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Course Criteria
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3.00 Credits
Explains the foundation and structure of how geometry develops, including projective, Euclidean, non-Euclidean and finite geometries studied by means of transformations and axiom systems. Lec. 3 hrs. Pre-requisite: MATH 176 & MATH 225 or CC.
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3.00 Credits
Continues MATH 431. Studies algebraic projective geometry; linear algebra; vector algebra; generalized coordinate systems, and linear transformations. Lec. 3 hrs. Pre-requisite: MATH 431 or CC.
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3.00 Credits
Develops tangent vectors, normal planes, curvature, principal normals, torsion, Frenet equations, co-ordinate systems, tangent planes, and normal lines. Also involves the first and second fundamental forms, normal and principal curves, Gaussian, and mean curvature, in addition to the fundamental theorem of surfaces, applications of multilinear algebra to surfaces, geodesics, and differential forms. Lec. 3 hrs. Pre-requisite: MATH 254 or MATH 260, and MATH 352 or CC.
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3.00 Credits
Examines open sets, topologies, closed sets, neighborhoods, limit points, and closures and interiors. Also covers derived sets, bases, continuity, homeomorphisms, and connectedness and compactness. Lec. 3 hrs. Pre-requisite: MATH 176 or CC.
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3.00 Credits
Examines metric spaces, the Bolzano-Weierstrass theorem, Cantor sets, sequences of functions, Borel sets and Baire functions. Also examines well orderings, measure and measurable sets, and Lebesgue integration and measure. Lec. 3 hrs. Pre-requisite: MATH 352 or CC.
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3.00 Credits
Continuation of MATH 451. Includes Banach and Hilbert spaces, the Hahn-Banach theorem, the open-mapping theorem, operators, dual and double dual spaces, and reflexive Banach spaces. Lec. 3 hrs. Pre-requisite: MATH 451 or CC.
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3.00 Credits
Investigates complex numbers and their geometry, functions and limits, derivatives and elementary functions, line integrals, and Cauchy's theorems and applications. Also includes power and Laurent series, and residues and applications. Lec. 3 hrs. Pre-requisite: MATH 351 or CC.
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3.00 Credits
Continues MATH 461. Further examines topics in power series, conformal mappings, and harmonic functions and their applications. Lec. 3 hrs. Pre-requisite: MATH 461 or CC.
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3.00 Credits
Includes propositional logic and predicate logic. Also covers the formalization of arithmetic and Gödel's theorems, and applications to automata and data structures. Provides instruction for students who have had some experience proving theorems and desire a rigorous introduction to the foundations of mathematics. Lec. 3 hrs. Pre-requisite: MATH 411 or CC.
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3.00 Credits
Explores distribution and functions of random variables, sampling theory, order statistics, point estimation, confidence intervals, and introduction to tests of hypothesis and analysis of variance from mathematical point of view. Usually offered every fall. Lec. 3 hrs. Pre-requisite: MATH 351 & MATH 382 or CC.
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