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Course Criteria
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4.00 Credits
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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4.00 Credits
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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4.00 Credits
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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4.00 Credits
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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4.00 Credits
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics.
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4.00 Credits
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics.
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4.00 Credits
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics.
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4.00 Credits
Existence, uniqueness, and stability; the geometry of phase space; linear systems and hyperbolicity; maps and diffeomorphisms.
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4.00 Credits
Hyperbolic structure and chaos; center manifolds; bifurcation theory; and the Feigenbaum and Ruelle-Takens cascades to strange attractors.
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4.00 Credits
Complex numbers, functions, differentiability, series extensions of elementary functions, complex integration, calculus of residues, conformal maps, mapping functions, applications.
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