2014-2015 2015-2016 2016-2017 2017-2018 2018-2019
 Browseby subject... Scheduleview...

# 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
Filter Results:
term offered
 Autumn Winter Spring Summer
updating results...
number of units
 1 unit 2 units 3 units 4 units 5 units >5 units
updating results...
time offered
 early morning (before 10am) morning (10am-12pm) lunchtime (12pm-2pm) afternoon (2pm-5pm) evening (after 5pm)
updating results...
days
 Monday Tuesday Wednesday Thursday Friday Saturday Sunday
updating results...
UG Requirements (GERs)
 WAY-A-II WAY-AQR WAY-CE WAY-ED WAY-ER WAY-FR WAY-SI WAY-SMA Language Writing 1 Writing 2 Writing SLE DB:Hum DB:Math DB:SocSci DB:EngrAppSci DB:NatSci EC:EthicReas EC:GlobalCom EC:AmerCul EC:Gender IHUM1 IHUM2 IHUM3
updating results...
component
 Lecture (LEC) Seminar (SEM) Discussion Section (DIS) Laboratory (LAB) Lab Section (LBS) Activity (ACT) Case Study (CAS) Colloquium (COL) Workshop (WKS) Independent Study (INS) Intro Dial, Sophomore (IDS) Intro Sem, Freshman (ISF) Intro Sem, Sophomore (ISS) Internship (ITR) Arts Intensive Program (API) Language (LNG) Practicum (PRA) Practicum (PRC) Research (RES) Sophomore College (SCS) Thesis/Dissertation (T/D)
updating results...
career