers.
Advanced treatment of calculus concepts, including limits, the derivative, the integral, sequences, and series. Applications of calculus to real-world problems. 3 credits DEMAND.
MATH 660. Number Theory.
Prime and composite integers. Diophantine analysis, number congruences, quadratic residues. Prereq.: 561 or consent of instructor. 3 credits DEMAND.
MATH 661. Contemporary Geometry.
Geometric transformations on the Euclidean plane and in higher dimensions, axiomatic and analytic projective geometry, projective transformations, topological transformations, topology of surfaces and Euler's formula. Prereq.: 312, 561. 3 credits DEMAND.
MATH 662. History of Mathematics.
Historical survey of the development of mathematics. Prereq.: 221. 3 credits S, SUM, ALT.
MATH 699. Thesis.
1-6 credits DEMAND.
