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.

This course may not be taken for credit after the successful completion of any course in the Calculus sequence.

• MW 11:40 a.m.-12:55 p.m.
• TR 6:10 p.m.-7:25 p.m.
• Instructor: Taeseok Lee
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• Instructor: Baiqing Zhu
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• 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)

• TR 10:10 a.m.-11:25 a.m.
• TR 2:40 p.m.-3:55 p.m.
• TR 6:10 p.m.-7:25 p.m.
• MW 2:40 p.m.-3:55 p.m.
• MW 4:10 p.m.-5:25 p.m.
• Instructor: Mrudul M Thatte
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• Instructor: Alex Xu
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• Instructor: Amal Mattoo
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• Instructor: Mrudul M Thatte
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• Instructor: Jorge Pineiro Barcelo
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• 3 points

CALCULUS II

Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)

• TR 10:10 a.m.-11:25 a.m.
• TR 1:10 p.m.-2:25 p.m.
• TR 6:10 p.m.-7:25 p.m.
• MW 11:40 a.m.-12:55 p.m.
• MW 2:40 p.m.-3:55 p.m.
• MW 4:10 p.m.-5:25 p.m.
• Instructor: Lucy Yang
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• Instructor: Tomasz Owsiak
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• Instructor: Fan Zhou
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• Instructor: Davis M Lazowski
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• Instructor: Andres Fernandez Herrero
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• 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 1:10 p.m.-2:25 p.m.
• TR 11:40 a.m.-12:55 p.m.
• TR 2:40 p.m.-3:55 p.m.
• TR 4:10 p.m.-5:25 p.m.
• Instructor: Ivan Horozov
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• Instructor: Shaoyun Bai
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• Instructor: Jeanne Boursier
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• 3 points

CALCULUS IV

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent Multiple integrals, Taylor's formula in several variables, line and surface integrals, calculus of vector fields, Fourier series. (SC)

• MW 4:10 p.m.-5:25 p.m.
• TR 2:40 p.m.-3:55 p.m.
• Instructor: Qiao He
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• 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 11:40 a.m.-12:55 p.m.
• Instructor: Sam Collingbourne
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• 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: George Dragomir
  CULPA: 5 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).

• TR 1:10 p.m.-2:25 p.m.
• Instructor: Giulia Sacca
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• 3 points

INTRODUCTION TO MATHEMATICS PROOFS

INTRO TO MATHEMATICAL PRO

This is a seminar course that covers the basics of mathematical proofs and in particular the epsilon-delta argument in single variable calculus.

Students who have little experience with mathematical proofs are strongly encouraged to take this course concurrently with Honors Math, Into to Modern Algebra, or Intro to Modern Analysis.

• F 11 a.m.-1 p.m.
• Instructor: Mu-Tao Wang
  CULPA: 27 Wikipedia h-index: 25 Info
• 0 points

LINEAR ALGEBRA

Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)

• MW 10:10 a.m.-11:25 a.m.
• MW 11:40 a.m.-12:55 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: Amadou Bah
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• 3 points

Linear Algebra and Probability

Linear algebra with a focus on probability and statistics. The course covers the standard linear algebra topics: systems of linear equations, matrices, determinants, vector spaces, bases, dimension, eigenvalues and eigenvectors, the Spectral Theorem and singular value decompositions. It also teaches applications of linear algebra to probability, statistics and dynamical systems giving a background sufficient for higher level courses in probability and statistics. The topics covered in the probability theory part include conditional probability, discrete and continuous random variables, probability distributions and the limit theorems, as well as Markov chains, curve fitting, regression, and pattern analysis. The course contains applications to life sciences, chemistry, and environmental life sciences. No a prior i background in the life sciences is assumed.

This course is best suited for students who wish to focus on applications and practical approaches to problem solving. It is recommended to students majoring in engineering, technology, life sciences, social sciences, and economics. Math majors, joint majors, and math concentrators must take MATH UN2010 Linear Algebra, which focuses on linear algebra concepts and foundations that are needed for upper-level math courses. MATH UN2015 (Linear Algebra and Probability) does NOT replace MATH UN2010 (Linear Algebra) as prerequisite requirements of math courses. Students may not receive full credit for both courses MATH UN2010 and MATH UN2015.

