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Course Criteria
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1.00 - 3.00 Credits
Individualized special projects in mathematics and its applications for inquisitive and well-prepared sophomore-level undergraduate students. No credit allowed toward a major or minor in mathematics. S/U grading. Prerequisites: approval of department chair and instructor.
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3.00 Credits
Logic and methods of proof, set theory, combinations and permutations, equivalence relations and functions, mathematical induction and recurrence relations, cardinality (finite, countably infinite, and uncountable sets), and decimal representation of the rational and real numbers. Prerequisites: MA 172 and either MA 201 or MA 244.
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3.00 Credits
This course is a calculus-based introduction to probability with special emphasis on the interplay between probability and statistics. Topics include descriptive statistics; probability spaces; discrete distributions (including the binomial, geometric, hypergeometric, and Poisson); continuous distributions (including the uniform, exponential, and normal); joint distributions; mean, variance, and general expected value; independence and correlation; the law of large numbers; and the central limit theorem. Prerequisites: MA 120 or MA 172, and one MA course at the 200-level or above.
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3.00 Credits
Individualized special projects in mathematics and its applications for inquisitive and well-prepared junior-level undergraduate students. No credit allowed toward a major or minor in mathematics. S/U grading. Prerequisites: approval of department chair and instructor. 321 415 Introduction to Numerical Methods (3 hrs) Derivation and analysis of approximate methods for the solution of nonlinear equations, interpolation and integration of functions, and techniques for the solution of systems of linear equations and for approximating solutions of elementary differential equations. Emphasis is placed on obtaining an intuitive understanding of both the problem at hand and the numerical method used to solve it. Prerequisites: MA 201, MA 244, CS 121. Lab fee: $40.
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3.00 Credits
This is a second course in differential equations. Course topics include series solutions for second order differential equations and the method of Frobenious; eigenvalue and eigenvector methods for solving systems of linear first order equations; the qualitative theory of nonlinear equations; boundary value problems and the Sturm-Liouville theory. Prerequisites: MA 201, MA 238, and MA 244.
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3.00 Credits
Axiomatic development of geometry, introduction to non-Euclidean geometries with emphasis in elliptic and hyperbolic geometries, selected topics in Euclidean geometry. Prerequisites: MA 244 and MA 330.
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3.00 Credits
Mappings, binary operations, equivalence relations, groups and subgroups, Lagrange's theorem, homomorphisms and isomorphisms, normal subgroups and quotient groups, rings, fields, ordered integral domains, fields of quotients, error correcting codes, linear codes, and decoding. Prerequisites: MA 244 and either MA 330 or MA 385.
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3.00 Credits
Counting, pigeonhole principle, permutations and combinations, generating functions, principle of inclusion and exclusion, Polya's theory of counting. Prerequisites: MA 385 or MA 442. (MA 442 may be taken as a prerequisite with concurrency.)
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3.00 Credits
Sequences, limits, continuity, differentiation of functions of one real variable, Riemann integration, uniform convergence, sequences and series of functions, power series, and Taylor series. Prerequisites: MA 330.
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3.00 Credits
Complex algebra, analytic functions, Cauchy-Riemann equations, exponential, trigonometric, and logarithmic functions, integration, Cauchy integral theorem, Morera's theorem, Liouville's theorem, maximum modulus theorem, residue theory,Taylor and Laurent series, and applications. Prerequisites: MA 201 and one MA course at the 300 level or above.
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