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Course Criteria
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3.00 Credits
Solutions of linear systems of equations, matrix algebra, determinants. Introduction to abstract vector spaces and linear transformations, eigen values, and eigenvectors. Prerequisite: Mathematics 102, 121, 131, or 161. Four credit hours. BRETSCHER, LAMBERT, MATHES, TAYLOR
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3.00 Credits
An introduction to fundamental mathematical techniques used in upper-level mathematics courses. Presents the principles of mathematical logic and uses them to examine standard methods of direct and indirect proof, including mathematical induction. Topics include techniques from finite mathematics, the set theoretic approach to functions and relations, and the theory of infinite sets. Credit can be received for only one of Mathematics 274 and 275. Prerequisite: Mathematics 102, 121, 131, or 161. Two semesters of calculus is recommended. Four credit hours. KIESERMAN, LIVSHITS
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3.00 Credits
An independent study of introductory topics in abstract mathematics used in upper-level mathematics courses. Topics include the set-theoretic approach to functions and relations, the theory of infinite sets, elementary algebraic structures, and techniques from discrete mathematics. Credit can be received for only one of Mathematics 274 and 275. Prerequisite: Mathematics 161 and 162 and permission of the department. Two credit hours. LIVSHITS
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3.00 Credits
An advanced calculus course. Vectors, lines, and planes; limits, continuity, derivatives, and integrals of vector-valued functions; polar, spherical, and cylindrical coordinates; partial and directional derivatives; multiple integrals; line and surface integrals; Green's Theorem; Stokes's Theorem; Fourier series; applications. Typically involves the use of a large computer mathematics package such as Mathematica or Maple. Prerequisite: Mathematics 122 or 162. Four credit hours. BRETSCHER, KIESERMAN
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3.00 Credits
Theory and solution methods of ordinary differential equations; linear differential equations; first-order linear systems; qualitative behavior of solutions; nonlinear dynamics; existence and uniqueness of solutions; applications. Prerequisite: Mathematics 122 or 162, and 253. Four credit hours. HOLLY
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3.00 Credits
An introduction to partial differential equations. Linear and nonlinear partial differential equations, systems; initial value problems, boundary value problems; analytic and numerical methods of solution; applications. Prerequisite: Mathematics 253 and 311. Four credit hours.
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3.00 Credits
An introduction to the differential geometry of curves and surfaces in three-dimensional space. Curves: tangent, normal, and binormal vectors; curvature and torsion; the moving frame. Surfaces: the first and second fundamental forms, the Theorema Egregium, sectional and Gaussian curvature, and selected additional topics. Prerequisite: Mathematics 122 or 162, and 253, and 274 or 275. Four credit hours.
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3.00 Credits
Point-set, differential and algebraic topology. Prerequisite: Mathematics 274 or 275. Four credit hours. TAYLOR
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3.00 Credits
Solution by numerical methods of linear and nonlinear equations, systems of equations, and differential equations; numerical integration; polynomial approximation; matrix inversion; error analysis. Prerequisite: Mathematics 122 or 162, and 253. Four credit hours.
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3.00 Credits
Introduction to algebraic structures, such as groups, rings, integral domains, and fields. Prerequisite: Mathematics 253, and 274 or 275. Four credit hours. LIVSHITS
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