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MATH
5509
General Algebra I
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Groups, rings, modules, homology, fields and Galois theory, valuations, matrices, and multilinear algebra. Prerequisite: MATH 410 or equivalent. Note: Continued in MATH 5519.
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3 hrs
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MATH
5510
Complex Variables I
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The group of linear fractional transformations, complex integration, Cauchy's theorem, the maximum modulus theorem, analytic continuation, Riemann surfaces. Note: Continued in MATH 5520. Prerequisite: MATH 402 and MATH 407, or consent of instructor.
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3 hrs
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MATH
5513
Real Variables I
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Theory of measure with applications to analysis. Riemann and Lebesgue integration. Note: Continued in MATH 5523. Prerequisite: MATH 402.
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3 hrs
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MATH
5514
Mathematics For Secondary Teachers: Algebra And Analysis
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Designed for secondary-school teachers. Examine high school mathematics from a higher point of view. Real and complex numbers, functions, algebraic structures of equations, integers and polynomials, number system structures; analyses of alternate approaches, extensions and applications of mathematical ideas, discussion of historical contexts and connections between ideas that may have been studied separately in different courses, relationships of ideas studied in secondary-school to those students may encounter in later study. When taken for graduate credit as MATH 5514, an extra project is required. Prerequisites: MATH 220 , MATH 301, and one of MATH 402 or MATH 410 Offered: Every Winter
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3 hrs
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MATH
5517
Matrix Theory I
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Unitary matrices, normal matrices, Jordan canonical form, nonnegative matrices and their applications, the symmetric eigenvalue problem. Prerequisites: MATH 402 and MATH 420, or consent of the instructor
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3 hrs
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MATH
5521
Differential Equations
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This course offers an introduction to the qualitative theory and applications of ordinary differential equations (ODE). The presentation of the course will be a blend of fundamental theory and examples. The basic results will be proved rigorously and more advanced results will be only illustrated by examples that demonstrate when and how they may be applied. Prerequisites: MATH 345,MATH 412 and MATH 420, or consent of the instructor.
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3 hrs
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MATH
5524
Mathematics For Secondary Teachers: Geometry
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Designed for secondary-school teachers. Examine high school mathematics from a higher point of view. Congruence, distance and similarity, trigonometry, area and volume, axiomatics and Euclidean geometry; analyses of alternate approaches, extensions, and applications of mathematical ideas, discussion of historical contexts and connections between ideas that may have been studied separately in different courses, relationships of ideas studied in secondary-school to those students may encounter in later study. When taken for graduate credit as MATH 5524, an extra project is required. Prerequisites: MATH 220, MATH 301, and one of MATH 402 or MATH 410 Offered: Every Fall on Demand
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3 hrs
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MATH
5530
Axiomatic Set Theory
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Zermelo-Fraenkel set theory, transfinite induction equivalents of the axiom of choice, cardinal and ordinal arithmetic, the generalized continuum hypothesis, inaccessible cardinals.
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3 hrs
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MATH
5532
Advanced Numerical Analysis I
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Error Analysis, Solving Systems of Linear Equations, Solutions of Nonlinear Equations, the Least-Squares Problems, and Approximating functions. Prerequisite: MATH 402 and MATH 420 or consent of instructor. Note: Continued in MATH 5542.
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3 hrs
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MATH
5542
Advanced Numerical Analysis II
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Eigenvalues and Eigenvectors, Linear Programming, Optimization, Numerical Differentiation and Integration, Numerical Solution of Ordinary and Partial Differential Equations. Prerequisite: MATH 532 or consent of instructor. Note: Continuation of MATH 5532.
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3 hrs
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MATH
5545
Mathematical Methods In Science And Engineering
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This course offers applied linear algebra and Fourier analysis which are indispensable tools in science and engineering. It is designed for beginning graduate students with moderate background in linear algebra and real analysis. Many of the results that are presented in the course will be proved rigorously from mathematical point of view. Prerequisites: MATH 402 and MATH 420
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3 hrs
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MATH
5552
General Topology
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Topological spaces, continuity, metric spaces, topological products, connectedness, compactness, separation axioms, convergence, metrization theorems, Tychynoff's Theorem. Other topics may include: homotopy, fundamental group, function spaces. Prerequisites: MATH 402, or consent of instructor
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3 hrs
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MATH
5557
Functional Analysis
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Hilbert spaces, linear operators, compact operators, Banach spaces, the Hahn-Banach theorem, the open mapping and closed graph theorems, the principle of uniform boundedness, locally convex spaces. Prerequisites: MATH 402 and MATH 420
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3 hrs
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Selected topics in various fields of mathematics. May be repeated for credit when the topic varies. Prerequisite: Consent of instructor.
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1-3 hrs
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MATH
5699
Research And Thesis
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Doctoral dissertation.
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1-16 hrs
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MATH
5899
Required Graduate Enrollment
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1 hr
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Graduate Courses