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Course Criteria
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4.00 Credits
A team-based, project-oriented, hands-on introduction to great concepts and discoveries in logic and computability, including Turing Machines, first order logic, the limitations of computing machines, Godel's incompleteness results and so forth. A hands-on laboratory component is included. Prerequisites/Corequisites: Prerequisite: PHIL 2140. When Offered: Spring term annually . Cross Listed: (Cross-listed as PHIL 4420. Students cannot obtain credit for both this course and PHIL 4420.) Credit Hours: 4
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4.00 Credits
Topics include general topological spaces, connectedness, compactness, continuity, and product spaces. Additional topics may be chosen from identification spaces, homotopy, the fundamental group, covering maps, lifts, classification of surfaces, Baire category, dimension, and the Jordan curve theorem. Prerequisites/Corequisites: Prerequisite: MATH 4090 or graduate standing or permission of the instructor. When Offered: Fall term even numbered years. Credit Hours: 4
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4.00 Credits
The course provides an opportunity for the development of theorem-proving skills in the field of mathematical analysis. Expansion of a knowledge base comes as a by-product of energy expended in theorem proving and subsequent exposition. Analysis topics included are: sets, functions, the real numbers, cardinality, induction, decimal representations of real numbers, Euclidean spaces, abstract vector spaces and metric spaces. This is a communication-intensive course. Prerequisites/Corequisites: Prerequisite: Mathematics major, Corequisite: MATH-2010 or permission of instructor. When Offered: Fall and spring. Credit Hours: 4
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4.00 Credits
The theory underlying vector spaces, algebra of subspaces, bases; linear transformations, dual spaces; eigenvectors, eigenvalues, minimal polynomials, canonical forms of linear transformations; inner products, adjoints, orthogonal projections and complements. Prerequisites/Corequisites: Prerequisite: MATH 2010. When Offered: Fall term annually. Credit Hours: 4
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4.00 Credits
Topics may be chosen from differential geometry of curves and surfaces, involutes and evolutes, order of contact, developable surfaces, Euler's and Meusnier's Theorem, mean and Gaussian curvatures, geodesics and parallel transport, The Theorem Egregium of Gauss, Gauss-Bonnet Theorem, computer-aided geometric design, computational geometry, tessellations, tiling and patterns, projective and non-Euclidean geometries, postulates and axiomatic systems, advanced Euclidean geometry, and the history of geometry.Prerequisites/Corequisites: Prerequisites: MATH 2010 and MATH 4600 or permission of the instructor. When Offered: Spring term even-numbered years. Credit Hours: 4
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4.00 Credits
Fundamental concepts and methods of graph theory and its applications in various areas of computing and the social and natural sciences. Topics include graphs as models, representation of graphs, trees, distances, matchings, connectivity, flows in networks, graph colorings, Hamiltoniancycles, traveling salesman problem, planarity. All concepts, methods, and applications are presented through a sequence of exercises and problems, many of which are done with the help of novel software systems for combinatorial computing. Prerequisites/Corequisites: Prerequisite: MATH 2800 and CSCI 1100. Spring term even-numbered years. When Offered: Spring term even-numbered years. Cross Listed: Crosslisted as CSCI 4260. Students cannot obtain credit for both this course and CSCI 4260. Credit Hours: 4
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4.00 Credits
Fundamental concepts of mathematical analysis. A two-term sequence covering such topics as the real number system, limits, sequences, series, convergence, uniform convergence, functions of one variable, continuity, differentiability, Riemann integration, Stone-Weierstrass Theorem, functions of several variables, trigonometric series, differential forms on manifolds, and the higher dimensional Stokes Theorem. Prerequisites/Corequisites: Prerequisites: MATH 1020 and MATH 4090 or graduate standing or permission of the instructor. When Offered: Spring-fall sequence annually. Credit Hours: 4
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4.00 Credits
Fundamental concepts of mathematical analysis. A two-term sequence covering such topics as the real number system, limits, sequences, series, convergence, uniform convergence, functions of one variable, continuity, differentiability, Riemann integration, Stone-Weierstrass Theorem, functions of several variables, trigonometric series, differential forms on manifolds, and the higher dimensional Stokes Theorem. Prerequisites/Corequisites: Prerequisites: MATH 1020 and MATH 4090 or graduate standing or permission of the instructor. When Offered: Spring-fall sequence annually. Credit Hours: 4
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4.00 Credits
An introduction to the theory and applications of complex variables. Topics include analytic functions, Riemann surfaces, complex integration, Taylor and Laurent series, residues, conformal mapping, harmonic functions, and Laplace transforms. Applications will be to problems in science and engineering such as fluid and heat flow, dynamical systems, and electrostatics. Prerequisites/Corequisites: Prerequisite: MATH 2010 or equivalent. When Offered: Spring term annually . Credit Hours: 4
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4.00 Credits
An intermediate course emphasizing a modern geometric approach and applications in science and engineering. Topics include first-order equations, linear systems, phase plane, linearization and stability, calculus of variations, Lagrangian and Hamiltonian mechanics, oscillations, basic bifurcation theory, chaotic dynamics, and existence and uniqueness. Prerequisites/Corequisites: Prerequisite: MATH 2400 or permission of instructor. When Offered: Fall term annually. Credit Hours: 4
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