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MAT 400 - Topics in 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 425 - Introduction to Real Analysis I
A study of functions of a real variable and the related topology of the real line. Concepts of limit, convergence, continuity and differentiability are studied.
Prerequisites & Notes
A grade of C or better in MAT 228 and MAT 261.
Credits: 3
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MAT 426 - Introduction to Real Analysis II
A continuation of MAT 425 emphasizing integration and sequences and series of functions. Contents may vary from year to year.
Prerequisites & Notes
MAT 425.
Credits: 3
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MAT 434 - Introduction to Statistics
Topics include probability, random variables, continuous and discrete distributions, point and interval estimation, tests of hypotheses, linear regression and correlation, analysis of variance.
Prerequisites & Notes
A grade of C or better in MAT 228.
Credits: 4
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MAT 435 - Introduction to Mathematical Statistics
Topics include moment generating functions, distribution of functions of random variables, sampling distributions, principles of estimation and hypothesis testing, limit theorems and order statistics.
Prerequisites & Notes
A grade of C or better in MAT 434.
Credits: 3
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MAT 436 - Nonparametric Statistics
Surveys nonparametric alternatives to standard parametric techniques. Emphasis on situations in which the use of a parametric technique is incorrect or, at best, marginal.
Prerequisites & Notes
A grade of C or better in MAT 434 or MAT 437.
Credits: 3
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MAT 437 - Statistical Methods in Research
An introduction to analysis of variance and regression analysis using a unifying approach to theory; application and illustrations from many fields.
Prerequisites & Notes
A grade of C or better in MAT 232 or MAT 434 or permission.
Credits: 3
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MAT 445 - History of Mathematics
Deals with the lives and times of mathematicians, while focusing on mathematical ideas. Designed to acquaint the student with the evolution of various mathematical disciplines and to develop an appreciation of the problems faced by and often solved by mathematicians.
Prerequisites & Notes
A grade of C or better in MAT 127 or permission.
Credits: 3
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MAT 451 - Dynamical Systems
A study of the nature and behavior of solutions of linear and nonlinear systems of differential and difference equations through mathematical analysis and the use of available menu-driven PC software. For students in mathematics and the sciences. Some knowledge of vectors and matrices and some familiarity with personal computers is recommended.
Prerequisites & Notes
A grade of C or better in MAT 258 or MAT 259 or permission.
Credits: 3
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MAT 452 - Complex Analysis
An introduction to functions of complex variables including differentiation, integration, series, mappings and applications.
Prerequisites & Notes
A grade of C or better in MAT 228.
Credits: 3
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MAT 453 - Partial Differential Equations I
Introduction to general properties of partial differential equations followed by solutions of specific equations. Techniques include eigen function expansions, operational methods, and Green’s functions.
Prerequisites & Notes
A grade of C or better in MAT 259 or permission.
Credits: 3
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MAT 454 - Partial Differential Equations II
A continuation of MAT 453.
Prerequisites & Notes
A grade of C or better in MAT 453.
Credits: 3
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MAT 463 - Introduction to Abstract Algebra I
A study of algebraic systems composed of non-empty sets with binary operations defined on them, and characterized by specific axiom systems. Begins with a study of set theory, functions, and operations, and continues with topics selected from group theory and abstract linear algebra.
Prerequisites & Notes
A grade of C or better in MAT 261 and MAT 262.
Credits: 3
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MAT 464 - Introduction to Abstract Algebra II
A continuation of MAT 463, with emphasis on properties of rings and fields.
Prerequisites & Notes
A grade of C or better in MAT 463.
Credits: 3
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MAT 465 - Theory of Numbers
Elementary properties of integers including divisibility, prime and composite numbers, uniqueness of prime factorization, Diophantine equations, congruences and continued fractions.
Prerequisites & Notes
A grade of C or better in MAT 261 or permission.
Credits: 3
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MAT 471 - Differential Geometry
The application of multivariable calculus to the study of curves, surfaces and their higher-dimensional analogues.
Prerequisites & Notes
A grade of C or better in MAT 228 and either MAT 258 or MAT 262.
Credits: 3
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MAT 475 - Higher Geometry
Topics include: constructions, Euclidean properties, Ceva’s and Menelaus’ theorems with applications–Desargues’, Pappus’ and Pascal’s theorems, isometries, axiometric approach to one of the geometries, algebraic models for geometry, Klein’s Erlanger program, classical construction problems.
Prerequisites & Notes
A grade of C or better in MAT 228 or permission.
Credits: 3
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MAT 481 - Discrete Mathematics
Primarily designed for both mathematics and computer science majors. While the calculus-based mathematics of classical engineering and physical science is essentially “continuous,” the finite mathematics of computer science and some social sciences is essentially “discrete” or “combinatorial.” MAT 481 is an introductory course offered in this spirit. Topics covered typically include graphs and networks, analysis of algorithms, generating functions and recurrence relations, graph coloring, satisfiability, computational complexity, automata and languages, Turing machines and computability, and a brief introduction to the theory of NP-completeness.
Prerequisites & Notes
A grade of C or better in MAT 261 or MAT 262 or permission.
Credits: 3
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MAT 486 - 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
Some basic familiarity with probability and permission of the instructor.
Credits: 3
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MAT 487 - Numerical Analysis
An introduction to computational methods for solving numerical problems. Topics such as interpolation, systems of linear or nonlinear equations, numerical integration, eigenvalues, optimization, ordinary and partial differential equations are considered.
Prerequisites & Notes
A grade of C or better in MAT 127 or permission.
Credits: 3
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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 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, MAT 434 or permission.
Credits: 3
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MAT 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 MAT 531.
Credits: 3
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MAT 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 MAT 434.
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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Graduate School
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