Courses - Fall 2019

MATH 1011 Academic Support for MATH 1110

Reviews material presented in MATH 1110 lectures, provides problem-solving techniques and tips as well as prelim review. Provides further instruction for students who need reinforcement. Not a substitute for attending MATH 1110 lectures.

Academic Career: UG Instructor: Raymond Cole (rbc6)
Full details for MATH 1011 : Academic Support for MATH 1110
MATH 1012 Academic Support for MATH 1120

Reviews material presented in MATH 1120 lectures, provides problem-solving techniques and tips as well as prelim review. Provides further instruction for students who need reinforcement. Not a substitute for attending MATH 1120 lectures or discussions.

Academic Career: UG Instructor: Mark Jauquet (maj29)
Full details for MATH 1012 : Academic Support for MATH 1120
MATH 1021 Academic Support for MATH 2210

Reviews material presented in MATH 2210 lectures, provides problem-solving techniques and tips as well as prelim review. Provides further instruction for students who need reinforcement. Not a substitute for attending MATH 2210 lectures or discussions.

Academic Career: UG Instructor: Mark Jauquet (maj29)
Full details for MATH 1021 : Academic Support for MATH 2210
MATH 1101 Calculus Preparation

Introduces topics in calculus: limits, rates of change, definition of and techniques for finding derivatives, relative and absolute extrema, and applications. The calculus content of the course is similar to 1/3 of the content covered in MATH 1106 and MATH 1110. In addition, the course includes a variety of topics of algebra, with emphasis on the development of linear, power, exponential, logarithmic, and trigonometric functions. Because of the strong emphasis on graphing, students will have a better understanding of asymptotic behavior of these functions.

Academic Career: UG Instructor: David Ruth (dcr7)
Full details for MATH 1101 : Calculus Preparation
MATH 1105 Finite Mathematics for the Life and Social Sciences

Introduction to linear algebra, probability, and Markov chains that develops the parts of the theory most relevant for applications. Specific topics include equations of lines, the method of least squares, solutions of linear systems, matrices; basic concepts of probability, permutations, combinations, binomial distribution, mean and variance, and the normal approximation to the binomial distribution. Examples from biology and the social sciences are used.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Federico Fuentes (ff245)
Full details for MATH 1105 : Finite Mathematics for the Life and Social Sciences
MATH 1110 Calculus I

Topics include functions and graphs, limits and continuity, differentiation and integration of algebraic, trigonometric, inverse trig, logarithmic, and exponential functions; applications of differentiation, including graphing, max-min problems, tangent line approximation, implicit differentiation, and applications to the sciences; the mean value theorem; and antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, substitution in integration, the area under a curve. Graphing calculators are used, and their pitfalls are discussed, as applicable to the above topics.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Fiona Young (fy79)
Full details for MATH 1110 : Calculus I
MATH 1120 Calculus II

Focuses on integration: applications, including volumes and arc length; techniques of integration, approximate integration with error estimates, improper integrals, differential equations (separation of variables, initial conditions, systems, some applications). Also covers infinite sequences and series: definition and tests for convergence, power series, Taylor series with remainder, and parametric equations.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Ayah Almousa (aka66)
Full details for MATH 1120 : Calculus II
MATH 1300 Mathematical Explorations

For students who wish to experience how mathematical ideas naturally evolve. The course emphasizes ideas and imagination rather than techniques and calculations. Homework involves students in actively investigating mathematical ideas. Topics vary depending on the instructor. Some assessment through writing assignments.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Inna Zakharevich (iiz5)
Full details for MATH 1300 : Mathematical Explorations
MATH 1710 Statistical Theory and Application in the Real World

Introductory statistics course discussing techniques for analyzing data occurring in the real world and the mathematical and philosophical justification for these techniques. Topics include population and sample distributions, central limit theorem, statistical theories of point estimation, confidence intervals, testing hypotheses, the linear model, and the least squares estimator. The course concludes with a discussion of tests and estimates for regression and analysis of variance (if time permits). The computer is used to demonstrate some aspects of the theory, such as sampling distributions and the Central Limit Theorem. In the lab portion of the course, students learn and use computer-based methods for implementing the statistical methodology presented in the lectures.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Michael Nussbaum (mn66)
Full details for MATH 1710 : Statistical Theory and Application in the Real World
MATH 1910 Calculus for Engineers

