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Course Criteria
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3.00 Credits
Prerequisite: MATH 221 or permission of the instructor. Algebra of complex numbers, polar form, powers, and roots. Derivatives and geometry of elementary functions. Line integrals, the Cauchy Integral Theorem, the Cauchy Integral formula, Taylor and Laurent Series, residues, and poles. Applications.
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3.00 Credits
Prerequisite: The equivalent of MATH 221 with C grade or better. Probability, probability density and distribution functions, mathematical expectation, discrete and continuous random variables, and moment generating functions.
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3.00 Credits
Prerequisite: MATH 309. Sampling distributions, point and interval estimation, testing hypotheses, regression and correlation, and analysis of variance.
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3.00 Credits
Prerequisites: MATH 221 with C grade or better; MATH 301 is recommended. Basic properties of real numbers, elementary topology of the real line and Euclidean spaces, and continuity and differentiability of real-valued functions on Euclidean spaces.
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3.00 Credits
Prerequisite: MATH 311. Riemann integration, nature and consequences of various types of convergence of sequences and series of functions, some special series, and related topics.
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3.00 Credits
Prerequisites: MATH 222; MATH 301 is recommended. Groups, including normal subgroups, quotient groups, permutation groups. Cauchy’s theorem and Sylow’s theorems.
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3.00 Credits
Prerequisite: MATH 321. Rings, including ideals, quotient rings, Euclidean rings, polynomial rings. Fields of quotients of an integral domain. Further field theory as time permits.
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3.00 Credits
Prerequisite: MATH 221 with C grade or better. First and second order differential equations, systems of differential equations, and applications. Techniques employed are analytic, qualitative, and numerical.
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3.00 Credits
Prerequisite: MATH 332. An introduction to the study of boundary value problems and partial differential equations. Topics include modeling heat and wave phenomena, Fourier series, separation of variables, and Bessel functions. Techniques employed are analytic, qualitative, and numerical.
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3.00 Credits
Prerequisite: MATH 221. A study of the shape of space focusing on characteristics not detected by geometry alone. Topics are approached pragmatically and include point set topology of Euclidean space, map-coloring problems, knots, the shape of the universe, surfaces, graphs and trees, the fundamental group, the Jordan Curve Theorem, and homology.
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