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Course Criteria
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3.00 Credits
An introduction to the basic techniques and modes of reasoning for combinatorial problem solving. Emphasis on the three principal aspects of combinatorial reasoning: the systematic analysis of different possibilities, the exploration of the logical structure of a problem, and ingenuity. Topics include the basic properties of graphs and diagraphs, trees and searching, and graph coloring in graph theory and the basic counting rules, generating functions, recurrence relations, and inclusionexclusion in enumeration. Prerequisites: MA 114A and MA 118A. Three hours a week.
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3.00 Credits
A course in readings in mathematical literature and literature in mathematics. Topical, historical and cultural approaches will be used. Topics explored will include Euclidean and non-Euclidean geometry, logic and philosophy of mathematics, classical number theory, infinity and cardinal numbers and aspects of modern mathematics. Each student will be responsible for reading selected articles and researching a topic for final presentation. Prerequisite: MA 118A. Three hours a week. Offered in the fall semester of odd-numbered years.
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3.00 Credits
Selected topics that illustrate the strong link between combinatorics and geometry. Applications to other areas of mathematics and the real world will be included. Possible areas of concentration include convex polytope theory, symmetries of Cayley graphs, the mathematics of paper folding, robotics, error-correcting codes, Buckyballs, and geodesic dome structures. Prerequisite: MA 223A (or consent of instructor). Three hours a week.
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3.00 Credits
Theory and application of selected topics from analysis. Topics include: solutions of equations and systems of equations, interpolation, numerical differentiation and integration, and numerical solution of differential equations. Error bounds are treated. Emphasis given to methods that can be implemented on a computer. Prerequisites: MA 219A and CS 161A (or consent of instructor). Three hours a week.
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3.00 Credits
An introduction, with emphasis on theory of vector spaces, linear transformations and matrices. Prerequisite: MA 114A and MA 118A. Three hours a week.
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3.00 Credits
An introduction to the theory of groups, rings and fields. Prerequisite: MA 335A or consent of the instructor. Three hours a week.
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3.00 Credits
An introduction, with emphasis on theory, to the foundations of the calculus of functions of one and several variables. Prerequisite: MA 219A or consent of the instructor. Three hours a week.
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3.00 Credits
An introduction to the calculus of functions of a complex variable for students of science, engineering, and mathematics. Topics include complex differentiation, harmonic functions, the Cauchy- Riemann equations, contour integrals, the Cauchy integral theorem and Cauchy integral formula, Taylor series, Laurent series and the residue theorem. Prerequisite: MA 219A. Three hours a week.
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3.00 Credits
Introduction to modeling and computer simulation. Examples will be drawn from numerous areas in the physical, biological and social sciences, and business. Probabilistic as well as deterministic models will be considered. Prerequisites: MA 220A, consent of the instructor, and a knowledge of a higher level language. Three hours a week.
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6.00 Credits
Selected topics from vector analysis, Fourier series, partial differential equations, and complex variables. The two semesters are independent and may be taken separately. Prerequisite: MA 220A. Three hours a week, two semesters.
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