Essentially a second course in calculus. Topics include techniques of integration, finding areas and volumes by integration, exponential growth, partial fractions, infinite sequences and series, tests of convergence, and power series.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Clifford Pollock (crp10)
Full details for MATH 1910 : Calculus for Engineers
MATH 1920 Multivariable Calculus for Engineers

Introduction to multivariable calculus. Topics include partial derivatives, double and triple integrals, line and surface integrals, vector fields, Green's theorem, Stokes' theorem, and the divergence theorem.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Reyer Sjamaar (rs73)
Full details for MATH 1920 : Multivariable Calculus for Engineers
MATH 2210 Linear Algebra

Topics include vector algebra, linear transformations, matrices, determinants, orthogonality, eigenvalues, and eigenvectors. Applications are made to linear differential or difference equations. The lectures introduce students to formal proofs. Students are required to produce some proofs in their homework and on exams.

Distribution: (MQR-AS)
Academic Career: UG Instructor: James West (jew13)
Full details for MATH 2210 : Linear Algebra
MATH 2220 Multivariable Calculus

Differential and integral calculus of functions in several variables, line and surface integrals as well as the theorems of Green, Stokes, and Gauss.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Harrison Chen (hic7)
Full details for MATH 2220 : Multivariable Calculus
MATH 2230 Theoretical Linear Algebra and Calculus

Topics include vectors, matrices, and linear transformations; differential calculus of functions of several variables; inverse and implicit function theorems; quadratic forms, extrema, and manifolds; multiple and iterated integrals.

Distribution: (MQR-AS)
Academic Career: UG Instructor: John Hubbard (jhh8)
Full details for MATH 2230 : Theoretical Linear Algebra and Calculus
MATH 2310 Linear Algebra with Applications

Introduction to linear algebra for students who wish to focus on the practical applications of the subject. A wide range of applications are discussed and computer software may be used. The main topics are systems of linear equations, matrices, determinants, vector spaces, orthogonality, and eigenvalues. Typical applications are population models, input/output models, least squares, and difference equations.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Brian Hwang (bwh59)
Full details for MATH 2310 : Linear Algebra with Applications
MATH 2930 Differential Equations for Engineers

Introduction to ordinary and partial differential equations. Topics include: first-order equations (separable, linear, homogeneous, exact); mathematical modeling (e.g., population growth, terminal velocity); qualitative methods (slope fields, phase plots, equilibria, and stability); numerical methods; second-order equations (method of undetermined coefficients, application to oscillations and resonance, boundary-value problems and eigenvalues); and Fourier series. A substantial part of this course involves partial differential equations, such as the heat equation, the wave equation, and Laplace's equation. (This part must be present in any outside course being considered for transfer credit to Cornell as a substitute for MATH 2930.)

Distribution: (MQR-AS)
Academic Career: UG Instructor: Steven Strogatz (shs7)
Full details for MATH 2930 : Differential Equations for Engineers
MATH 2940 Linear Algebra for Engineers

Linear algebra and its applications. Topics include matrices, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and inner product spaces; applications include brief introductions to difference equations, Markov chains, and systems of linear ordinary differential equations. May include computer use in solving problems.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Alex Townsend (ajt253)
Full details for MATH 2940 : Linear Algebra for Engineers
MATH 3040 Prove It!

In mathematics, the methodology of proof provides a central tool for confirming the validity of mathematical assertions, functioning much as the experimental method does in the physical sciences. In this course, students learn various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and in set theory and combinatorics, and then moving to applications and illustrations of these via topics in one or more of the three main pillars of mathematics: algebra, analysis, and geometry. Since cogent communication of mathematical ideas is important in the presentation of proofs, the course emphasizes clear, concise exposition.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Ed Swartz (ebs22)
Full details for MATH 3040 : Prove It!
MATH 3110 Introduction to Analysis

Provides a transition from calculus to real analysis. Topics include rigorous treatment of fundamental concepts in calculus: including limits and convergence of sequences and series, compact sets; continuity, uniform continuity and differentiability of functions. Emphasis is placed upon understanding and constructing mathematical proofs.

