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Mathematics 141: Introduction to Topology
4.00 Credits
University of California-Irvine
Lecture, three hours. The elements of naive set theory and the basic properties of metric spaces. Introduction to topological properties. Prerequisite: Mathematics 140A. Formerly Mathematics 141A.
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Mathematics 141 - Introduction to Topology
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Mathematics 146: Fourier Analysis
4.00 Credits
University of California-Irvine
Lecture, three hours. Rigorous introduction to the theory of Fourier series and orthogonal expansions. Fourier transform. Prerequisites: Mathematics 3D and 140A-B. Mathematics 112A recommended.
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Mathematics 146 - Fourier Analysis
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Mathematics 147: Complex Analysis W
4.00 Credits
University of California-Irvine
Rigorous treatment of basic complex analysis: complex numbers, analytic functions, Cauchy integral theory and its consequences (Morera's Theorem, Argument Principle, Fundamental Theorem of Algebra, Maximum Modulus Principle, Liouville's Theorem), power series, residue calculus harmonic functions, conformal mapping. Students are expected to do proofs. Corequisite: Mathematics 140B. Prerequisite: Mathematics 140A. Mathematics 114A may not be taken for credit after 147. Mathematics 147 and 114B may not both be taken for credit.
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Mathematics 147 - Complex Analysis W
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Mathematics 150: Introduction to Mathematical Logic
4.00 Credits
University of California-Irvine
Lecture, three hours. Firstorder logic through the Completeness Theorem for predicate logic. Prerequisite: consent of instructor. Only one course from Mathematics 150, Philosophy 105B, and Logic and Philosophy of Science 105B may be taken for credit.
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Mathematics 150 - Introduction to Mathematical Logic
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Mathematics 151: Set Theory W
4.00 Credits
University of California-Irvine
Lecture, three hours. Axiomatic development; infinite sets; cardinal and ordinal numbers. Prerequisite: Mathematics 150. Only one course from Mathematics 151, Philosophy 105A, and Logic and Philosophy of Science 105A may be taken for credit.
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Mathematics 151 - Set Theory W
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Mathematics 152: Computability
4.00 Credits
University of California-Irvine
Lecture, three hours. Computable functions; undecidability; G del's Incompleteness Theorem. Prerequisite: Mathematics 150. Only one course from Mathematics 152, Philosophy 105C, and Logic and Philosophy of Science 105C may be taken for credit.
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Mathematics 152 - Computability
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Mathematics 161: Modern Geometry
4.00 Credits
University of California-Irvine
Lecture, three hours. Euclidean geometry; Hilbert's axioms; absolute geometry; hyperbolic geometry; the Poincare models; geometric transformations. Prerequisites: Mathematics 2D, 3A, 120A. Formerly Mathematics 182.
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Mathematics 161 - Modern Geometry
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Mathematics 162A: B Introduction to Differential Geometry
4.00 Credits
University of California-Irvine
Lecture, three hours. Applications of advanced calculus and linear algebra to the geometry of curves and surfaces in space. Prerequisites: Mathematics 2D-E, 2J. Not offered every year.
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Mathematics 162A - B Introduction to Differential Geometry
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Mathematics 171A: Linear Programming
4.00 Credits
University of California-Irvine
Simplex algorithm, duality, optimization in networks. Prerequisite: Mathematics 3A or 6G.
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Mathematics 171A - Linear Programming
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Mathematics 171B: Nonlinear Programming
4.00 Credits
University of California-Irvine
Conditions for optimality, quadratic and convex programming, search methods, geometric programming. Prerequisites: Mathematics 2D and either 3A or 6G.
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Mathematics 171B - Nonlinear Programming
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