COLLEGE ALGEBRA-ANLYTC GEOMTRY
Prerequisites: score of 550 on the mathematics portion of the SAT completed within the last year, or the appropriate grade on the General Studies Mathematics Placement Examination. For students who wish to study calculus but do not know analytic geometry. Algebra review, graphs and functions, polynomial functions, rational functions, conic sections, systems of equations in two variables, exponential and logarithmic functions, trigonometric functions and trigonometric identities, applications of trigonometry, sequences, series, and limits.
- MW 1:10 p.m.-2:25 p.m.
- TR 6:10 p.m.-7:25 p.m.
-
Instructor:
Nguyen C Dung
Info -
Instructor:
Shalin Parekh
Info - 3 points
CALCULUS I
Prerequisites: (see Courses for First-Year Students). Functions, limits, derivatives, introduction to integrals, or an understanding of pre-calculus will be assumed. (SC)
- MW 2:40 p.m.-3:55 p.m.
- MW 4:10 p.m.-5:25 p.m.
- TR 10:10 a.m.-11:25 a.m.
- TR 11:40 a.m.-12:55 p.m.
- TR 4:10 p.m.-5:25 p.m.
-
Instructor:
Sayan Das
h-index: 2 Info -
Instructor:
Kevin J Smith
Info -
Instructor:
Panagiota Daskalopoulos
CULPA: 19
Wikipedia
Info
-
Instructor:
George Dragomir
CULPA: 5
Info
-
Instructor:
Tobias Schaefer
Info - 3 points
CALCULUS II
Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)
- MW 11:40 a.m.-12:55 p.m.
- MW 4:10 p.m.-5:25 p.m.
- TR 11:40 a.m.-12:55 p.m.
- TR 1:10 p.m.-2:25 p.m.
-
Instructor:
Maithreya A Sitaraman
Info -
Instructor:
Yier Lin
Info -
Instructor:
Evgeni Dimitrov
CULPA: 4
h-index: 6
Info
- 3 points
CALCULUS III
Prerequisites: MATH UN1101 or the equivalent Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramers rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)
- MW 10:10 a.m.-11:25 a.m.
- MW 11:40 a.m.-12:55 p.m.
- MW 1:10 p.m.-2:25 p.m.
- TR 2:40 p.m.-3:55 p.m.
-
Instructor:
Nicholas Salter
CULPA: 7
Info
- 3 points
ACCELERATED MULTIVARIABLE CALC
Prerequisites: (MATH UN1101 and MATH UN1102) Vectors in dimensions 2 and 3, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, optimization, Lagrange multipliers, double and triple integrals, line and surface integrals, vector calculus. This course is an accelerated version of MATH UN1201 - MATH UN1202. Students taking this course may not receive credit for MATH UN1201 and MATH UN1202.
- TR 1:10 p.m.-2:25 p.m.
-
Instructor:
Kanstantsin Matetski
Info - 4 points
HONORS MATHEMATICS B
Prerequisites: (see Courses for First-Year Students). The second term of this course may not be taken without the first. Multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major. (SC)
- TR 1:10 p.m.-2:25 p.m.
-
Instructor:
Evan Warner
CULPA: 7
Info
- 4 points
INTRO TO HIGHER MATHEMATICS
Introduction to understanding and writing mathematical proofs. Emphasis on precise thinking and the presentation of mathematical results, both in oral and in written form. Intended for students who are considering majoring in mathematics but wish additional training. CC/GS: Partial Fulfillment of Science Requirement. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).
- MW 10:10 a.m.-11:25 a.m.
-
Instructor:
Gus K Schrader
CULPA: 6
Info
- 3 points
LINEAR ALGEBRA
Prerequisites: MATH UN1201 or the equivalent. Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)
- MW 10:10 a.m.-11:25 a.m.
- MW 1:10 p.m.-2:25 p.m.
- TR 11:40 a.m.-12:55 p.m.
- TR 1:10 p.m.-2:25 p.m.
- TR 6:10 p.m.-7:25 p.m.
-
Instructor:
Konstantin Aleshkin
CULPA: 4 Info -
Instructor:
Gus K Schrader
CULPA: 6
Info
-
Instructor:
Stephen Miller
Info -
Instructor:
Andrew Ahn
CULPA: 3
h-index: 25
Info
-
Instructor:
Elliott V Stein
CULPA: 16
Info
- 3 points
ORDINARY DIFFERENTIAL EQUATION
Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent. Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.
- MW 2:40 p.m.-3:55 p.m.
- TR 10:10 a.m.-11:25 a.m.
