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Course Criteria
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0.00 - 4.00 Credits
This course will cover the fundamental theorems and algorithms of graph theory. The main topics are: connectivity, matching, graph coloring, planarity, the four-color theorem, extremal problems, network flows, and related algorithms.
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0.00 - 4.00 Credits
307 introduces students to Combinatorics, a fundamental mathematical discipline as well as an essential component of many mathematical areas. While in the past many of the basic combinatorial results were obtained by ingenuity and detailed reasoning, modern theory has grown out of this early stage and relies on deep, well-developed tools. The course covers over a dozen virtually independent topics including Ramsey Theory, Turan Theorem and Extremal Graph Theory, Probabilistic Arguments, Algebraic Methods and Spectral Techniques, chosen to illustrate several such techniques. This is a fun course, showcasing the gems of modern Combinatorics.
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0.00 - 4.00 Credits
The mathematical concept of a game is an abstraction which encompasses conflict-cooperation situations in which strategy (not just chance) plays a role. Central topics of the theory and some of its applications will be discussed. Introductory aspects of algorithmic game theory will be covered, if time permits.
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0.00 - 4.00 Credits
Propositional and predicate calculus. Godel completeness theorem. Finitary methods. Godel incompleteness theorem.
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0.00 - 4.00 Credits
Introduction to real analysis, Lebesgue theory of measure and integration on the line and n-dimensional space, introduction to Fourier Series.
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0.00 - 4.00 Credits
Calculus of functions of one complex variable, power series expansions, residues, and conformal mapping. Although the theory will be given adequate treatment, the emphasis of this course is the use of complex analysis as a tool for solving problems.
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0.00 - 4.00 Credits
Group theory, field extensions, splitting fields, the main theorem of Galois theory, cyclotomic extensions, Kummer extensions, solvability by radicals.
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0.00 - 4.00 Credits
Algebra & Applications: To develop curiousity about algebraic structures by exploring examples that connect to higher mathematics and to applications in computer science, the natural sciences and electrical engineering. This is an undergrad course for sophomores and juniors The only prereq. is a solid understanding of linear algebra. There will be opportunities for a student to explore an advanced topic in great depth, possibly for a junior project.
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0.00 - 4.00 Credits
An introduction to point set topology, the fundamental group, covering spaces, methods of calculation and applications.
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0.00 - 4.00 Credits
Singular homology, cellular complexes, Poincare duality, Lefschetz fixed point theorem.
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