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MATH 115A: Introduction to Number Theory
4.00 Credits
University of California-Santa Barbara
Divisibility, congruences, primitive roots an indices, quadratic residues and the quadratic reciprocity law, number-theoretic functions, Diophantine equations, the distribution of primes, number-theorhetic methods in cryptography, quadratic forms, continued fractions, and the approximation of real numbers, algebraic number theory, partitions.
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MATH 115B: Introduction to Number Theory
4.00 Credits
University of California-Santa Barbara
Divisibility, congruences, primitive roots and indices, quadratic residues and the quadradic reciprocity law, number-theorhetic functions, Diophantine equations, the distribution of primes, number-theorhetic methods in cryptography, quadratic forms, continued fractions, and the approximation of real numbers, algebraic number theory, partitions.
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MATH 116: Combinatorial Analysis
4.00 Credits
University of California-Santa Barbara
Elementary counting principles, binomial coefficients, generating functions, recurrence relations, the principle of inclusion and exclusion, distributions and partitions, systems of distinct representatives, applications to computation.
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MATH 116 - Combinatorial Analysis
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MATH 117: Methods of Analysis
4.00 Credits
University of California-Santa Barbara
Introduction to methods of proof in analysis. topics include limits, sequences and series, continuity, compactness, as well as other topics. This course is intended to follow Mathematics 8 and to introduce students to the level of sophistication of upper-division mathematics.
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MATH 118A: Introduction to Real Analysis
4.00 Credits
University of California-Santa Barbara
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics.
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MATH 118A - Introduction to Real Analysis
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MATH 118B: Introduction to Real Analysis
4.00 Credits
University of California-Santa Barbara
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics.
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MATH 118B - Introduction to Real Analysis
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MATH 118C: Introduction to Real Analysis
4.00 Credits
University of California-Santa Barbara
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics.
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MATH 118C - Introduction to Real Analysis
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MATH 119A: Ordinary Differential Equations
4.00 Credits
University of California-Santa Barbara
Existence, uniqueness, and stability; the geometry of phase space; linear systems and hyperbolicity; maps and diffeomorphisms.
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MATH 119A - Ordinary Differential Equations
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MATH 119B: Chaotic Dynamics and Bifurcation Theory
4.00 Credits
University of California-Santa Barbara
Hyperbolic structure and chaos; center manifolds; bifurcation theory; and the Feigenbaum and Ruelle-Takens cascades to strange attractors.
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MATH 122A: Introduction to Theory of Complex Variables
4.00 Credits
University of California-Santa Barbara
Complex numbers, functions, differentiability, series extensions of elementary functions, complex integration, calculus of residues, conformal maps, mapping functions, applications.
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MATH 122A - Introduction to Theory of Complex Variables
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