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 10:10 a.m.-11:25 a.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.
- MW 6:10 p.m.-7:25 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.
- TR 6:10 p.m.-7:25 p.m.
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Instructor:
Marco Castronovo
Info - 3 points
CALCULUS II
Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)
- MW 1:10 p.m.-2:25 p.m.
- MW 2:40 p.m.-3:55 p.m.
- TR 8:40 a.m.-9:55 a.m.
- TR 10:10 a.m.-11:25 a.m.
- TR 6:10 p.m.-7:25 p.m.
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Instructor:
Andres Ibanez Nunez
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 8:40 a.m.-9:55 a.m.
- MW 11:40 a.m.-12:55 p.m.
- MW 2:40 p.m.-3:55 p.m.
- TR 11:40 a.m.-12:55 p.m.
- TR 1:10 p.m.-2:25 p.m.
- TR 2:40 p.m.-3:55 p.m.
- TR 4:10 p.m.-5:25 p.m.
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Instructor:
Deeparaj Bhat
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Instructor:
Brian Harvie
Info - 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 6:10 p.m.-7:25 p.m.
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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.
- MW 1:10 p.m.-2:25 p.m.
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Instructor:
Dawei Shen
Info - 4 points
HONORS MATHEMATICS A
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.
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Instructor:
Giulia Sacca
Info - 4 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 1 p.m.-3 p.m.
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Instructor:
Julien Dubedat
CULPA: 4 Info - 0 points
LINEAR ALGEBRA
Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)
- MW 2:40 p.m.-3:55 p.m.
- TR 10:10 a.m.-11:25 a.m.
- TR 1:10 p.m.-2:25 p.m.
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Instructor:
Siddhi Krishna
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Instructor:
Amadou Bah
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 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.
- TR 11:40 a.m.-12:55 p.m.
- TR 1:10 p.m.-2:25 p.m.
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Instructor:
Evan Sorensen
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 1:10 p.m.-2:25 p.m.
- TR 10:10 a.m.-11:25 a.m.
- TR 1:10 p.m.-2:25 p.m.
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Instructor:
Panagiota Daskalopoulos
CULPA: 19
Wikipedia
Info
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Instructor:
Jeanne Boursier
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 4:10 p.m.-5:25 p.m.
- TR 10:10 a.m.-11:25 a.m.
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Instructor:
Qiao He
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Instructor:
Roger W Van Peski
Info - 3 points
COMPLEX VARIABLES
Prerequisites: MATH UN1202 An elementary course in functions of a complex variable. Fundamental properties of the complex numbers, differentiability, Cauchy-Riemann equations. Cauchy integral theorem. Taylor and Laurent series, poles, and essential singularities. Residue theorem and conformal mapping.(SC)
- TR 11:40 a.m.-12:55 p.m.
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Instructor:
Ovidiu Savin
CULPA: 22 Wikipedia 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.
- TR 1:10 p.m.-2:25 p.m.
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Instructor:
Dorian Goldfeld
CULPA: 23
Wikipedia
Info
- 3 points
SUPERVISED READINGS I
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.
- 1-3 points
SUPERVISED READINGS I
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.
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Instructor:
Elena Giorgi
h-index: 5 Info -
Instructor:
Peter G Woit
CULPA: 6 Info -
Instructor:
Chiu-Chu Liu
CULPA: 1 Wikipedia Info -
Instructor:
Robert D Friedman
CULPA: 44 Info -
Instructor:
Dorian Goldfeld
CULPA: 23
Wikipedia
Info
- 1-3 points
SENIOR THESIS IN MATHEMATICS I
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.
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Instructor:
Robert D Friedman
CULPA: 44 Info -
Instructor:
Yoonjoo Kim
Info -
Instructor:
Mu-Tao Wang
CULPA: 27
Wikipedia
h-index: 25
Info
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Instructor:
Chiu-Chu Liu
CULPA: 1 Wikipedia Info -
Instructor:
Andrew J Blumberg
h-index: 33 Info -
Instructor:
Duong H Phong
Wikipedia Info -
Instructor:
Ivan Corwin
CULPA: 1 Wikipedia h-index: 34 Info - 4 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.
- TR 10:10 a.m.-11:25 a.m.
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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.
- MW 1:10 p.m.-2:25 p.m.
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Instructor:
Robert D Friedman
CULPA: 44 Info - 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 10:10 a.m.-11:25 a.m.
