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Course Criteria
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3.00 Credits
This course explores what computers can and can't do, although it does not require any background in computer science or programming.Topics include finite state machines, push-down automata, Turing machines and recursive functions; mechanisms for formal languages, such as regular grammars, context-free grammars, context-sensitive grammars; and decidable versus undecidable problems.Also listed as CS 342.(Prerequisite: MA 231 or permission of the department chair) Three credits.
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3.00 Credits
Topics in this course include counting techniques; axiomatic probability theory; discrete and continuous sample spaces; random variables, cumulative distribution functions, probability density and mass functions; joint distributions; expected value and moments; common distributions like the normal, binomial, and Poisson distributions; and limit laws.(Prerequisites: MA 231 or ME 241 and MA 227 or MA 271, or permission of the department chair) Three credits.
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3.00 Credits
This course covers transformations of random variables; statistical application of probability; theory of sampling and the Central Limit Theorem; variances of sums and averages; estimation and hypothesis testing; and least squares, curve-fitting, and regression.(Prerequisite: MA 351 or permission of the department chair) Three credits.
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3.00 Credits
This course investigates three topics in greater depth than can be done in the first linear or abstract algebra course.Topics may include canonical forms for matrices, metric linear algebra, ideal theory, finite non-abelian groups, and Galois theory.The course typically includes one linear and one abstract algebra topic.(Prerequisite: MA 334 or permission of the department chair) Three credits.
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3.00 Credits
This course examines the set of real numbers as a complete, ordered, archimedean field; R as a linear vector space equipped with inner product and norm; metrics, particularly Euclidean, on R, topological concepts: continuity, connectedness, and compactness; the intermediate value, extreme value, monotone convergence, Bolzano/Weierstrass and Heine/Borel theorems; convergence and uniform convergence of sequences of continuous functions; differentiation: the mean value, implicit and inverse function theorems.(Prerequisites: MA 231 and MA 272 or permission of the department chair) Three credits.
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3.00 Credits
Topics in this course include algebra of complex numbers, Cauchy-Riemann equations and analytic functions, complex differentiation, integration in the complex plane, Cauchy's Theorem and integral formula, conformal mapping, Laurent series and residue theory, and applications.(Prerequisite: MA 371 or permission of the department chair) Three credits.
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3.00 Credits
This course investigates computer arithmetic, round-off errors, the solution of nonlinear equations, polynomial approximation, numerical differentiation and integration, and the solution of systems of linear equations via student-written code to implement the algorithms and/or the use of available software.Also listed as CS 377.(Prerequisites: MA 172, MA 235 and proficiency in a computer language, or permission of the department chair) Three credits.
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3.00 Credits
Topics in this course include: foundation for plane geometries; theorems of Menelaus, Ceva, Desargues, Pascal, Brianchon, and Feuerbach; inversion and reciprocation transformations; projective, Riemannian and Lobachevskian geometries; and Poincarè model.(Prerequisites: MA 231 and MA 235 or permission of the department chair) Three credits.
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3.00 Credits
This course considers topological spaces, continuous functions; product, metric, and quotient spaces; countability and separation axioms; existence and extension of continuous functions; compactification; metrization theorems and complete metric spaces.(Prerequisite: MA 371 or permission of the department chair) Three credits.
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3.00 Credits
Participation is open to senior mathematics majors with a 3.50 or higher GPA in mathematics and invited junior and senior mathematics majors with demonstrated ability who have been recommended by the mathematics faculty.This seminar provides talented students with an opportunity to undertake individualized study under faculty direction.Participants present several reports on their findings before a group of peers.The seminar's subject matter varies each semester.Three credits.
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