MATH 5509      General Algebra I
Groups, rings, modules, homology, fields and Galois theory, valuations, matrices, and multilinear algebra. Prerequisite: MATH 410 and Math 420. Note: Continued in MATH 5519.
Credits: 3 hours
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MATH 5510      Complex Variables I
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.
Credits: 3 hours
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MATH 5513      Real Variables I
Theory of measure with applications to analysis. Riemann and Lebesgue integration. Note: Continued in MATH 5523. Prerequisite: Math 402 and Math 412, or consent of instructor.
Credits: 3 hours
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MATH 5514      Mathematics For Secondary Teachers: Algebra And Analysis
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 300 and Math 201
Credits: 3 hours
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MATH 5517      Matrix Theory I
Unitary matrices, normal matrices, Jordan canonical form, nonnegative matrices and their applications, the symmetric eigenvalue problem. Prerequisites: MATH 420.
Credits: 3 hours
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MATH 5519      General Algebra II
Continuation of MATH 5509.
Credits: 3 hours
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MATH 5520      Complex Variables II
Continuation of MATH 5510.
Credits: 3 hours
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MATH 5521      Differential Equations
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.
Credits: 3 hours
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MATH 5523      Real Variables II
Continuation of MATH 5513.
Credits: 3 hours
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MATH 5524      Mathematics For Secondary Teachers: Geometry
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 300 and Math 301.
Credits: 3 hours
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MATH 5527      Matrix Theory II
Continuation of Math 517.
Credits: 3 hours
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MATH 5532      Advanced Numerical Analysis I
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.
Credits: 3 hours
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MATH 5542      Advanced Numerical Analysis II
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.
Credits: 3 hours
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MATH 5545      Mathematical Methods In Science And Engineering
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, Math 406, and Math 420, or consent of instructor.
Credits: 3 hours
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MATH 5557      Functional Analysis
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
Credits: 3 hours
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MATH 5590      Special Topics
Selected topics in various fields of mathematics. May be repeated for credit when the topic varies. Prerequisite: Consent of instructor.
Credits: 1-3 hours
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MATH 5699      Research And Thesis
Doctoral dissertation.
Credits: 1-16 hours
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MATH 5899      Required Graduate Enrollment
Credits: 1 hours
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