Distribution: (MQR-AS)
Academic Career: UG Instructor: David Zywina (djz44)
Full details for MATH 3110 : Introduction to Analysis
MATH 3210 Manifolds and Differential Forms

A manifold is a type of subset of Euclidean space that has a well-defined tangent space at every point. Such a set is amenable to the methods of multivariable calculus. After a review of some relevant calculus, this course investigates manifolds and the structures that they are endowed with, such as tangent vectors, boundaries, orientations, and differential forms. The notion of a differential form encompasses such ideas as surface and volume forms, the work exerted by a force, the flow of a fluid, and the curvature of a surface, space, or hyperspace. The course re-examines the integral theorems of vector calculus (Green, Gauss, and Stokes) in the light of differential forms and applies them to problems in partial differential equations, topology, fluid mechanics, and electromagnetism.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Xiaodong Cao (xc46)
Full details for MATH 3210 : Manifolds and Differential Forms
MATH 3230 Introduction to Differential Equations

A brief one-semester introduction to the theory and techniques of both ordinary and partial differential equations. Topics for ordinary differential equations may include initial-value and two-point boundary value problems, the basic existence and uniqueness theorems, continuous dependence on data, stability of fix-points, numerical methods, special functions. Topics for partial differential equations may include the Poisson, heat and wave equations, boundary and initial-boundary value problems, maximum principles, continuous dependence on data, separation of variables, Fourier series, Green's functions, numerical methods, transform methods.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Christian Noack (cjn59)
Full details for MATH 3230 : Introduction to Differential Equations
MATH 3320 Introduction to Number Theory

An introductory course on number theory, the branch of algebra that studies the deeper properties of integers and their generalizations. Usually includes most of the following topics: the Euclidean algorithm, continued fractions, Pythagorean triples, Diophantine equations such as Pell's equation, congruences, quadratic reciprocity, binary quadratic forms, Gaussian integers, and factorization in quadratic number fields. May include a brief introduction to Fermat's Last Theorem.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Nicolas Templier (npt27)
Full details for MATH 3320 : Introduction to Number Theory
MATH 3610 Mathematical Modeling

Introduction to the theory and practice of mathematical modeling. This course compares and contrasts different types of mathematical models (discrete vs. continuous, deterministic vs. stochastic), focusing on advantages, disadvantages and limits of applicability for each approach. Case-study format covers a variety of application areas including economics, physics, sociology, traffic engineering, urban planning, robotics, and resource management. Students learn how to implement mathematical models on the computer and how to interpret/describe the results of their computational experiments.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Alexander Vladimirsky (abv8)
Full details for MATH 3610 : Mathematical Modeling
MATH 3850 Modal Logic

Modal logic is a general logical framework for systematizing reasoning about qualified and relativized truth. It has been used to study the logic of possibility, time, knowledge, obligation, provability, and much more. This course will explore both the theoretical foundations and the various philosophical applications of modal logic. On the theoretical side, we will cover basic metatheory, including Kripke semantics, soundness and completeness, correspondence theory, and expressive power. On the applied side, we will examine temporal logic, epistemic logic, deontic logic, counterfactuals, two-dimensional logics, and quantified modal logic. 

