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MATH 133: Geometry
4.00 Credits
University of California-Riverside
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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MATH 133 - Geometry
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MATH 135A: Numerical Analysis
4.00 Credits
University of California-Riverside
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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MATH 135A - Numerical Analysis
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MATH 135B: Numerical Analysis
4.00 Credits
University of California-Riverside
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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MATH 135B - Numerical Analysis
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MATH 136: Introduction to the Theory of Numbers
4.00 Credits
University of California-Riverside
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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MATH 136 - Introduction to the Theory of Numbers
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MATH 137: Plane Curves
4.00 Credits
University of California-Riverside
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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MATH 137 - Plane Curves
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MATH 138A: Introduction to Differential Geometry
4.00 Credits
University of California-Riverside
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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MATH 138A - Introduction to Differential Geometry
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MATH 138B: Introduction to Differential Geometry
4.00 Credits
University of California-Riverside
S Lecture, 3 hours; discussion, 1 hour. Prerequisite(s): MATH 010B, MATH 138A. Gaussian curvature; geodesics; Gauss-Bonnet Theorem.
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MATH 138B - Introduction to Differential Geometry
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MATH 140: Polynomials and Number Systems
4.00 Credits
University of California-Riverside
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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MATH 140 - Polynomials and Number Systems
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MATH 141: Fractal Geometry with Applications
4.00 Credits
University of California-Riverside
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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MATH 141 - Fractal Geometry with Applications
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MATH 144: Introduction to Set Theory
4.00 Credits
University of California-Riverside
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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MATH 144 - Introduction to Set Theory
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