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 6:10 p.m.-7:25 p.m.
- 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.
- TR 8:40 a.m.-9:55 a.m.
- TR 10:10 a.m.-11:25 a.m.
-
Instructor:
Roger W Van Peski
Info -
Instructor:
Tang-Kai Lee
Info - 3 points
CALCULUS II
Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)
- MW 8:40 a.m.-9:55 a.m.
- TR 1:10 p.m.-2:25 p.m.
- TR 2:40 p.m.-3:55 p.m.
-
Instructor:
Lucy Yang
Info -
Instructor:
Tianqing Zhu
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 2:40 p.m.-3:55 p.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.
-
Instructor:
Andres Ibanez Nunez
Info -
Instructor:
Abigail G Hickok
Info -
Instructor:
Rostislav Akhmechet
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)
- TR 2:40 p.m.-3:55 p.m.
-
Instructor:
Deeparaj Bhat
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.
-
Instructor:
Mu-Tao Wang
CULPA: 27
Wikipedia
h-index: 25
Info
- 4 points
HONORS MATHEMATICS B
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)
- TR 1:10 p.m.-2:25 p.m.
-
Instructor:
George Dragomir
CULPA: 5
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.
- T 6:10 p.m.-7 p.m.
-
Instructor:
Mu-Tao Wang
CULPA: 27
Wikipedia
h-index: 25
Info
- 0 points
HONORS MATHEMATICS B-REC
Recitation section for MATH UN1208 Honors Math B.
Students must register for both UN1208 and UN1218.
- R 6:10 p.m.-7 p.m.
-
Instructor:
George Dragomir
CULPA: 5
Info
- 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. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).
- MW 2:40 p.m.-3:55 p.m.
-
Instructor:
James E Hotchkiss
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.
- F 1 p.m.-3 p.m.
-
Instructor:
Julien Dubedat
CULPA: 4 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 6:10 p.m.-7:25 p.m.
-
Instructor:
Anh Duc Vo
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.
- MW 11:40 a.m.-12:55 p.m.
- MW 1:10 p.m.-2:25 p.m.
-
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.
- TR 4:10 p.m.-5:25 p.m.
- TR 6:10 p.m.-7:25 p.m.
-
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)
- TR 1:10 p.m.-2:25 p.m.
-
Instructor:
Myungsin Cho
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)
- MW 4:10 p.m.-5:25 p.m.
-
Instructor:
Dawei Shen
Info - 3 points
NUMBER THEORY AND CRYPTOGRAPHY
Prerequisites: one year of calculus. Prerequisite: One year of Calculus. Congruences. Primitive roots. Quadratic residues. Contemporary applications.
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 10:10 a.m.-11:25 a.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
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 1:10 p.m.-2:25 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:
Aise Johan de Jong
CULPA: 5 Wikipedia 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 1:10 p.m.-2:25 p.m.
-
Instructor:
Robert D Friedman
CULPA: 44 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.
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.
- TR 11:40 a.m.-12:55 p.m.
-
Instructor:
Yoonjoo Kim
Info - 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.
- MW 2:40 p.m.-3:55 p.m.
-
Instructor:
Soren Galatius
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.
- MW 8:40 a.m.-9:55 a.m.
-
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.
- TR 4:10 p.m.-5:25 p.m.
-
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.
-
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.
- TR 4:10 p.m.-5:25 p.m.
-
Instructor:
Jaehyuk Choi
Info - 3 points
MATH FINANCE PRACTITIONERS SEMINAR II
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.
- R 7:40 p.m.-8:55 p.m.
-
Instructor:
Jaehyuk Choi
Info - 1.5 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.-7:50 p.m.
- 3 points
FINANCIAL RISK MGMT & REGULATION
Prerequisites: student expected to be mathematically mature and familiar with probability and statistics, arbitrage pricing theory, and stochastic processes. The course will introduce the notions of financial risk management, review the structure of the markets and the contracts traded, introduce risk measures such as VaR, PFE and EE, overview regulation of financial markets, and study a number of risk management failures. After successfully completing the course, the student will understand the basics of computing parametric VaR, historical VaR, Monte Carlo VaR, cedit exposures and CVA and the issues and computations associated with managing market risk and credit risk. The student will be familiar with the different categories of financial risk, current regulatory practices, and the events of financial crises, especially the most recent one.
- W 7:40 p.m.-9:30 p.m.
- 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.
- 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
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.
- S 2:40 p.m.-4:30 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.
- F 1:10 p.m.-3:40 p.m.
- 3 points
A MATHEMATICAL APPROACH TO GENERATIVE AI
MATHMATCL APPRCH GENERATI
Generative AI (“GenAI") is reshaping the global economy and the future of work by revolutionizing problem-solving, optimizing complex systems, and enabling data-driven decision-making. Its profound impact spans across natural language understanding, image generation, and predictive analytics, marking a paradigm shift that necessitates a deep and rigorous understanding of its mathematical foundations. This course is designed to equip students with a comprehensive framework for exploring the mathematical principles underpinning GenAI. Emphasizing statistical modeling, optimization, and computational techniques, the curriculum provides the essential tools to develop and analyze cutting-edge generative models.
- S 4:45 p.m.-6:35 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:
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.
- TR 11:40 a.m.-12:55 p.m.
-
Instructor:
Jaehyuk Choi
Info - 0 points
THE TEACHING OF MATHEMATICS
A seminar required of all incoming graduate students, designed to instill effective teaching techniques.
- R 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:
Ovidiu Savin
CULPA: 22 Wikipedia Info - 4.5 points
PROBABILITY II
Prerequisites: MATH GR6151 MATH G4151 Analysis & Probability I. Continuation of MATH GR6152x (see fall listing).
- MW 1:10 p.m.-2:25 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.
- TR 4:10 p.m.-5:25 p.m.
-
Instructor:
Michael Thaddeus
CULPA: 24
Wikipedia
Info
- 4.5 points
LIE GROUPS & REPRESENTATIONS
Continuation of MATH GR6343x (see Fall listing).
- MW 4:10 p.m.-5:25 p.m.
-
Instructor:
Tommaso M Botta
Info - 4.5 points
MODERN GEOMETRY
Continuation of Mathematics GR6402x (see Fall listing).
- MW 11:40 a.m.-12:55 p.m.
-
Instructor:
Elena Giorgi
h-index: 5 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:
Michael Harris
CULPA: 6 Wikipedia Info - 4.5 points
TOPICS IN GEOMETRIC ANALYSIS
Topics of linear and non-linear partial differential equations of second order, with particular emphasis to Elliptic and Parabolic equations and modern approaches.
- MW 2:40 p.m.-3:55 p.m.
-
Instructor:
Panagiota Daskalopoulos
CULPA: 19
Wikipedia
Info
- 4.5 points