• MW 1:10 p.m.-2:25 p.m.
• Instructor: Chen-Chih Lai
  h-index: 3 Info
• 3 points

ORDINARY DIFFERENTIAL EQUATIONS

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 10:10 a.m.-11:25 a.m.
• TR 11:40 a.m.-12:55 p.m.
• Instructor: Ovidiu Savin
  CULPA: 22 Wikipedia Info
• Instructor: Yin Li
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• 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)

• TR 11:40 a.m.-12:55 p.m.
• Instructor: Wenjian Liu
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• 3 points

NUMBER THEORY AND CRYPTOGRAPHY

Prerequisites: one year of calculus. Prerequisite: One year of Calculus. Congruences. Primitive roots. Quadratic residues. Contemporary applications.

• MW 10:10 a.m.-11:25 a.m.
• Instructor: Yoonjoo Kim
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• 3 points

PARTIAL DIFFERENTIAL EQUATIONS

Prerequisites: (MATH UN2010 and MATH UN2030) 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.

• TR 1:10 p.m.-2:25 p.m.
• Instructor: Simon Brendle
  CULPA: 1 Wikipedia 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. 

Supervising Readings do NOT count towards major requirements, with the exception of an advanced written approval by the DUS.

• Instructor: Julien Dubedat
  CULPA: 4 Info
• Instructor: Amadou Bah
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• Instructor: Andrew J Blumberg
  h-index: 33 Info
• Instructor: Simon Brendle
  CULPA: 1 Wikipedia Info
• Instructor: Francesco Lin
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• Instructor: Mu-Tao Wang
  CULPA: 27 Wikipedia h-index: 25 Info
• 1-3 points

SENIOR THESIS IN MATHEMATICS II

SENIOR THESIS MATHEMATICS

Majors in Mathematics are offered the opportunity to write an honors senior thesis under the guidance of a faculty member. Interested students should contact a faculty member to determine an appropriate topic, and receive written approval from the faculty advisor and the Director of Undergraduate Studies (faculty sponsorship is limited to full-time instructors on the staff list). Research is conducted primarily during the fall term; the final paper is submitted to the Director of Undergraduate Studies during the subsequent spring term.

MATH UN3994 SENIOR THESIS IN MATHEMATICS I must be taken in the fall term, during which period the student conducts primary research on the agreed topic. An optional continuation course MATH UN3995 SENIOR THESIS IN MATHEMATICS II is available during the spring. The second term of this sequence may not be taken without the first. Registration for the spring continuation course has no impact on the timeline or outcome of the final paper.

Sections of SENIOR THESIS IN MATHEMATICS I and II do NOT count towards the major requirements, with the exception of an advanced written approval by the DUS.

• Instructor: Gyujin Oh
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• Instructor: Xi S Shen
  h-index: 4 Info
• Instructor: Qiao He
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• Instructor: Ioannis Karatzas
  CULPA: 7 h-index: 58 Info
• Instructor: Daniela de Silva
  CULPA: 21 Wikipedia Info
• Instructor: Mu-Tao Wang
  CULPA: 27 Wikipedia h-index: 25 Info
• 2 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 2:40 p.m.-3:55 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: Yujie Xu
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• 3 points

INTRO TO MOD ALGEBRA II

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: Konstantin Aleshkin
  CULPA: 4 Info
• 3 points

ALGEBRAIC NUMBER THEORY

Prerequisites: MATH GU4041 and MATH GU4042 or the equivalent Algebraic number fields, unique factorization of ideals in the ring of algebraic integers in the field into prime ideals. Dirichlet unit theorem, finiteness of the class number, ramification. If time permits, p-adic numbers and Dedekind zeta function.