-
Instructor:
Igor Krichever
CULPA: 13
Wikipedia
h-index: 48
Info
-
Instructor:
Aleksander Doan
Info - 3 points
ANALYSIS AND OPTIMIZATION
Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent and MATH UN2010. Mathematical methods for economics. Quadratic forms, Hessian, implicit functions. Convex sets, convex functions. Optimization, constrained optimization, Kuhn-Tucker conditions. Elements of the calculus of variations and optimal control. (SC)
- MW 1:10 p.m.-2:25 p.m.
- MW 2:40 p.m.-3:55 p.m.
-
Instructor:
Yash A Jhaveri
CULPA: 1 Info - 3 points
PARTIAL DIFFERENTIAL EQUATIONS
Prerequisites: MATH UN3027 and MATH UN2010 or the equivalent Introduction to partial differential equations. First-order equations. Linear second-order equations; separation of variables, solution by series expansions. Boundary value problems.
- MW 1:10 p.m.-2:25 p.m.
-
Instructor:
Florian Johne
CULPA: 5 Info - 3 points
DISCRETE TIME MODELS IN FINANC
Prerequisites: (MATH UN1102 and MATH UN1201) or (MATH UN1101 and MATH UN1102 and MATH UN1201) and MATH UN2010 Recommended: MATH UN3027 (or MATH UN2030 and SIEO W3600). Elementary discrete time methods for pricing financial instruments, such as options. Notions of arbitrage, risk-neutral valuation, hedging, term-structure of interest rates.
- MW 6:10 p.m.-7:25 p.m.
-
Instructor:
Mikhail Smirnov
CULPA: 16 Info - 3 points
SUPERVISED READINGS II
Prerequisites: The written permission of the faculty member who agrees to act as sponsor (sponsorship limited to full-time instructors on the staff list), as well as the permission of the Director of Undergraduate Studies. The written permission must be deposited with the Director of Undergraduate Studies before registration is completed. Guided reading and study in mathematics. A student who wishes to undertake individual study under this program must present a specific project to a member of the staff and secure his or her willingness to act as sponsor. Written reports and periodic conferences with the instructor.
-
Instructor:
Dusa McDuff
CULPA: 10
Info
-
Instructor:
Francesco Lin
Info -
Instructor:
Dorian Goldfeld
CULPA: 23
Wikipedia
Info
-
Instructor:
Guillaume Remy
CULPA: 2 Info -
Instructor:
Ivan Corwin
CULPA: 1 Wikipedia h-index: 34 Info -
Instructor:
Ioannis Karatzas
CULPA: 7 h-index: 58 Info -
Instructor:
Stephen Miller
Info -
Instructor:
Panagiota Daskalopoulos
CULPA: 19
Wikipedia
Info
-
Instructor:
Stephen Miller
Info -
Instructor:
Evan Warner
CULPA: 7
Info
-
Instructor:
Giulia Sacca
Info -
Instructor:
Peter G Woit
CULPA: 6 Info -
Instructor:
Stephen Miller
Info -
Instructor:
Mikhail Khovanov
CULPA: 2 Wikipedia Info - 3 points
ANALYTIC NUMBER THEORY
Prerequisites: MATH UN3007 A one semeser course covering the theory of modular forms, zeta functions, L -functions, and the Riemann hypothesis. Particular topics covered include the Riemann zeta function, the prime number theorem, Dirichlet characters, Dirichlet L-functions, Siegel zeros, prime number theorem for arithmetic progressions, SL (2, Z) and subgroups, quotients of the upper half-plane and cusps, modular forms, Fourier expansions of modular forms, Hecke operators, L-functions of modular forms.
- TR 11:40 a.m.-12:55 p.m.
-
Instructor:
Dorian Goldfeld
CULPA: 23
Wikipedia
Info
- 3 points
INTRO MODERN ALGEBRA I
Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent. The second term of this course may not be taken without the first. Groups, homomorphisms, normal subgroups, the isomorphism theorems, symmetric groups, group actions, the Sylow theorems, finitely generated abelian groups.
- MW 10:10 a.m.-11:25 a.m.
-
Instructor:
Daniele Alessandrini
CULPA: 7 h-index: 10 Info - 3 points
INTRO MODERN ALGEBRA II
Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent. The second term of this course may not be taken without the first. Rings, homomorphisms, ideals, integral and Euclidean domains, the division algorithm, principal ideal and unique factorization domains, fields, algebraic and transcendental extensions, splitting fields, finite fields, Galois theory.
