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61 - 70 of 161 results for: MATH

MATH 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: not given this year | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

MATH 144: Riemannian Geometry

Smooth manifolds, tensor fields, geometry of Riemannian and Lorentz metrics, the Levi-Civita connection and curvature tensor, Ricci curvature, scalar curvature, and Einstein manifolds, spaces of constant curvature. Prerequisites: Math 51, 52, and 53.
Terms: Win | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: Schoen, R. (PI)

MATH 145: Algebraic Geometry

Hilbert's nullstellensatz, complex affine and projective curves, Bezout's theorem, the degree/genus formula, blow-up, Riemann-Roch theorem. Prerequisites: 120, and 121 or knowledge of fraction fields. Recommended: familiarity with surfaces equivalent to 143, 146, 147, or 148.
Terms: not given this year | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

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: not given this year | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

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: Spr | Units: 3 | UG Reqs: GER:DB-Math | 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: not given this year | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

MATH 149: Applied Algebraic Topology

Introduction to algebraic topology and its applications, in particular persistent homology as a tool for shape and pattern recognition from high dimensional data sets, with examples analyzed using state-of-the-art software. Prerequisite: linear algebra.
Terms: Win | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: Carlsson, G. (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 | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit
Instructors: Dembo, A. (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 | Units: 3 | UG Reqs: GER:DB-Math | 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: alternate years, given next year | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit
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