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Course Criteria
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3.00 Credits
Topics include matrix algebra, theory of determinants, introduction to vector spaces, linear independence and span, and properties of linear transformations on finite dimensional vector spaces. Spring.
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3.00 Credits
Euclidean and non-Euclidean geometries, geodisics, triangle congruence theorems, area and holonomy, parallelism, symmetry, and isometries. Writing Intensive. Spring, even years.
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3.00 Credits
Topics include analyses of alternate definitions, languages, and approaches to mathematical ideas; extensions and generalizations of familiar theorems; discussions of the history of mathematics and historical contexts in which concepts arose; applications of mathematics in various settings; analyses of common problems of high school mathematics from a deeper mathematical level; demonstrations of alternate ways of approaching problems, including ways with and without calculator and use of technology; connections between ideas that may have been studied separately in different courses; and relationships of ideas studied in school to ideas students may encounter in later study. Fall, odd years.
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3.00 Credits
Groups and elementary theory of groups: cyclic groups, permutation groups, homomorphism, isomorphism, cosets and Lagrange's theorem, factor groups, Homomorphism theorem, and an intro to other algebraic structures such as rings, domains and fields. Fall, odd years.
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3.00 Credits
Rings: definition and properties, quotient rings and ideals, and homomorphisms of rings. Polynomial rings, integral domains, and fields. Sylow Theory and group actions, other algebraic structures including algebras, group rings, and vector spaces. Spring, even years.
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3.00 Credits
Topological properties of Euclidean spaces, limits of sequences and functions and continuity and differentiability for functions of one variable. Fall, even years.
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3.00 Credits
Integrability, sequences of functions and infinite series. Spring, odd years.
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3.00 Credits
Complex numbers and their geometric representation, analytic functions, elementary functions, transformations, complex integration, Taylor and Laurent series, and the calculus of residues, conformal mappings, and applications to hyperbolic geometry. Fall, odd years.
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3.00 Credits
Fourier series; Fourier Integral and Fourier Transform; Sturm-Liouville Theory; techniques to solve partial differential equations; Bessel functions and their application in solving boundary value problems. Fall, even years.
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3.00 Credits
Vector algebra; vector integration and differentiation; the del operator; the gradient, divergence and curl; line and surface integrals; the classical integral theorems of vector analysis - Stokes' Theorem, Green's Theorem, and the Divergence Theorem; and curvilinear coordinates. Periodically.
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