- MW 2:40 p.m.-3:55 p.m.
-
Instructor:
Inbar Klang
CULPA: 17
Info
- 3 points
INTRO MODERN ANALYSIS I
Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first. Real numbers, metric spaces, elements of general topology, sequences and series, continuity, differentiation, integration, uniform convergence, Ascoli-Arzela theorem, Stone-Weierstrass theorem.
INTRO MODERN ANALYSIS II
Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first. Power series, analytic functions, Implicit function theorem, Fubini theorem, change of variables formula, Lebesgue measure and integration, function spaces.
- TR 4:10 p.m.-5:25 p.m.
-
Instructor:
Henri P Roesch
CULPA: 4 Info - 3 points
PROBABILITY THEORY
Prerequisites: MATH GU4061 or MATH UN3007 A rigorous introduction to the concepts and methods of mathematical probability starting with basic notions and making use of combinatorial and analytic techniques. Generating functions. Convergence in probability and in distribution. Discrete probability spaces, recurrence and transience of random walks. Infinite models, proof of the law of large numbers and the central limit theorem. Markov chains.
- TR 2:40 p.m.-3:55 p.m.
-
Instructor:
Ioannis Karatzas
CULPA: 7 h-index: 58 Info - 3 points
INTRO TO QUANTUM MECHANICS II
Continuation of GU4391. This course will focus on quantum mechanics, paying attention to both the underlying mathematical structures as well as their physical motivations and consequences. It is meant to be accessible to students with no previous formal training in quantum theory. The role of symmetry, groups and representations will be stressed.
- TR 4:10 p.m.-5:25 p.m.
-
Instructor:
Peter G Woit
CULPA: 6 Info - 3 points
INTRO TO THE MATH OF FINANCE
Prerequisites: MATH UN1102 and MATH UN1201 , or their equivalents. Introduction to mathematical methods in pricing of options, futures and other derivative securities, risk management, portfolio management and investment strategies with an emphasis of both theoretical and practical aspects. Topics include: Arithmetic and Geometric Brownian ,motion processes, Black-Scholes partial differential equation, Black-Scholes option pricing formula, Ornstein-Uhlenbeck processes, volatility models, risk models, value-at-risk and conditional value-at-risk, portfolio construction and optimization methods.
- MW 7:40 p.m.-8:55 p.m.
-
Instructor:
Mikhail Smirnov
CULPA: 16 Info - 3 points
NUMERICAL METHODS IN FINANCE
Prerequisites: some familiarity with the basic principles of partial differential equations, probability and stochastic processes, and of mathematical finance as provided, e.g. in MATH W5010. Prerequisites: some familiarity with the basic principles of partial differential equations, probability and stochastic processes, and of mathematical finance as provided, e.g. in MATH W5010. Review of the basic numerical methods for partial differential equations, variational inequalities and free-boundary problems. Numerical methods for solving stochastic differential equations; random number generation, Monte Carlo techniques for evaluating path-integrals, numerical techniques for the valuation of American, path-dependent and barrier options.
- MW 7:40 p.m.-8:44 p.m.
-
Instructor:
Tat Sang Fung
Info - 3 points
MATH FINANCE PRACTITIONERS SEM
Prerequisites: MATH W5010 or knowledge of J. Hulls book Options, futures. Prerequisites: Math GR5010 or knowledge of J. Hulls book Options, futures. Seminar consists of presentations and mini-courses by leading industry specialists in quantitative finance. Topics include portfolio optimization, exotic derivatives, high frequency analysis of data and numerical methods. While most talks require knowledge of mathematical methods in finance, some talks are accessible to general audience.
- TR 7:40 p.m.-8:55 p.m.
-
Instructor:
Lars T Nielsen
h-index: 17 Info - 3 points
PROG FOR QUANT & COMP FINANCE
This course covers programming with applications to finance. The applications may include such topics as yield curve building and calibration, short rate models, Libor market models, Monte Carlo simulation, valuation of financial instruments such as options, swaptions and variance swaps, and risk measurement and management, among others. Students will learn about the underlying theory, learn coding techniques, and get hands-on experience in implementing financial models and systems.
MATH MTHDS-FIN PRICE ANALYSIS
Course covers modern statistical and physical methods of analysis and prediction of financial price data. Methods from statistics, physics and econometrics will be presented with the goal to create and analyze different quantitative investment models.
- S 7 p.m.-9:20 p.m.
