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MATH 431: Modern Geometry I
3.00 Credits
University of the District of Columbia
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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MATH 431 - Modern Geometry I
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MATH 432: Modern Geometry II
3.00 Credits
University of the District of Columbia
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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MATH 432 - Modern Geometry II
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MATH 435: Differential Geometry
3.00 Credits
University of the District of Columbia
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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MATH 435 - Differential Geometry
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MATH 445: Topology
3.00 Credits
University of the District of Columbia
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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MATH 445 - Topology
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MATH 451: Real Analysis I
3.00 Credits
University of the District of Columbia
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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MATH 451 - Real Analysis I
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MATH 452: Real Analysis II
3.00 Credits
University of the District of Columbia
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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MATH 452 - Real Analysis II
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MATH 461: Complex Analysis I
3.00 Credits
University of the District of Columbia
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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MATH 461 - Complex Analysis I
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MATH 462: Complex Analysis II
3.00 Credits
University of the District of Columbia
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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MATH 462 - Complex Analysis II
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MATH 475: Mathematical Logic
3.00 Credits
University of the District of Columbia
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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MATH 475 - Mathematical Logic
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MATH 480: Mathematical Statistics I
3.00 Credits
University of the District of Columbia
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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MATH 480 - Mathematical Statistics I
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