Academic Career: UG Instructor: Alexander Kocurek (awk78)
Full details for MATH 3850 : Modal Logic
MATH 4030 History of Mathematics

Survey of the development of mathematics from antiquity to the present, with an emphasis on the achievements, problems, and mathematical viewpoints of each historical period and the evolution of such basic concepts as number, geometry, construction, and proof.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Anil Nerode (an17)
Full details for MATH 4030 : History of Mathematics
MATH 4130 Honors Introduction to Analysis I

Introduction to the rigorous theory underlying calculus, covering the real number system and functions of one variable. Based entirely on proofs. The student is expected to know how to read and, to some extent, construct proofs before taking this course. Topics typically include construction of the real number system, properties of the real number system, continuous functions, differential and integral calculus of functions of one variable, sequences and series of functions.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Florin Camil Muscalu (fm69)
Full details for MATH 4130 : Honors Introduction to Analysis I
MATH 4200 Differential Equations and Dynamical Systems

Covers ordinary differential equations in one and higher dimensions: qualitative, analytic, and numerical methods. Emphasis is on differential equations as models and the implications of the theory for the behavior of the system being modeled and includes an introduction to bifurcations.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Andy Borum (adb328)
Full details for MATH 4200 : Differential Equations and Dynamical Systems
MATH 4220 Applied Complex Analysis

Covers complex variables, Fourier transforms, Laplace transforms and applications to partial differential equations. Additional topics may include an introduction to generalized functions.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Richard Rand (rhr2)
Full details for MATH 4220 : Applied Complex Analysis
MATH 4250 Numerical Analysis and Differential Equations

Introduction to the fundamentals of numerical analysis: error analysis, approximation, interpolation, numerical integration. In the second half of the course, the above are used to build approximate solvers for ordinary and partial differential equations. Strong emphasis is placed on understanding the advantages, disadvantages, and limits of applicability for all the covered techniques. Computer programming is required to test the theoretical concepts throughout the course.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Federico Fuentes (ff245)
Full details for MATH 4250 : Numerical Analysis and Differential Equations
MATH 4310 Linear Algebra

Introduction to linear algebra, including the study of vector spaces, linear transformations, matrices, and systems of linear equations. Additional topics are quadratic forms and inner product spaces, canonical forms for various classes of matrices and linear transformations.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Michael Stillman (mes15)
Full details for MATH 4310 : Linear Algebra
MATH 4330 Honors Linear Algebra

Honors version of a course in advanced linear algebra, which treats the subject from an abstract and axiomatic viewpoint. Topics include vector spaces, linear transformations, polynomials, determinants, tensor and wedge products, canonical forms, inner product spaces, and bilinear forms. Emphasis is on understanding the theory of linear algebra; homework and exams include at least as many proofs as computational problems.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Martin Kassabov (mdk35)
Full details for MATH 4330 : Honors Linear Algebra
MATH 4370 Computational Algebra

Introduction to algebraic geometry and computational algebra. In this course, students learn how to compute a Gröbner basis for polynomials in many variables. Covers the following applications: solving systems of polynomial equations in many variables, solving diophantine equations in many variables, 3-colorable graphs, and integer programming. Such applications arise, for example, in computer science, engineering, economics, and physics.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Karola Meszaros (km626)
Full details for MATH 4370 : Computational Algebra
MATH 4410 Introduction to Combinatorics I

Combinatorics is the study of discrete structures that arise in a variety of areas, particularly in other areas of mathematics, computer science, and many areas of application. Central concerns are often to count objects having a particular property (e.g., trees) or to prove that certain structures exist (e.g., matchings of all vertices in a graph). The first semester of this sequence covers basic questions in graph theory, including extremal graph theory (how large must a graph be before one is guaranteed to have a certain subgraph) and Ramsey theory (which shows that large objects are forced to have structure). Variations on matching theory are discussed, including theorems of Dilworth, Hall, König, and Birkhoff, and an introduction to network flow theory. Methods of enumeration (inclusion/exclusion, Möbius inversion, and generating functions) are introduced and applied to the problems of counting permutations, partitions, and triangulations.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Ed Swartz (ebs22)
Full details for MATH 4410 : Introduction to Combinatorics I
MATH 4530 Introduction to Topology

Topology may be described briefly as qualitative geometry. This course begins with basic point-set topology, including connectedness, compactness, and metric spaces. Later topics may include the classification of surfaces (such as the Klein bottle and Möbius band), elementary knot theory, or the fundamental group and covering spaces.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Kathryn Mann (kpm85)
Full details for MATH 4530 : Introduction to Topology
MATH 4710 Basic Probability

