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.

• 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)

• 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)

• 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)

• 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)

• 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)

• 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)

• 3 points

CALCULUS II

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

• 3 points

CALCULUS II

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

• 3 points

CALCULUS II

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

• Instructor: Elliott V Stein
  CULPA: 16 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)

• 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)

• 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)

• Instructor: Anh Duc Vo
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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)

• Instructor: Anh Duc Vo
  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)

• 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)

• 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)

• Instructor: Mikhail Smirnov
  CULPA: 16 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.

• Instructor: Deeparaj Bhat
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• 4 points

HONORS MATHEMATICS A

Prerequisites: (see "Guidance for First-Year Students" in the Bulletin). 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)

• Instructor: Tianqing Zhu
  Info
• 4 points

ACCELERATED MULTIVARIABLE CALC-REC

ACCEL MULTIVARIABLE CALC-

Recitation section for MATH UN1205 - Accelerated Multivariable Calculus.
Students must register for both UN1205 and UN1215.

• Instructor: Deeparaj Bhat
  Info
• 0 points

ACCELERATED MULTIVARIABLE CALC-REC

ACCEL MULTIVARIABLE CALC-

Recitation section for MATH UN1205 - Accelerated Multivariable Calculus.
Students must register for both UN1205 and UN1215.

• Instructor: Deeparaj Bhat
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• 0 points

HONORS MATHEMATICS A-REC

Recitation section for MATH UN1207 Honors Math A.
Students must register for both UN1207 and UN1217.

• Instructor: Tianqing Zhu
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• 0 points

HONORS MATHEMATICS A-REC

Recitation section for MATH UN1207 Honors Math A.
Students must register for both UN1207 and UN1217.

• Instructor: Tianqing Zhu
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• 0 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.

• Instructor: Tang-Kai Lee
  Info
• 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.

• 0 points

LINEAR ALGEBRA

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

• Instructor: Andrew J Blumberg
  h-index: 33 Info
• Instructor: Tianqing Zhu
  Info
• Instructor: Yujie Xu
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• Instructor: Yoonjoo Kim
  Info
• 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 priori 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 or MATH UN1207 Honors Math A, which focus 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. Students who have taken MATH UN2015 and consider taking higher level Math courses should contact a major advisor to discuss alternative pathways.

• Instructor: George Dragomir
  CULPA: 5 Info
• 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 priori 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 or MATH UN1207 Honors Math A, which focus 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. Students who have taken MATH UN2015 and consider taking higher level Math courses should contact a major advisor to discuss alternative pathways.

• Instructor: George Dragomir
  CULPA: 5 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.

• Instructor: Panagiota Daskalopoulos
  CULPA: 19 Wikipedia Info
• Instructor: Dawei Shen
  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.

• Instructor: Dawei Shen
  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)

• Instructor: Myungsin Cho
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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)

• Instructor: Myungsin Cho
  Info
• 3 points

MAKING, BREAKING CODES

Prerequisites: (MATH UN1101 and MATH UN1102 and MATH UN1201) and and MATH UN2010. A concrete introduction to abstract algebra. Topics in abstract algebra used in cryptography and coding theory.

• Instructor: Dorian Goldfeld
  CULPA: 23 Wikipedia Info
• 3 points

DIFFERENTIAL GEOMETRY

• Instructor: Mu-Tao Wang
  CULPA: 27 Wikipedia h-index: 25 Info
• 3 points

UNDERGRADUATE SEMINARS I

Prerequisites: Two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies permission. The subject matter is announced at the start of registration and is different in each section. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow.

• Instructor: Chiu-Chu Liu
  CULPA: 1 Wikipedia Info
• 3 points

FOURIER ANALYSIS

Prerequisites: three terms of calculus and linear algebra or four terms of calculus. Prerequisite: three terms of calculus and linear algebra or four terms of calculus. Fourier series and integrals, discrete analogues, inversion and Poisson summation formulae, convolution. Heisenberg uncertainty principle. Stress on the application of Fourier analysis to a wide range of disciplines.

• Instructor: Simon Brendle
  CULPA: 1 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.

• Instructor: Giulia Sacca
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• 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.

