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Course Criteria
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3.00 Credits
Introductory concepts, topologies and topological spaces, functions, continuity, homeomorphisms, connected spaces, compact spaces and applications of topology in analysis. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions..
Prerequisite:
MATH 311
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3.00 Credits
This course provides the linear algebra background necessary for a variety or applied fields as well as advanced work in algebra and analysis. Topics include vector spaces, linear transformations, dual spaces, matrices, matrix factorizations, matrix norms, determinants, eigenvalues and diagonalization, bilinear forms, projections, orthogonal and unitary transformations, Jordan canonical form, and infinite dimensional linear spaces. Applications such as an approximation theory, positive matrices, computation, multilinear algebra, and spectral theory will be selected by the instructor. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
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3.00 Credits
This course is a continuation of MATH 303. Topics will be chosen from rings, fields, ideals, factor rings, extension fields, automorphisms and Galois Theory. F. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions..
Prerequisite:
MATH 303
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3.00 Credits
The sequel to MATH 311, intended to prepare students for graduate study in measure theory and other analysis. Topics may include topological concepts in Rn, the calculus of multivariate and vector-valued functions, power series and uniform convergence, the Weierstrauss Approximation Theorem and generalizations of the Riemann integral. S. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions..
Prerequisite:
MATH 203 AND MATH 311
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3.00 Credits
This course provides a proof-based introduction to Complex Analysis. Topics include the complex number system, analytic and harmonic functions, power series, integrations, residue theory, analytic continuation, conformal mapping, and applications. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
Prerequisite:
MATH 311
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1.00 - 3.00 Credits
Directed reading in mathematics. Open to qualified seniors with permission of the Department of Mathematics. A student may take this course for one or two semesters, earning one to three hours credit each semester. Credit value in each case will be determined by the type of problem considered. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions..
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1.00 - 3.00 Credits
Directed reading in mathematics. Open to qualified seniors with permission of the Department of Mathematics. A student may take this course for one or two semesters, earning one to three hours credit each semester. Credit value in each case will be determined by the type of problem considered. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions..
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3.00 Credits
A systematic development of the differential and integral calculus of vector and tensor functions, followed by a brief introduction to differential geometry and the mathematics of theoretical physics. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions..
Prerequisite:
MATH 311
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3.00 Credits
This course provides an introduction to the three main classes of partial differential equations (hyperbolic, parabolic, and elliptic) that arise in the description of wave motion, diffusion processes, and potential theory. Topics include the study of initial and boundary value problems, and solution methods such as fundamental solutions and separation of variables. Additional topics may include the method of characteristics, Sturm-Liouville theory, Green's functions, integral transformations, and nonlinear partial differential equations. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
Prerequisite:
MATH 221 AND MATH 323
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3.00 Credits
This is a calculus based probability and statistics course. Topics will include probability functions and densities, mathematical expectations, sums of random variables, and sampling distributions. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
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