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Course Criteria
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3.00 Credits
Studies the elementary theory of groups, rings, fields, polynomials, group and ring homomorphisms, and isomorphisms. Prereq., MATH 3000, 3110, 3130, or 3200.
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3.00 Credits
Covers basic methods and results in combinatorial theory. Includes numeration methods, elementary properties of functions and relations, and graph theory. Emphasizes applications. Prereq., Calculus 2.
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3.00 Credits
Helps prepare students for MATH 4310 through studying the underlying structure of a space, with particular attention to open and closed sets and continuous functions. Includes basic set theory, metric spaces, Hausdorff spaces, general topological spaces, continuity, limits, homeomorphisms, connectedness, and compactness. Prereq., Calculus 3. Approved for the arts and sciences core curriculum: critical thinking.
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3.00 Credits
Axiomatic systems. Foundations of Euclidean and Lobachevskian geometries. Prereq., Calculus 3.
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3.00 Credits
Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Prereq., one upper-division mathematics course.
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3.00 Credits
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation, and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Prereqs., MATH 3130 or APPM 3310. Same as MATH 5120 and APPM 4120.
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3.00 Credits
Covers group actions, Sylow theory, Field theory, and some Galois theory. Prereq., MATH 3140.
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3.00 Credits
Introduces the modern differential geometry of plane curves, space curves, and surfaces in space. Computers are used, but no prior knowledge of computer programming is required. Prereqs., Calculus 3 and MATH 3130.
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3.00 Credits
Acquaints students with calculus of one variable. Topics include the real number system, continuity, differentiation, sequences and series, convergence, uniform convergence, Taylor's theorem, and integration. Prereqs., Calculus 3, and MATH 3000 or 3200. MATH 3130 highly recommended.
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3.00 Credits
Instructs students in calculus of several variables. Topics include continuity, differentiation and integration, implicit function theorem, inverse function theorem, and if time permits, Fourier series. Prereqs., MATH 4310, and MATH 3130 or APPM 2360.
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