Introduction to probability theory, which prepares the student to take MATH 4720. The course begins with basics: combinatorial probability, mean and variance, independence, conditional probability, and Bayes formula. Density and distribution functions and their properties are introduced. The law of large numbers and the central limit theorem are stated and their implications for statistics are discussed.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Michael Nussbaum (mn66)
Full details for MATH 4710 : Basic Probability
MATH 4820 Topics in Logic and the Foundations of Mathematics

After reviewing some material on standard logics (classical and intuitionistic), and covering Tarskian consequence relations, we will focus on logics for monadic operators (especially for necessity and possibility, for which the logics are called modal).  Time permitting, we will also consider dyadic operators (especially conditionals). Logics will be considered proof-theoretically and model-theoretically. A background in logic is required.

Distribution: (MQR-AS)
Academic Career: UG Instructor: Harold Hodes (hth3)
Full details for MATH 4820 : Topics in Logic and the Foundations of Mathematics
MATH 4860 Applied Logic

Propositional and predicate logic, compactness and completeness using tableaux, natural deduction, and/or resolution. Other topics chosen from the following: Equational logic. Herbrand Universes and unification. Rewrite rules and equational logic, Knuth-Bendix method, and the congruence-closure algorithm and lambda-calculus reduction strategies. Modal logics, intuitionistic logic, Prolog, LISP, ML, or Nuprl. Applications to expert systems and program verification. Noncomputability (Turing) and incompleteness (Gödel).

Distribution: (MQR-AS)
Academic Career: UG Instructor: Bob Constable (rlc7)
Full details for MATH 4860 : Applied Logic
MATH 4900 Supervised Research

An independent research course by arrangement with an individual professor.  The goal is for the student to perform an independent investigation into a specific mathematical question.  The student and professor will set expectations and grading policies at the beginning of the term.

Academic Career: UG Instructor: Marcelo Aguiar (ma18)
Full details for MATH 4900 : Supervised Research
MATH 4901 Supervised Reading

An independent reading course by arrangement with an individual professor. The goal is for the student to master a body of mathematics outside the normal curriculum. The student and professor will set expectations and grading policies at the beginning of the term.

Academic Career: UG Instructor: Marcelo Aguiar (ma18)
Full details for MATH 4901 : Supervised Reading
MATH 5080 Special Study for Teachers

Examines principles underlying the content of the secondary school mathematics curriculum, including connections with the history of mathematics, technology, and mathematics education research. One credit is awarded for attending three of the four Saturday workshops per year. Other credit options are available by permission of instructor for students completing additional work (e.g., independent study projects or presentations).

Academic Career: GR Instructor: Mary Ann Huntley (mh688)
Full details for MATH 5080 : Special Study for Teachers
MATH 6110 Real Analysis

This course covers measure and integration and functional analysis.

Academic Career: GR Instructor: Florin Camil Muscalu (fm69)
Full details for MATH 6110 : Real Analysis
MATH 6150 Partial Differential Equations

This course emphasizes the "classical" aspects of partial differential equations (PDEs).  The usual topics include fundamental solutions for the Laplace/Poisson, heat and and wave equations in Rn, mean-value properties, maximum principles, energy methods, Duhamel's principle, and an introduction to nonlinear first-order equations, including shocks and weak solutions. Additional topics may include Hamilton-Jacobi equations, distribution theory, and the Fourier transform.

Academic Career: GR Instructor: Gennady Uraltsev (gu35)
Full details for MATH 6150 : Partial Differential Equations
MATH 6210 Measure Theory and Lebesgue Integration

Covers measure theory, integration, and Lp spaces.

