printer friendly pageMATH 143: Differential Geometry
Geometry of curves and surfaces in three-space and higher dimensional manifolds. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces.
Terms: Win
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Units: 3
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UG Reqs: GER:DB-Math
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Grading: Letter or Credit/No Credit
Instructors:
Ionel, E. (PI)
MATH 146: Analysis on Manifolds
Differentiable manifolds, tangent space, submanifolds, implicit function theorem, differential forms, vector and tensor fields. Frobenius' theorem, DeRham theory. Prerequisite: 52 or 52H.
Terms: Aut
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Units: 3
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UG Reqs: GER:DB-Math
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Grading: Letter or Credit/No Credit
Instructors:
Andrade, R. (PI)
MATH 147: Differential Topology
Smooth manifolds, transversality, Sards' theorem, embeddings, degree of a map, Borsuk-Ulam theorem, Hopf degree theorem, Jordan curve theorem. Prerequisite: 115 or 171.
Terms: alternate years, given next year
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Units: 3
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UG Reqs: GER:DB-Math
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Grading: Letter or Credit/No Credit
MATH 148: Algebraic Topology
Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120.
Terms: Win
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Units: 3
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UG Reqs: GER:DB-Math
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Grading: Letter or Credit/No Credit
Instructors:
Andrade, R. (PI)
MATH 151: Introduction to Probability Theory
Counting; axioms of probability; conditioning and independence; expectation and variance; discrete and continuous random variables and distributions; joint distributions and dependence; central limit theorem and laws of large numbers. Prerequisite: 52 or consent of instructor.
Terms: Win
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Units: 3
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UG Reqs: GER:DB-Math
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Grading: Letter or Credit/No Credit
Instructors:
Rhoades, R. (PI)
MATH 152: Elementary Theory of Numbers
Euclid's algorithm, fundamental theorems on divisibility; prime numbers; congruence of numbers; theorems of Fermat, Euler, Wilson; congruences of first and higher degrees; quadratic residues; introduction to the theory of binary quadratic forms; quadratic reciprocity; partitions.
Terms: Win
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Units: 3
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UG Reqs: GER:DB-Math
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Grading: Letter or Credit/No Credit
MATH 154: Algebraic Number Theory
Properties of number fields and Dedekind domains, quadratic and cyclotomic fields, applications to some classical Diophantine equations; introduction to elliptic curves. Prerequisites: 120 and 121, especially modules over principal ideal domains and Galois theory of finite fields.
Terms: Aut
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Units: 3
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UG Reqs: GER:DB-Math
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Grading: Letter or Credit/No Credit
Instructors:
Bump, D. (PI)
MATH 155: Analytic Number Theory
Topics in analytic number theory such as the distribution of prime numbers, the prime number theorem, twin primes and Goldbach's conjecture, the theory of quadratic forms, Dirichlet's class number formula, Dirichlet's theorem on primes in arithmetic progressions, and the fifteen theorem. Prerequisite: 152, or familiarity with the Euclidean algorithm, congruences, residue classes and reduced residue classes, primitive roots, and quadratic reciprocity.
Terms: alternate years, given next year
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Units: 3
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UG Reqs: GER:DB-Math
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Grading: Letter or Credit/No Credit
MATH 159: Discrete Probabilistic Methods
Modern discrete probabilistic methods suitable for analyzing discrete structures of the type arising in number theory, graph theory, combinatorics, computer science, information theory and molecular sequence analysis. Prerequisite:
STATS 116/
MATH 151 or equivalent.
Terms: not given this year
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Units: 3
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Grading: Letter or Credit/No Credit
MATH 161: Set Theory
Informal and axiomatic set theory: sets, relations, functions, and set-theoretical operations. The Zermelo-Fraenkel axiom system and the special role of the axiom of choice and its various equivalents. Well-orderings and ordinal numbers; transfinite induction and transfinite recursion. Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic. Open problems in set theory. Prerequisite: students should be comfortable doing proofs.
Terms: Aut
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Units: 3
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UG Reqs: GER:DB-Math
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Grading: Letter or Credit/No Credit
Instructors:
Sommer, R. (PI)
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