• TR 4:10 p.m.-5:25 p.m.
• Instructor: Gyujin Oh
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• 3 points

ALGEBRAIC CURVES

Prerequisites: (MATH GU4041 and MATH GU4042) and MATH UN3007 Plane curves, affine and projective varieties, singularities, normalization, Riemann surfaces, divisors, linear systems, Riemann-Roch theorem.

• MW 2:40 p.m.-3:55 p.m.
• Instructor: Nathan H Chen
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• 3 points

INTRO TO ALGEBRAIC TOPOLOGY

Prerequisites: MATH UN2010 and MATH GU4041 and MATH GU4051 The study of topological spaces from algebraic properties, including the essentials of homology and the fundamental group. The Brouwer fixed point theorem. The homology of surfaces. Covering spaces.

• TR 11:40 a.m.-12:55 p.m.
• Instructor: Lucy Yang
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• 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.

• MW 1:10 p.m.-2:25 p.m.
• Instructor: Ivan Corwin
  CULPA: 1 Wikipedia h-index: 34 Info
• 3 points

INTRO MODERN ANALYSIS II

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: Nikolaos Apostolakis
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• 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 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.-8:55 p.m.
• MW 5:40 p.m.-6:55 p.m.
• Instructor: Tat Sang Fung
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• Instructor: Luca Capriotti
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• 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.
• 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.

• F 6:10 p.m.-8 p.m.
• Instructor: Ka-Yi Ng
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• 3 points

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

Credit Analytics

This course uses a combination of lectures and case studies to introduce students to the modern credit analytics. The objective for the course is to cover major analytic concepts, ideas with a focus on the underlying mathematics used in both credit risk management and credit valuation.  We will start from an empirical analysis of default probabilities (or PD), recovery rates and rating transitions. Then we will introduce the essential concepts of survival analysis as a scientific way to study default.  For credit portfolio we will study and compare different approaches such as CreditPortfolio View, CreditRisk+ as well as copula function approach. For valuation we will cover both single name and portfolio models.

• W 1:10 p.m.-3:40 p.m.
• Instructor: David X Li
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• 3 points

INTEREST RATES MODELS

The objective of this course is to introduce students to interest rates models and to build step by step a coherent understanding of the interest rates world, from the stripping of a yield curve to the modern frameworks of option pricing. Adopting a practitioner’s perspective, it will put an emphasis on building a strong intuition on the products and models, and will adopt a balanced approach between formal derivation and concrete applications.

• W 7:25 p.m.-9:15 p.m.
• Instructor: Paul-Guillaume Fournie
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• 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.

• 1-3 points

Career Development for Quantitative Fina

Career Develop for Quant

This course helps the students understand the job search process and develop the professional skills necessary for career advancement. The students will not only learn the best practices in all aspects of job-seeking but will also have a chance to practice their skills. Each class will be divided into two parts: a lecture and a workshop.

In addition, the students will get support from Teaching Assistants who will be available to guide and prepare the students for technical interviews.

• MW 11:40 a.m.-12:55 p.m.
• Instructor: Lars T Nielsen
  h-index: 17 Info
• 0 points

THE TEACHING OF MATHEMATICS

A seminar required of all incoming graduate students, designed to instill effective teaching techniques.

• T 2:40 p.m.-3:55 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: Daniela de Silva
  CULPA: 21 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: Julien Dubedat
  CULPA: 4 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.

• MW 1:10 p.m.-2:25 p.m.
• Instructor: Robert D Friedman
  CULPA: 44 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
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• 4.5 points

LIE GROUPS & REPRESENTATIONS

Continuation of MATH GR6343x (see Fall listing).

• MW 11:40 a.m.-12:55 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.

• TR 11:40 a.m.-12:55 p.m.
• Instructor: Eric Urban
  CULPA: 12 Wikipedia Info
• 4.5 points

TPCS IN REPRESENTATION THEORY

• MW 2:40 p.m.-3:55 p.m.
• Instructor: Peter G Woit
  CULPA: 6 Info
• 4.5 points