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.-8 p.m.
• TR 10:10 a.m.-11:25 a.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 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.
• TR 4:10 p.m.-5:25 p.m.
• TR 10:10 a.m.-11:25 a.m.
• TR 2:40 p.m.-3:55 p.m.
• MW 4:10 p.m.-5:25 p.m.
• TR 6:10 p.m.-8:15 p.m.
• Instructor: Evan Sorensen
  Info
• Instructor: Qiao He
  Info
• 3 points

CALCULUS II

Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (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.
• TR 6:10 p.m.-8:15 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)

• MW 4:10 p.m.-5:25 p.m.
• MW 6:10 p.m.-8 p.m.
• TR 10:10 a.m.-11:25 a.m.
• TR 11:40 a.m.-12:55 p.m.
• Instructor: Deeparaj Bhat
  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.-8:15 p.m.
• TR 10:10 a.m.-11:25 a.m.
• Instructor: Mikhail Smirnov
  CULPA: 16 Info
• Instructor: Ovidiu Savin
  CULPA: 22 Wikipedia Info
• 3 points

INTRO TO HIGHER MATHEMATICS

Introduction to understanding and writing mathematical proofs. Emphasis on precise thinking and the presentation of mathematical results, both in oral and in written form. Intended for students who are considering majoring in mathematics but wish additional training. CC/GS: Partial Fulfillment of Science Requirement. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

• TR 10:10 a.m.-11:25 a.m.
• Instructor: George Dragomir
  CULPA: 5 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 11 a.m.-1 p.m.
• 0 points

LINEAR ALGEBRA

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

• MW 8:40 a.m.-9:55 a.m.
• MW 11:40 a.m.-12:55 p.m.
• TR 10:10 a.m.-11:25 a.m.
• TR 4:10 p.m.-5:25 p.m.
• Instructor: Yoonjoo Kim
  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 11:40 a.m.-12:55 p.m.
• MW 6:10 p.m.-8:15 p.m.
• TR 1:10 p.m.-2:25 p.m.
• 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)

• MW 4:10 p.m.-5:25 p.m.
• TR 10:10 a.m.-11:25 a.m.
• Instructor: Xi S Shen
  h-index: 4 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.
• Instructor: Dorian Goldfeld
  CULPA: 23 Wikipedia Info
• 3 points

DIFFERENTIAL GEOMETRY

• MW 1:10 p.m.-2:25 p.m.
• Instructor: Elena Giorgi
  h-index: 5 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.

• TR 10:10 a.m.-11:25 a.m.
• 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.
• Instructor: Robert D Friedman
  CULPA: 44 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 10:10 a.m.-11:25 a.m.
• Instructor: Yujie Xu
  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 11:40 a.m.-12:55 p.m.
• Instructor: Aise Johan de Jong
  CULPA: 5 Wikipedia 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 6:10 p.m.-8:15 p.m.
• Instructor: Rostislav Akhmechet
  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 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 6:10 p.m.-8:15 p.m.
• Instructor: Jeanne Boursier
  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 10:10 a.m.-11:25 a.m.
• 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.

• TR 2:40 p.m.-3:55 p.m.
• Instructor: Ioannis Karatzas
  CULPA: 7 h-index: 58 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 1:10 p.m.-2:25 p.m.
• Instructor: Peter G Woit
  CULPA: 6 Info
• 3 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.

• MW 1:10 p.m.-2:25 p.m.
• Instructor: Ivan Corwin
  CULPA: 1 Wikipedia h-index: 34 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 2:40 p.m.-3:55 p.m.
• 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.

• MW 11:40 a.m.-12:55 p.m.
• Instructor: Lucy Yang
  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 1:10 p.m.-2:25 p.m.
• 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 2:40 p.m.-3:55 p.m.
• Instructor: Chiu-Chu Liu
  CULPA: 1 Wikipedia Info
• 4.5 points

TOPICS IN NUMBER THEORY

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