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

# 71 - 80 of 161 results for: MATH

## 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 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

## 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: Win | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: Dembo, A. (PI)

## MATH 162:Philosophy of Mathematics (PHIL 162, PHIL 262)

(Graduate students register for PHIL 262.) 20th-century approaches to the foundations and philosophy of mathematics. The background in mathematics, set theory, and logic. Schools and programs of logicism, predicativism, platonism, formalism, and constructivism. Readings from leading thinkers. Prerequisite: PHIL151 or consent of instructor.
Terms: not given this year | Units: 4 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

## MATH 172:Lebesgue Integration and Fourier Analysis

Similar to 205A, but for undergraduate Math majors and graduate students in other disciplines. Topics include Lebesgue measure on Euclidean space, Lebesgue integration, L^p spaces, the Fourier transform, the Hardy-Littlewood maximal function and Lebesgue differentiation. Prerequisite: 171 or consent of instructor.
Terms: Win | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit
Instructors: Vasy, A. (PI)

## MATH 174:Calculus of Variations

An introductory course emphasizing the historical development of the theory, its connections to physics and mechanics, its independent mathematical interest, and its contacts with daily life experience. Applications to minimal surfaces and to capillary surface interfaces. Prerequisites: Math 171 or equivalent.
Terms: not given this year | Units: 3 | Grading: Letter or Credit/No Credit

## MATH 180:Introduction to Financial Mathematics

Financial derivatives: contracts and options. Hedging and risk management. Arbitrage, interest rate, and discounted value. Geometric random walk and Brownian motion as models of risky assets. Initial boundary value problems for the heat and related partial differential equations. Self-financing replicating portfolio. Black-Scholes pricing of European options. Dividends. Implied volatility. Optimal stopping and American options. Prerequisite: 53. Corequisites: 131, 151 or STATS 116.
Terms: not given this 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