• 3 points

REPRESENTATNS OF FINITE GROUPS

Prerequisites: MATH UN2010 and MATH GU4041 or the equivalent. Finite groups acting on finite sets and finite dimensional vector spaces. Group characters. Relations with subgroups and factor groups. Arithmetic properties of character values. Applications to the theory of finite groups: Frobenius groups, Hall subgroups and solvable groups. Characters of the symmetric groups. Spherical functions on finite groups.

• Instructor: Robert D Friedman
  CULPA: 44 Info
• 3 points

TOPOLOGY

Prerequisites: (MATH UN1202 and MATH UN2010) and rudiments of group theory (e.g. MATH GU4041). MATH UN1208 or MATH GU4061 is recommended, but not required. Metric spaces, continuity, compactness, quotient spaces. The fundamental group of topological space. Examples from knot theory and surfaces. Covering spaces.

• Instructor: Soren Galatius
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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.

• Instructor: Sven Hirsch
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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.

• Instructor: Sven Hirsch
  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.

• Instructor: Ovidiu Savin
  CULPA: 22 Wikipedia Info
• 3 points

HONORS COMPLEX VARIABLES

Prerequisites: (MATH UN1207 and MATH UN1208) or MATH GU4061 A theoretical introduction to analytic functions. Holomorphic functions, harmonic functions, power series, Cauchy-Riemann equations, Cauchy's integral formula, poles, Laurent series, residue theorem. Other topics as time permits: elliptic functions, the gamma and zeta function, the Riemann mapping theorem, Riemann surfaces, Nevanlinna theory.

• Instructor: Francesco Lin
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• 3 points

ADVANCED PROBABILITY THEORY

This course will cover advance topics in probability, including: the theory of martingales in discrete and in continuous time; Brownian motion and its properties, stochastic integration, ordinary and partial stochastic differential equations; Applications to optimal filtering, stopping, control, and finance; Continuous-time Markov chains, systems of interacting particles, relative entropy dissipation, notions of information theory; Electrical networks, random walks on graphs and groups, percolation.

• Instructor: Roger W Van Peski
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• 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.

• 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.

• 3 points

MATH FINANCE PRACTITIONERS SEMINAR I

MATH FINANCE PRACTITION S

This seminar offers participants the opportunity to listen to practitioners discuss a range of important topics in the financial industry.  Topics may 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 a more general audience.

• Instructor: Jaehyuk Choi
  Info
• 1.5 points

QUANT MTHDS IN INVESTMENT MGMT

Prerequisites: Knowledge of statistics basics and programming skills in any programming language. Surveys the field of quantitative investment strategies from a buy side perspective, through the eyes of portfolio managers, analysts and investors. Financial modeling there often involves avoiding complexity in favor of simplicity and practical compromise. All necessary material scattered in finance, computer science and statistics is combined into a project-based curriculum, which give students hands-on experience to solve real world problems in portfolio management. Students will work with market and historical data to develop and test trading and risk management strategies. Programming projects are required to complete this course.

• 3 points

CAPITAL MARKETS & INVESTMENTS

Risk/return tradeoff, diversification and their role in the modern portfolio theory, their consequences for asset allocation, portfilio optimization. Capitol Asset Pricing Model, Modern Portfolio Theory, Factor Models, Equities Valuation, definition and treatment of futures, options and fixed income securities will be covered.

• 3 points

HEDGE FUNDS STRATEGIES & RISK

The hedge fund industry has continued to grow after the financial crisis, and hedge funds are increasingly important as an investable asset class for institutional investors as well as wealthy individuals. This course will cover hedge funds from the point of view of portfolio managers and investors. We will analyze a number of hedge fund trading strategies, including fixed income arbitrage, global macro, and various equities strategies, with a strong focus on quantitative strategies. We distinguish hedge fund managers from other asset managers, and discuss issues such as fees and incentives, liquidity, performance evaluation, and risk management. We also discuss career development in the hedge fund context.

• 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.

• 3 points

MODEL & TRADE DERIVATIVES

Required Prerequisite: Math GR5010 Intro to the Math of Finance (or equivalent). Recommended Prerequisite: Stat GR5264 Stochastic Processes – Applications I (or equivalent).

