Graduate Courses

To see a complete list of courses offered and their descriptions, visit the academic catalog.

For current course schedule information and registration visit SIS or consult the table below.

Spring 2023

Algebra I
AS.110.601 (01)

The first of a two semester algebra sequence to provide the student with the foundations for Number Theory, Algebraic Geometry, Representation Theory, and other areas. Topics include refined elements of group theory, commutative algebra, Noetherian rings, local rings, modules, and rudiments of category theory, homological algebra, field theory, Galois theory, and non-commutative algebras.

Credits: 4.00
Level: Graduate
Days/Times: TTh 12:00PM - 1:15PM
Instructor: Riehl, EMILY
Room: Bloomberg 276
Status: Open
Seats Available: 12/19
PosTag(s): n/a

Real Variables
AS.110.605 (01)

This course covers the theory of the Lebesgue theory of integration in d-dimensional Euclidean space, and offers a brief introduction to the theory of Hilbert spaces. Closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, Lp classes, and various results about differentiation are examined in detail. applications are basic facts about convolution operators and Fourier series, including results for the conjugate function and the Hardy-Littlewood maximal function.

Credits: 4.00
Level: Graduate
Days/Times: MW 12:00PM - 1:15PM
Instructor: Staff
Room:
Status: Open
Seats Available: 14/15
PosTag(s): n/a

Riemann Surfaces
AS.110.608 (01)

Abstract Riemann surfaces. Examples: algebraic curves, elliptic curves and functions on them. Holomorphic and meromorphic functions and differential forms, divisors and the Mittag-Leffler problem. The analytic genus. Bezout's theorem and applications. Introduction to sheaf theory, with applications to constructing linear series of meromorphic functions. Serre duality, the existence of meromorphic functions on Riemann surfaces, the equality of the topological and analytic genera, the equivalence of algebraic curves and compact Riemann surfaces, the Riemann-Roch theorem. Period matrices and the Abel-Jacobi mapping, Jacobi inversion, the Torelli theorem. Uniformization (time permitting).

Credits: 4.00
Level: Graduate
Days/Times: MW 12:00PM - 1:15PM
Instructor: Mese, CHIKAKO
Room: Gilman 10
Status: Open
Seats Available: 3/6
PosTag(s): n/a

Algebraic Topology I
AS.110.615 (01)

Singular homology theory, cohomology and products, category theory and homological algebra, Künneth and universal coefficient theorems, Poincaré and Alexander duality theorems, Lefschetz fixed-point theorem, covering spaces and fundamental groups. Prerequsites: the equivalent of one semester in both Abstract Algebra and Real Analysis (specifically, point set topology).

Credits: 4.00
Level: Graduate
Days/Times: MW 1:30PM - 2:45PM
Instructor: Campion, Tim Francis
Room: Bloomberg 172
Status: Open
Seats Available: 9/15
PosTag(s): n/a

Number Theory I
AS.110.617 (01)

Elements of advanced algebra and number theory. Possible topics for the year-long sequence include local and global fields, Galois cohomology, semisimple algebras, class field theory, elliptic curves, modular and automorphic forms, integral representations of L-functions, adelic geometry and function fields, fundamental notions in arithmetic geometry (including Arakelov and diophantine geometry).

Credits: 4.00
Level: Graduate
Days/Times: TTh 9:00AM - 10:15AM
Instructor: Li, Huajie
Room:
Status: Open
Seats Available: 15/15
PosTag(s): n/a

Partial Differential Equations I
AS.110.631 (01)

This course is the first in the sequence about the general theory of PDEs. The beginning of the course will describe several important results of functional analysis which are instrumental for the study of PDEs: Hahn-Banach theorem, Uniform boundedness and closed graph theorems, reflexive spaces and weak topologies, elements of semi-group theory. Then we will describe the basic theory of Sobolev spaces and the standard existence theory for (initial) boundary value problems of elliptic/parabolic type. Finally, the rest of the course will be devoted to finer properties of solutions of elliptic equations such as maximum principles, Harnack principles and regularity.

