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Course Criteria
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4.00 Credits
This course covers the basic theory of functions of one complex variable. Topics include the geometry of complex numbers, holomorphic and harmonic functions, Cauchy's theorem and its consequences, Taylor and Laurent series, singularities, residues, elliptic functions, and other topics as time permits. Prerequisite: Mathematics 361 or permission of the instructor.
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4.00 Credits
A survey of the theory and applications of graphs. Topics are chosen fromamong connectivity, trees, Hamiltonian and Eulerian paths and cycles; isomorphism and reconstructability; planarity, coloring, color-critical graphs, and the four-color theorem; intersection graphs and vertex and edge domination; matchings and network flows; matroids and their relationship with optimization; and random graphs. Applications of graph theory are also discussed in depth. Prerequisite: Mathematics 261 or permission of the instructor.
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4.00 Credits
An introduction to mathematical logic. Topics include first-order logic, completeness and compactness theorems, model theory, nonstandard analysis, decidability and undecidability, incompleteness, and Turing machines. Prerequisite: Mathematics 332 or permission of the instructor.
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2.00 Credits
Juniors and seniors concentrating in computer science or mathematics are strongly urged to take this two-credit course. Each senior presents personal research in progress or significant material from the literature. Each junior presents an interesting paper of personal choice from the literature. The purpose of the seminar is to enhance communication among seniors about their research and to encourage juniors to become familiar with both the academic literature and research undertaken in the program. Prerequisite: moderated status or permission of the instructor.
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4.00 Credits
A continuation of Mathematics 332. The primary goal is to develop the Galois theory of fields. Students explore the theory of field extensions, including algebraic extensions, automorphisms of fields, splitting fields, and separable extensions. As time permits, students may develop some topics in advanced group theory. Prerequisites: Mathematics 331 and 332, or permission of the instructor.
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4.00 Credits
The course covers a selection of topics in algebraic combinatorics and computational algebra, including convex polytopes, simplicial complexes, hyperplane arrangements, Groebner bases, and multivariate splines. Prerequisite: Mathematics 331 or 332.
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4.00 Credits
This course covers the basic theory of representations of finite groups in characteristic zero: Schur's lemma, Maschke's theorem and completereducibility, character tables and orthogonality, and direct sums and tensor products. If time permits, the theory of Brauer characters and modular representations will be introduced. Prerequisites: Mathematics 242 and 332.
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4.00 Credits
The course covers topics in algebraic, geometric, and differential topology chosen according to student interest and background. Possible topics include the fundamental group, covering spaces, simplicial homology, classification of compact connected surfaces, topological and smooth manifolds, critical points of smooth maps, and vector fields. Prerequisite: Mathematics 351 or permission of the instructor.
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4.00 Credits
Students hone listening skills as selected musical works from 1700 to the present are introduced and studied in both musical and historical/cultural contexts. Key examples from the symphonic, chamber, operatic, jazz, popular, and musical theater genres are examined, primarily from the perspective of developing informed and open listening skills. The ability to read music is not required.
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4.00 Credits
This course serves as an introduction to reading, studying, and analyzing tonal music for nonmusic majors and potential music majors who have had little or no exposure to reading music. It begins with the basics of musical notation and progresses to the identification of scales, triads, and seventh chords. The class has an ear-training component that allows for practical reinforcement of the aural concepts presented.
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