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2015-2016 Graduate Catalog [ARCHIVED CATALOG]
Graduate Courses
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Mathematics and Statistics |
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MAT 500 - Topics in Graduate Mathematics
Topics in mathematics not regularly covered in other courses. Content varies to suit current needs. May be repeated for credit.
Prerequisites & Notes
departmental permission.
Credits: 1-3
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MAT 523 - Functions of a Real Variable I
Topics include construction of Lebesgue measure and Lebesgue integral on the Euclidean Space, convergence, differentiation, general measure and integration, the Radon-Nikodym Theorem, the Daniell integral, topics in functional analysis.
Prerequisites & Notes
A grade of C or better in MAT 426 or permission.
Credits: 3
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MAT 524 - Functions of a Real Variable II
A continuation of MAT 523.
Prerequisites & Notes
A grade of C or better in MAT 523.
Credits: 3
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MAT 527 - Functions of a Complex Variable I
Elementary properties of holomorphic functions including the classification of isolated singularities, Laurent expansion and infinite product representations. Introduction to conformal mapping and the Riemann Mapping Theorem.
Prerequisites & Notes
A grade of C or better in MAT 426 or permission.
Credits: 3
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MAT 528 - Functions of a Complex Variable II
A grade of C or better in Continuation of MAT 527.
Prerequisites & Notes
MAT 527.
Credits: 3
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MAT 562 - Advanced Linear Algebra
Topics covered include vector spaces, homomorphisms, bilinear forms, multilinear maps and tensor products, Jordan canonical forms of matrices, normed linear spaces, real and complex inner product spaces, basic ideas of functional analysis, applications.
Prerequisites & Notes
A grade of C or better in MAT 262 and MAT 425 and MAT 463 or their equivalent.
Credits: 3
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MAT 563 - Abstract Algebra
A study of basic structure theorems for groups, rings, fields and modules.
Prerequisites & Notes
A grade of C or better in two courses from among MAT 262, MAT 463 and MAT 464.
Credits: 3
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MAT 564 - Abstract Algebra II
A continuation of MAT 563, to include more advanced topics in ring theory; module theory with applications to canonical forms in linear algebra; fields and Galois theory; other topics in algebra as time and interest allow.
Prerequisites & Notes
MAT 563
Credits: 3
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MAT 577 - Topology I
Fundamental concepts of topology, including cardinal and ordinal numbers, topological spaces, cartesian products, connectedness, compactness, continuity, separation axioms and metric spaces.
Prerequisites & Notes
A grade of C or better in MAT 425 or permission.
Credits: 3
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MAT 578 - Topology II
A continuation of MAT 577.
Prerequisites & Notes
A grade of C or better in MAT 577.
Credits: 3
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MAT 586 - Biological Modeling and Simulation
Mathematical and computational models primarily from population biology and epidemiology, including deterministic and stochastic, discrete- and continuous-time, and spatial and network models. A software package such as Matlab or R will be used for simulations and visualization, and for additional topics such as vectorized calculations, function optimization, and differential equation solvers, which have a wide variety of applications in the sciences and engineering.
Prerequisites & Notes
Permission of instructor.
Credits: 3
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MAT 590 - Graduate Research Seminar
Current topics of mathematical interest are studied under faculty supervision. May be repeated for credit to a maximum of four times.
Credits: 1
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MAT 699 - Graduate Thesis/Research
Graduate thesis or research conducted under the supervision of student’s advisor.
Prerequisites & Notes
A “Responsible Conduct of Research” course approved by the Office of Research and Sponsored Programs and the Graduate School (www.umaine.edu/graduate/responsible-conduct-research) is required before or concurrently with completion of 3rd XXX 699 credit. Permission
Credits: Ar
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STS 531 - Mathematical Statistics I
Covers axioms of probability, random variables, continuous and discrete distributions, moment generating functions, distributions of functions of random variables, sampling distributions.
Prerequisites & Notes
A grade of C or better in MAT 425, STS 434 or permission.
Credits: 3
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STS 532 - Mathematical Statistics II
Topics include principles and methods of parametric point estimation, interval estimation and hypothesis testing, non-parametric inference.
Prerequisites & Notes
A grade of C or better in STS 531.
Credits: 3
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STS 533 - Stochastic Systems
The study of mathematical models which involve random processes. Topics include Poisson process, waiting-line models, Markov chains, decision analysis and reliability theory. Some emphasis on modeling problems encountered in business and industry.
Prerequisites & Notes
A grade of C or better in STS 434.
Credits: 3
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