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Instructor:
Michael Thaddeus
CULPA: 24
Wikipedia
Info
- 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.
- TR 1:10 p.m.-2:25 p.m.
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Instructor:
Andrei Okounkov
CULPA: 1 Wikipedia h-index: 55 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.
- TR 6:10 p.m.-7:25 p.m.
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Instructor:
Rostislav Akhmechet
Info - 3 points
INTRODUCTION TO KNOT THEORY
Prerequisites: MATH GU4051 Topology and / or MATH GU4061 Introduction To Modern Analysis I (or equivalents). Recommended (can be taken concurrently): MATH UN2010 linear algebra, or equivalent. The study of algebraic and geometric properties of knots in R^3, including but not limited to knot projections and Reidemeisters theorm, Seifert surfaces, braids, tangles, knot polynomials, fundamental group of knot complements. Depending on time and student interest, we will discuss more advanced topics like knot concordance, relationship to 3-manifold topology, other algebraic knot invariants.
- MW 11:40 a.m.-12:55 p.m.
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Instructor:
Siddhi Krishna
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.
- TR 1:10 p.m.-2:25 p.m.
- TR 2:40 p.m.-3:55 p.m.
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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.
- MW 11:40 a.m.-12:55 p.m.
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Instructor:
Milind Hegde
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.
- TR 11:40 a.m.-12:55 p.m.
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Instructor:
Francesco Lin
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.
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Instructor:
Ivan Corwin
CULPA: 1 Wikipedia h-index: 34 Info - 3 points
INTRO TO QUANTUM MECHANICS
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.
- MW 2:40 p.m.-3:55 p.m.
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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.
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Instructor:
Mikhail Smirnov
CULPA: 16 Info - 3 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.
- R 7:40 p.m.-10 p.m.
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Instructor:
Alberto Botter
Info - 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.
- S 7 p.m.-9:20 p.m.
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Instructor:
Alexei Chekhlov
CULPA: 3
h-index: 10
Info
- 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.
FIXED INCOME PORTFOLIO MGMT
Prerequisites: comfortable with algebra, calculus, probability, statistics, and stochastic calculus. The course covers the fundamentals of fixed income portfolio management. Its goal is to help the students develop concepts and tools for valuation and hedging of fixed income securities within a fixed set of parameters. There will be an emphasis on understanding how an investment professional manages a portfolio given a budget and a set of limits.
- T 10:10 a.m.-noon
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Instructor:
Rosanna Pezzo
Info - 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
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.
- S 10:10 a.m.-noon
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Instructor:
Amal Moussa
h-index: 7 Info - 3 points
Machine Learning for Finance
The application of Machine Learning (ML) algorithms in the Financial industry is now commonplace, but still nascent in its potential. This course provides an overview of ML applications for finance use cases including trading, investment management, and consumer banking.
Students will learn how to work with financial data and how to apply ML algorithms using the data. In addition to providing an overview of the most commonly used ML models, we will detail the regression, KNN, NLP, and time series deep learning ML models using desktop and cloud technologies.
The course is taught in Python using Numpy, Pandas, scikit-learn and other libraries. Basic programming knowledge in any language is required.
- T 12:10 p.m.-2 p.m.
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Instructor:
William G Ritter
Info - 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.
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Instructor:
Mikhail Smirnov
CULPA: 16 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.
- MW 10:10 a.m.-11:25 a.m.
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Instructor:
Mikhail Smirnov
CULPA: 16 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.
- TR 4:10 p.m.-5:25 p.m.
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Instructor:
Ioannis Karatzas
CULPA: 7 h-index: 58 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.
- TR 11:40 a.m.-12:55 p.m.
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Instructor:
Eric Urban
CULPA: 12 Wikipedia Info - 4.5 points
ALGEBRAIC TOPOLOGY I
Topics include homology and homotopy theory; covering spaces; homology with local coefficients; cohomology; Chech cohomology.
- TR 8:40 a.m.-9:55 a.m.
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Instructor:
Andrew J Blumberg
h-index: 33 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.
- TR 2:40 p.m.-3:55 p.m.
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Instructor:
John W Morgan
CULPA: 7 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.
- MW 10:10 a.m.-11:25 a.m.
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Instructor:
Chiu-Chu Liu
CULPA: 1 Wikipedia Info - 4.5 points