Academic Career: GR Instructor: Mahdi Asgari (ma735)
Full details for MATH 6210 : Measure Theory and Lebesgue Integration
MATH 6230 Differential Games and Optimal Control

This course is a self-contained introduction to the modern theory of optimal control and differential games. Dynamic programming uses Hamilton-Jacobi partial differential equations (PDEs) to encode the optimal behavior in cooperative and adversarial sequential decision making problems. The same PDEs have an alternative interpretation in the context of front propagation problems. We show how both interpretations are useful in constructing efficient numerical methods. We also consider a wide range of applications, including robotics, computational geometry, path-planning, computer vision, photolithography, economics, seismic imaging, ecology, financial engineering, crowd dynamics, and aircraft collision avoidance. Assumes no prior knowledge of non-linear PDEs or numerical analysis.

Academic Career: GR Instructor: Alexander Vladimirsky (abv8)
Full details for MATH 6230 : Differential Games and Optimal Control
MATH 6310 Algebra

MATH 6310-MATH 6320 are the core algebra courses in the mathematics graduate program. MATH 6310 covers group theory, especially finite groups; rings and modules; ideal theory in commutative rings; arithmetic and factorization in principal ideal domains and unique factorization domains; introduction to field theory; tensor products and multilinear algebra. (Optional topic: introduction to affine algebraic geometry.)

Academic Career: GR Instructor: Marcelo Aguiar (ma18)
Full details for MATH 6310 : Algebra
MATH 6340 Commutative Algebra with Applications in Algebraic Geometry

Covers Dedekind domains, primary decomposition, Hilbert basis theorem, and local rings.

Academic Career: GR Instructor: Michael Stillman (mes15)
Full details for MATH 6340 : Commutative Algebra with Applications in Algebraic Geometry
MATH 6390 Lie Groups and Lie Algebras

Covers the basics of Lie groups and Lie algebras. Topics include real and complex Lie groups, relations between Lie groups and Lie algebras, exponential map, homogeneous manifolds and the classification of simple Lie algebras.

Academic Career: GR Instructor: Birgit Speh (bes12)
Full details for MATH 6390 : Lie Groups and Lie Algebras
MATH 6520 Differentiable Manifolds

MATH 6510-MATH 6520 are the core topology courses in the mathematics graduate program. MATH 6520 is an introduction to geometry and topology from a differentiable viewpoint, suitable for beginning graduate students. The objects of study are manifolds and differentiable maps. The collection of all tangent vectors to a manifold forms the tangent bundle, and a section of the tangent bundle is a vector field. Alternatively, vector fields can be viewed as first-order differential operators. Students study flows of vector fields and prove the Frobenius integrability theorem. In the presence of a Riemannian metric, the notions of parallel transport, curvature, and geodesics are development. Students examine the tensor calculus and the exterior differential calculus and prove Stokes' theorem. If time permits, de Rham cohomology, Morse theory, or other optional topics are introduced.

Academic Career: GR Instructor: Allen Knutson (ak596)
Full details for MATH 6520 : Differentiable Manifolds
MATH 6640 Hyperbolic Geometry

An introduction to the topology and geometry of hyperbolic manifolds. The class will begin with the geometry of hyperbolic n-space, including the upper half-space, Poincaré disc, and Lorentzian models. Particular attention will be paid to the cases n=2 and n=3. Hyperbolic structures on surfaces will be parametrized using Teichmüller space, and discrete groups of isometries of hyperbolic space will be discussed. Other possible topics include the topology of hyperbolic manifolds and orbifolds; Mostow rigidity; hyperbolic Dehn filling; deformation theory of Kleinian groups; complex and quaternionic hyperbolic geometry; and convex projective structures on manifolds.

Academic Career: GR Instructor: Martin Kassabov (mdk35)
Full details for MATH 6640 : Hyperbolic Geometry
MATH 6670 Algebraic Geometry

A first course in algebraic geometry. Affine and projective varieties. The Nullstellensatz. Schemes and morphisms between schemes. Dimension theory. Potential topics include normalization, Hilbert schemes, curves and surfaces, and other choices of the instructor.

Academic Career: GR Instructor: Harrison Chen (hic7)
Full details for MATH 6670 : Algebraic Geometry
MATH 6710 Probability Theory I

A mathematically rigorous course in probability theory which uses measure theory but begins with the basic definitions of independence and expected value in that context. Law of large numbers, Poisson and central limit theorems, and random walks.

