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Course Criteria
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3.00 - 12.00 Credits
Full-time work experience in business, industry, government, and other areas of student career interest. Positions are paid and usually require relocation and registration in course for two consecutive quarters. Formal report and evaluation by work supervisor required. Total credit limited to 16 units. Credit/No Credit grading only. Prerequisite: Sophomore standing and consent of instructor.
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1.00 - 4.00 Credits
Individual research or advanced study planned and completed under the direction of a departmental faculty member. Open only to graduate students demonstrating ability to do independent work. Total credit limited to 12 units. Prerequisite: Graduate standing and consent of department chair. Change effective Winter 2007.
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4.00 Credits
Introduction to advanced methods of mathematics useful in the analysis of engineering problems. Theory of vector fields, Fourier analysis, Sturm-Liouville theory, functions of a complex variable. Selected topics in asymptotic analysis, special functions, perturbation theory. Not open to students in major or master's degree program in mathematics. MATH 501: Distance Learning Lab fee may be required-see the Schedule of Classes. 4 lectures . MATH 50 1 prerequisite: MATH 344 or AERO 300 or equivalent, and graduate standing, or consent of instructor . MATH 50 2 prerequisite: MATH 501.
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1.00 - 3.00 Credits
Principles and practice in effective teaching of college-level mathematics. Issues related to present and future teaching experiences, including time management, professionalism, student assessment, grading, classroom management, and qualities of good mathematics teachers. Reflection on individual teaching, and consideration of improvements in instruction. Credit/No Credit grading only. Total credit limited to 2 units. 1 seminar. Prerequisite: Graduate standing or consent of instructor.
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4.00 Credits
Advanced mathematical methods of analysis in science and engineering, integrated with modeling of physical phenomena. Topics include applica-tions of complex analysis, Fourier analysis, ordinary and partial differential equations. Additional topics to be drawn from perturbation methods, asymptotic analysis, dynamical systems, numerical methods, optimization, and the calculus of variations. 4 lectures. MATH 520 prerequisite: MATH 408, MATH 412 and graduate standing, or consent of instructor. Recommended: MATH 418. MATH 521 prerequisite: MATH 520.
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4.00 Credits
Advanced mathematical methods of discrete mathematics with applications. Topics will include probability theory with generating functions, difference equations and number theory. Additional topics to be drawn from the theory of algorithms, coding theory, set theory, and the relation of discrete mathematics to complex analysis. 4 lectures. MATH 530 prerequisite: MATH 481, MATH 306 and graduate standing, or consent of instructor. MATH 531 prerequisite: MATH 530.
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4.00 Credits
Introduction to general topological spaces with emphasis on surfaces and manifolds. Open and closed sets, continuity, compactness, connectedness. Quotient spaces. 4 lectures. Not open to students with credit in MATH 440. Prerequisite: MATH 412, concurrent enrollment in or completion of MATH 481, and graduate standing, or consent of instructor.
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4.00 Credits
Introduction to general topological spaces with emphasis on surfaces and manifolds. Fundamental group. Triangulations of spaces, classification of surfaces. Other topics may include covering spaces, simplicial homology, homotopy theory and topics from differential topology. 4 lectures. Not open to students with credit in MATH 441. Prerequisite: MATH 540 and graduate standing, or consent of instructor. Recommended: MATH 304.
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4.00 Credits
Introduction to Lebesgue measure and integration, convergence theorems, L1 spaces, Radon-Nikodym Theorem and Fubini's Theorem. 4 seminars. Prerequisite: Satisfactory completion of the Graduate Written Examination in Analysis or consent of the Graduate Committee.
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4.00 Credits
Polynomial rings, field extensions, normal and separable extensions, automorphisms of fields, fundamental theorem of Galois theory, solvable groups, solution by radicals, insolvability of the quintic. 4 lectures. Prerequisite: Satisfactory completion of the Graduate Written Examination in Algebra or consent of the Graduate Committee.
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