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)

• TR 1:10 p.m.-2:25 p.m.
• TR 2:40 p.m.-3:55 p.m.
• MW 10:10 a.m.-11:25 a.m.
• Instructor: Roger W Van Peski
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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)

• MW 11:40 a.m.-12:55 p.m.
• TR 10:10 a.m.-11:25 a.m.
• TR 11:40 a.m.-12:55 p.m.
• 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)

• TR 8:40 a.m.-9:55 a.m.
• TR 10:10 a.m.-11:25 a.m.
• MW 2:40 p.m.-3:55 p.m.
• TR 2:40 p.m.-3:55 p.m.
• Instructor: Tang-Kai Lee
  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 1:10 p.m.-2:25 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: 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.

• T 4:10 p.m.-5 p.m.
• 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.

• W 4:10 p.m.-5 p.m.
• W 6:10 p.m.-7 p.m.
• Instructor: Tianqing Zhu
  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.

• TR 10:10 a.m.-11:25 a.m.
• 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.
• 0 points

LINEAR ALGEBRA

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

• TR 2:40 p.m.-3:55 p.m.
• MW 11:40 a.m.-12:55 p.m.
• MW 10:10 a.m.-11:25 a.m.
• TR 6:10 p.m.-7:25 p.m.
• Instructor: James E Hotchkiss
  Info
• Instructor: Abigail G Hickok
  Info
• Instructor: Anh Duc Vo
  Info
• Instructor: Elliott V Stein
  CULPA: 16 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.

• TR 11:40 a.m.-12:55 p.m.
• TR 1:10 p.m.-2:25 p.m.
• Instructor: Tommaso M Botta
  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.
• MW 4:10 p.m.-5:25 p.m.
• Instructor: Elena Giorgi
  h-index: 5 Info
• 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)

• TR 4:10 p.m.-5:25 p.m.
• 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 8:40 a.m.-9:55 a.m.
• Instructor: Sangiovanni Vincentelli Marco
  Info
• 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
  Info
• 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.

• MW 1:10 p.m.-2:25 p.m.
• Instructor: Panagiota Daskalopoulos
  CULPA: 19 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

UNDERGRADUATE SEMINARS II

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. Prerequisite: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission.

• MW 2:40 p.m.-3:55 p.m.
• Instructor: Chiu-Chu Liu
  CULPA: 1 Wikipedia Info
• 3 points

ANALYTIC NUMBER THEORY

Prerequisites: MATH UN3007 A one semeser course covering the theory of modular forms, zeta functions, L -functions, and the Riemann hypothesis. Particular topics covered include the Riemann zeta function, the prime number theorem, Dirichlet characters, Dirichlet L-functions, Siegel zeros, prime number theorem for arithmetic progressions, SL (2, Z) and subgroups, quotients of the upper half-plane and cusps, modular forms, Fourier expansions of modular forms, Hecke operators, L-functions of modular forms.

• TR 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 4:10 p.m.-5:25 p.m.
• Instructor: Myungsin Cho
  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.

• TR 1:10 p.m.-2:25 p.m.
• Instructor: Michael Thaddeus
  CULPA: 24 Wikipedia 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.

• MW 11:40 a.m.-12:55 p.m.
• 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 1:10 p.m.-2:25 p.m.
• Instructor: Yoonjoo Kim
  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.

• TR 2:40 p.m.-3:55 p.m.
• Instructor: Deeparaj Bhat
  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.

• TR 4:10 p.m.-5:25 p.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.
• 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: Julien Dubedat
  CULPA: 4 Info
• 3 points

MATHEMATICS AND THE HUMANITIES

This course is being taught by two senior faculty members who are theorists and practitioners in disciplines as different as mathematics and literary criticism. The instructors believe that in today's world, the different ways in which theoretical mathematics and literary criticism mold the imaginations of students and scholars, should be brought together, so that the robust ethical imagination that is needed to combat the disintegration of our world can be produced. Except for the length of novels, the reading is no more than 100 pages a week.

Our general approach is to keep alive the disciplinary differences between literary/philosophical (humanities) reading and mathematical writing.  Some preliminary questions we have considered are: the survival skills of the logicist school over against the Foundational Crisis of the early 20th century; by way of Wittgenstein and others, we ask, Are mathematical objects real? Or are they linguistic conventions? We will consider the literary/philosophical use of mathematics, often by imaginative analogy; and the role of the digital imagination in the humanities: Can so-called creative work as well as mathematics be written by machines? Guest faculty from other departments will teach with us to help students and instructors understand various topics.  We will close with how a novel animates “science” in prose, stepping out of the silo of disciplinary mathematics to the arena where mathematics is considered a code-name for science: Christine Brooke-Rose’s novel
Subscript
.

• T 4:10 p.m.-6 p.m.
• Instructor: Michael Harris
  CULPA: 6 Wikipedia Info
• 4 points

THE TEACHING OF MATHEMATICS

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

• W 11:40 a.m.-12:55 p.m.
• Instructor: George Dragomir
  CULPA: 5 Info
• 0 points

ANALYSIS II

Continuation of MATH GR6151x (see Fall listing).

• TR 10:10 a.m.-11:25 a.m.
• Instructor: 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).

• TR 4:10 p.m.-5:25 p.m.
• Instructor: Ioannis Karatzas
  CULPA: 7 h-index: 58 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 4:10 p.m.-5:25 p.m.
• Instructor: Aise Johan de Jong
  CULPA: 5 Wikipedia Info
• 4.5 points

TOPICS IN ALGEBRAIC GEOMETRY

• MW 2:40 p.m.-3:55 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
  Info
• 4.5 points

LIE GROUPS & REPRESENTATIONS

Continuation of MATH GR6343x (see Fall listing).

• MW 1:10 p.m.-2:25 p.m.
• Instructor: Andrei Okounkov
  CULPA: 1 Wikipedia h-index: 55 Info
• 4.5 points

MODERN GEOMETRY

Continuation of Mathematics GR6402x (see Fall listing).

• TR 2:40 p.m.-3:55 p.m.
• Instructor: Simon Brendle
  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