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Course Criteria
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 113 or MATH 131 or consent of instructor. Elementary theory of affine and projective planes, the line at infinity, finite geometries, Euclidean and non-Euclidean geometries, groups of transformations, and other algebraic structures related to geometry.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): CS 010 or equivalent; MATH 113 or MATH 131 (may be taken concurrently). A study of numerical methods for determining solutions to nonlinear equations and simultaneous linear equations. Topics also include interpolation, techniques of error analysis, and computer applications.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): CS 010; MATH 113 or MATH 131; MATH 135A. Continuation of MATH 135A. Explores numerical methods, numerical integration, and the numerical solution of ordinary differential equations.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 113 or MATH 131. Prime and composite integers, number theoretic functions, diophantine equations, congruences, quadratic reciprocity, additive arithmetic.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): CS011/MATH 011; MATH 113 or MATH 131; MATH 171 and MATH 172. are recommended. A study of the complex projective plane, homogeneous polynominals, plane curves, intersection multiplicities, and Bezout's theorem.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 113 or MATH 131. Elementary theory of curves and surfaces. First and second fundamental forms.
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4.00 Credits
S Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 010B, MATH 138A. Gaussian curvature; geodesics; Gauss-Bonnet Theorem.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): CS 011/MATH 011; MATH 113 or MATH 131. Topics include number systems, elementary number theory, rings, fields, polynomials, congruencies, and applications of finite fields.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 010B, MATH 046, completion of or concurrent enrollment in MATH 144; or consent of instructor. Covers classical fractals, fractal dimensions, self-similar fractals, fractal curves and sets, random fractals, chaotic dynamics and fractals, iteration theory: Julia set and the Mandelbrot set. Also covers the beauty of fractals, mathematical description of irregular shapes (clouds, trees, coastlines, mountains, galaxies, lungs, snowflakes), and applications to physics, engineering, biology and computer graphics.
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4.00 Credits
Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 010A. Algebra of subsets of a set. Algebra of relations and functions. Cardinal and ordinal numbers and their arithmetic operations. The well-ordering theorem, transfinite induction, and Zorn's lemma.
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