-
Instructor:
Alexei Chekhlov
CULPA: 3
h-index: 10
Info
- 3 points
MULTI-ASSET PORTFOLIO MGMT
The course will cover practical issues such as: how to select an investment universe and instruments, derive long term risk/return forecasts, create tactical models, construct and implement an efficient portfolio,to take into account constraints and transaction costs, measure and manage portfolio risk, and analyze the performance of the total portfolio.
- MW 6:10 p.m.-7:25 p.m.
- 3 points
NON-LINEAR OPTION PRICING
Prerequisites: familiarity with Brownian motion, Itô's formula, stochastic differential equations, and Black-Scholes option pricing. Prerequisites: Familiarity with Brownian motion, Itô's formula, stochastic differential equations, and Black-Scholes option pricing. Nonlinear Option Pricing is a major and popular theme of research today in quantitative finance, covering a wide variety of topics such as American option pricing, uncertain volatility, uncertain mortality, different rates for borrowing and lending, calibration of models to market smiles, credit valuation adjustment (CVA), transaction costs, illiquid markets, super-replication under delta and gamma constraints, etc. The objective of this course is twofold: (1) introduce some nonlinear aspects of quantitative finance, and (2) present and compare various numerical methods for solving high-dimensional nonlinear problems arising in option pricing.
- F 6 p.m.-8:10 p.m.
- 3 points
MAFN FIELDWORK
Prerequisites: all 6 MAFN core courses, at least 6 credits of approved electives, and the instructors permission. See the MAFN website for details. This course provides an opportunity for MAFN students to engage in off-campus internships for academic credit that counts towards the degree. Graded by letter grade. Students need to secure an internship and get it approved by the instructor.
-
Instructor:
Lars T Nielsen
h-index: 17 Info - 1-3 points
THE TEACHING OF MATHEMATICS
A seminar required of all incoming graduate students, designed to instill effective teaching techniques.
- W 11:40 a.m.-12:55 p.m.
-
Instructor:
George Dragomir
CULPA: 5
Info
- 0 points
ANALYSIS II
Continuation of MATH GR6151x (see Fall listing).
- TR 10:10 a.m.-11:25 a.m.
-
Instructor:
Simon Brendle
CULPA: 1 Wikipedia Info - 4.5 points
PROBABILITY II
Prerequisites: MATH GR6151 MATH G4151 Analysis & Probability I. Continuation of MATH GR6152x (see fall listing).
- TR 4:10 p.m.-5:25 p.m.
-
Instructor:
Ivan Corwin
CULPA: 1 Wikipedia h-index: 34 Info - 4.5 points
COMPLEX ANALYSIS/RIEMANN SURF
Continuation of MATH GR6175x (see Fall listing).
- TR 1:10 p.m.-2:25 p.m.
-
Instructor:
Duong H Phong
Wikipedia Info - 4.5 points
ARITH & ALGEBRAIC GEOMETRY
Affine and projective varieties; schemes; morphisms; sheaves; divisors; cohomology theory; curves; Riemann-Roch theorem.
- TR 2:40 p.m.-3:55 p.m.
-
Instructor:
Giulia Sacca
Info - 4.5 points
ALGEBRAIC TOPOLOGY II
Continuation of MATH GR6307x (see Fall listing).
- MW 2:40 p.m.-3:55 p.m.
-
Instructor:
Francesco Lin
Info - 4.5 points
LIE GROUPS & REPRESENTATIONS
Continuation of MATH GR6343x (see Fall listing).
- MW 1:10 p.m.-2:25 p.m.
-
Instructor:
Andrei Okounkov
CULPA: 1 Wikipedia h-index: 55 Info - 4.5 points
MODERN GEOMETRY
Continuation of Mathematics GR6402x (see Fall listing).
- MW 10:10 a.m.-11:25 a.m.
-
Instructor:
Chiu-Chu Liu
CULPA: 1 Wikipedia Info - 4.5 points
ALGEBRAIC NUMBER THEORY
Local and global fields, group cohomology, local class field theory, global class field theory and applications.
PARTIAL DIFFERENTIAL EQUATIONS
Prerequisites: MATH GR8209 MATH G8209. Prerequisites: Math GR8209. Topics of linear and non-linear partial differential equations of second order, with particular emphasis to Elliptic and Parabolic equations and modern approaches.
- TR 2:40 p.m.-3:55 p.m.
-
Instructor:
Richard Hamilton
CULPA: 10 Wikipedia Info - 4.5 points
TOPICS IN STOCHASTIC ANALYSIS
- MW 2:40 p.m.-3:55 p.m.
-
Instructor:
Julien Dubedat
CULPA: 4 Info - 4.5 points