The objective of this course is to introduce students, from a practitioner’s perspective with formal derivations, to the advanced modeling, pricing and risk management techniques of vanilla and exotic options that are traded on derivatives desks, which goes beyond the classical option pricing courses focusing solely on the theory. It also presents the opportunity to design, implement and backtest vol trading strategies. The course is divided in four parts: Advanced Volatility Modeling; Vanilla and Exotic Options: Structuring, Pricing and Hedging; FX/Rates Components: Discounting, Forward Projection, Quanto and Compo Options; Designing and Backtesting Vol Trading Strategies in Python.

• 3 points

ADVANCED MACHINE LEARNING FOR FINANCE

ADV MACHINE LEARNING FOR

The application of Machine Learning (ML) algorithms in the Financial industry is now commonplace, but still nascent in its potential.  This course prepares the next generation of researchers and practitioners for the coming revolution, providing an advanced "deep dive" into machine learning methods (both theory and application) that are deemed to be useful for financial applications, including trading and investment management.

• 3 points

Algorithmic Trading with Market Simulato

Algo Trading with Market

The course will cover the fundamentals of Algorithmic Trading, the discipline that brings together computer software, and financial markets to open and close trades based on programmed code. The goal of the course is to help the students to get familiar with the different techniques and strategies used in algorithmic trading and to let them experiment with classical and new algorithms they will create.

During the course, the students will use a Trading Market Simulator: The Rotman Market Simulator – a platform which allows students to transact financial securities with each other on a real time basis. Using the simulator, the students will familiarize themselves with specific decision tasks associated with financial securities, market dynamics, and investment or risk management strategies and get ready for the Rotman Competition.

• 1.5 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: Jaehyuk Choi
  Info
• 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.

• Instructor: Jaehyuk Choi
  Info
• 0 points

Topics in Mathematical Finance

The purpose of this course is for MA in Mathematics of Finance students to gain knowledge and practical skills that are essential in the finance industry. The course will run as a series of lectures and discussions on various relevant topics, such as business communications and career talks that may feature guest speakers from the industry as well as the full-time faculty members. This will prepare the students for their job search, networking, and in their industry jobs in the future.

• Instructor: Jaehyuk Choi
  Info
• 0 points

ANALYSIS & PROBABILITY I

Prerequisites: the instructor's written permission. This is a course for Ph.D. students, and for majors in Mathematics. Measure theory; elements of probability; elements of Fourier analysis; Brownian motion.

• Instructor: Ioannis Karatzas
  CULPA: 7 h-index: 58 Info
• 4.5 points

COMPLEX ANALYSIS/RIEMANN SURF

Topics include holomorphic functions; analytic continuation; Riemann surfaces; theta functions and modular forms.

• Instructor: Duong H Phong
  Wikipedia Info
• 4.5 points

COMMUTATIVE ALGEBRA

Commutative rings; modules; localization; primary decoposition; integral extensions; Noetherian and Artinian rings; Nullstellensatz; Dedekind domains; dimension theory; regular local rings.

• Instructor: Michael Thaddeus
  CULPA: 24 Wikipedia Info
• 4.5 points

ALGEBRAIC TOPOLOGY I

Topics include homology and homotopy theory; covering spaces; homology with local coefficients; cohomology; Chech cohomology.

• Instructor: John W Morgan
  CULPA: 7 Info
• 4.5 points

LIE GROUPS & REPRESENTATIONS

Topics include basic notions of groups with algebraic and geometric examples; symmetry; Lie algebras and groups; representations of finite and compact Lie groups; finite groups and counting principles; maximal tori of a compact Lie group.

• Instructor: Andrei Okounkov
  CULPA: 1 Wikipedia h-index: 55 Info
• 4.5 points

MODERN GEOMETRY

Manifold theory; differential forms, tensors and curvature; homology and cohomology; Lie groups and Lie algebras; fiber bundles; homotopy theory and defects in quantum field theory; geometry and string theory.

• Instructor: Elena Giorgi
  h-index: 5 Info
• 4.5 points

TOPICS IN NUMBER THEORY

The course will cover various topics in number theory located at the interface of p-adic Hodge theory, p-adic geometry, and the p-adic Langlands program.

• 4.5 points