Academic Career: GR Instructor: Lionel Levine (ll432)
Full details for MATH 6710 : Probability Theory I
MATH 6840 Recursion Theory

Covers theory of effectively computable functions; classification of recursively enumerable sets; degrees of recursive unsolvability; applications to logic; hierarchies; recursive functions of ordinals and higher type objects; generalized recursion theory.

Academic Career: GR Instructor: Richard Shore (ras13)
Full details for MATH 6840 : Recursion Theory
MATH 7130 Functional Analysis

Covers topological vector spaces, Banach and Hilbert spaces, and Banach algebras. Additional topics selected by instructor.

Academic Career: GR Instructor: Timothy Healey (tjh10)
Full details for MATH 7130 : Functional Analysis
MATH 7290 Seminar on Scientific Computing and Numerics

Talks on various methods in scientific computing, the analysis of their convergence properties and computational efficiency, and their adaptation to specific applications.

Academic Career: GR Instructor: Anil Damle (asd239)
Alex Townsend (ajt253)
Full details for MATH 7290 : Seminar on Scientific Computing and Numerics
MATH 7310 Topics in Algebra

Selection of advanced topics from algebra. Course content varies.

Academic Career: GR Instructor: Allen Knutson (ak596)
Full details for MATH 7310 : Topics in Algebra
MATH 7510 Berstein Seminar in Topology

A seminar on an advanced topic in topology or a related subject. Content varies. The format is usually that the participants take turns to present.

Academic Career: GR Instructor: Inna Zakharevich (iiz5)
Full details for MATH 7510 : Berstein Seminar in Topology
MATH 7550 Topology and Geometric Group Theory Seminar

A weekly seminar in which visiting or local speakers present results in topology, geometric group theory, or related subjects.

Academic Career: GR Full details for MATH 7550 : Topology and Geometric Group Theory Seminar
MATH 7610 Topics in Geometry

Selection of advanced topics from modern geometry. Content varies.

Academic Career: GR Instructor: Robert Connelly (rc46)
Full details for MATH 7610 : Topics in Geometry
MATH 7740 Statistical Learning Theory: Classification, Pattern Recognition, Machine Learning

The course aims to present the developing interface between machine learning theory and statistics. Topics include an introduction to classification and pattern recognition; the connection to nonparametric regression is emphasized throughout. Some classical statistical methodology is reviewed, like discriminant analysis and logistic regression, as well as the notion of perception which played a key role in the development of machine learning theory. The empirical risk minimization principle is introduced, as well as its justification by Vapnik-Chervonenkis bounds. In addition, convex majoring loss functions and margin conditions that ensure fast rates and computable algorithms are discussed. Today's active high-dimensional statistical research topics such as oracle inequalities in the context of model selection and aggregation, lasso-type estimators, low rank regression and other types of estimation problems of sparse objects in high-dimensional spaces are presented.

Academic Career: GR Instructor: Marten Wegkamp (mhw73)
Full details for MATH 7740 : Statistical Learning Theory: Classification, Pattern Recognition, Machine Learning
MATH 7810 Seminar in Logic

A twice weekly seminar in logic. Typically, a topic is selected for each semester, and at least half of the meetings of the course are devoted to this topic with presentations primarily by students. Opportunities are also provided for students and others to present their own work and other topics of interest.

Academic Career: GR Instructor: Justin Moore (jtm237)
Full details for MATH 7810 : Seminar in Logic
MATH 7850 Topics in Logic

Covers topics in mathematical logic which vary from year to year, such as descriptive set theory or proof theory.  May also be used to further develop material from model theory (MATH 6830), recursion theory (MATH 6840), or set theory (MATH 6870).

Academic Career: GR Instructor: Slawomir Solecki (ss3777)
Full details for MATH 7850 : Topics in Logic
MATH 7900 Supervised Reading and Research

Supervised research for the doctoral dissertation.

Academic Career: GR Instructor: Karola Meszaros (km626)
Full details for MATH 7900 : Supervised Reading and Research