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Course Criteria
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3.00 Credits
Credits: 3 Finite difference methods for initial value problems, two-point boundary value problems, Poisson equation, heat equation, and first-order partial differential equations. Prerequisites MATH 214 and MATH 446 or 685. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Weak formulation of partial differential equations, energy principles, Galerkin approximations, and finite element methods. Includes review and development of necessary analysis. Prerequisites MATH 446 or 685, and elementary differential equations course. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Special topics in applied mathematics not covered in the regular applied mathematics sequence. May be repeated for credit. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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1.00 - 6.00 Credits
Credits: 1-6 In areas of importance, but with insufficient demand to justify a regular course, students may undertake a course of study under the supervision of a consenting faculty member. Written statement of the content of the course and a tentative reading list is normally submitted as part of the request for approval. Literature review, project report, or other written product is normally required. May be repeated for credit. Hours of Lecture or Seminar per week 0 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Rings, fields, and Galois theory. Prerequisites MATH 621. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Covers simplices and simplicial complexes, cycles and boundaries, simplicial homology, homological algebra, homotopy and the fundamental group, cohomology. Prerequisites MATH 621 and 631, or equivalent. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Studies structural properties of objects encountered in pure and applied combinatorics. Topics include partially ordered sets, codes, designs, matroids, buildings, symmetrical structures, permutation groups, and face lattices of polytopes. Prerequisites MATH 321 or equivalent. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Study of commutative rings and their ideals, and of modules over commutative rings and their homological properties. More specific topics include Noetherian rings, primary decomposition, completions, graded rings and dimension theory with applications to algebraic geometry. Prerequisites MATH 621. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Topics include review of basic set theory (including cardinal numbers products of sets, the Axiom of Choice), definition of topological spaces, bases for topological spaces, forming new topological spaces by taking subspace, quotients, and products, separation properties (Hausdorff, regular, Tychonoff, and normal spaces) compactness, the Lindelof property, separability, connectedness, continuity and homeomorphism, manifolds. Prerequisites MATH 631 or equivalent. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Topics include geometry of curves and surfaces, curvature, isometries, the Gauss-Bonet theorem, geodesics, differential forms, manifolds, smooth maps, vector fields, the Euler characteristic, integration on manifolds, de Rham cohomology. Prerequisites MATH 631 or equivalent. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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