Credits: 4.00
Level: Graduate
Days/Times: MW 1:30PM - 2:45PM
Instructor: Duncan, Jonah Alexander Jacob
Room: Gilman 10
Status: Open
Seats Available: 2/6
PosTag(s): n/a

Functional Analysis
AS.110.637 (01)

This class will explore basic aspects of functional analysis, focusing mostly on normed vector spaces. This will include the Hahn-Banach and open mapping theorems, a discussion of strong and weak topologies, the theory of compact operators, and spaces of integrable functions and Sobolev spaces, with applications to the study of some partial differential equations. Prerequisite: Real Analysis

Credits: 4.00
Level: Graduate
Days/Times: MW 12:00PM - 1:15PM
Instructor: Sire, Yannick
Room: Bloomberg 178
Status: Open
Seats Available: 13/15
PosTag(s): n/a

Algebraic Geometry I
AS.110.643 (01)

Introduction to affine varieties and projective varieties. Hilbert's theorems about polynomials in several variables with their connections to geometry. Abstract algebraic varieties and projective geometry. Dimension of varieties and smooth varieties. Sheaf theory and some notions of cohomology. Applications of sheaves to geometry; e.g., theory of divisors, rudiments of scheme theory for the understanding of the Riemann-Roch theorem for curves and surfaces. Other topics may include Jacobian varieties, resolution of singularities, birational geometry on surfaces, schemes, connections with complex analytic geometry and topology. 

Credits: 4.00
Level: Graduate
Days/Times: TTh 12:00PM - 1:15PM
Instructor: Meng, Fanjun
Room:
Status: Open
Seats Available: 9/10
PosTag(s): n/a

Riemannian Geometry I
AS.110.645 (01)

This course is a graduate-level introduction to foundational material in Riemannian Geometry. Riemannian manifolds, a smooth manifold equipped with a Riemannian metric. Topics include connections, geodesics, Jacobi fields, submanifold theory including the second fundamental form and Gauss equations, manifolds of constant curvature, comparison theorems, Morse index theorem, Hadamard theorem and Bonnet-Myers theorem.

Credits: 4.00
Level: Graduate
Days/Times: TTh 10:30AM - 11:45AM
Instructor: Bernstein, Jacob
Room: Maryland 114
Status: Open
Seats Available: 9/15
PosTag(s): n/a

Topics in Algebraic Topology
AS.110.727 (01)

The class will be specifically focused on topics related to -theory, and its connections to number theory and manifold theory.

Credits: 3.00
Level: Graduate
Days/Times: TTh 12:00PM - 1:15PM
Instructor: Staff
Room:
Status: Open
Seats Available: 6/10
PosTag(s): n/a

Topics In Alg Num Theory
AS.110.733 (01)

Topics covered will vary from year to year and are at the discretion of the instructor.

Credits: 3.00
Level: Graduate
Days/Times: TTh 4:30PM - 5:45PM
Instructor: Savitt, David Lawrence
Room:
Status: Open
Seats Available: 8/10
PosTag(s): n/a

Topics in Algebraic Geometry
AS.110.737 (01)

Topics covered will vary from year to year and are at the discretion of the instructor.

Credits: 3.00
Level: Graduate
Days/Times: MW 1:30PM - 2:45PM
Instructor: Meng, Fanjun
Room: Krieger 204
Status: Open
Seats Available: 8/10
PosTag(s): n/a

Topics in Data Science
AS.110.773 (01)

Topics covered will vary from year to year and are at the discretion of the instructor.

Credits: 3.00
Level: Graduate
Days/Times: TTh 10:30AM - 11:45AM
Instructor: Lu, Fei
Room: Maryland 202
Status: Open
Seats Available: 10/10
PosTag(s): n/a

Independent Study-Graduates
AS.110.800 (01)

This is an independent study course for students interested in a working with a professor on a specific topic.

Credits: 3.00 - 9.00
Level: Graduate Independent Academic Work
Days/Times:
Instructor: Riehl, EMILY
Room:
Status: Open
Seats Available: 4/5
PosTag(s): n/a

Independent Study-Graduates
AS.110.800 (02)

This is an independent study course for students interested in a working with a professor on a specific topic.

Credits: 3.00 - 9.00
Level: Graduate Independent Academic Work
Days/Times:
Instructor: Mramor, Alex Everest
Room:
Status: Open
Seats Available: 5/5
PosTag(s): n/a

Independent Study-Graduates
AS.110.800 (03)

This is an independent study course for students interested in a working with a professor on a specific topic.

Credits: 3.00 - 9.00
Level: Graduate Independent Academic Work
Days/Times:
Instructor: Kitchloo, Nitya
Room:
Status: Open
Seats Available: 5/5
PosTag(s): n/a

Independent Study-Graduates
AS.110.800 (04)

This is an independent study course for students interested in a working with a professor on a specific topic.

Credits: 3.00 - 9.00
Level: Graduate Independent Academic Work
Days/Times:
Instructor: Sogge, Chris
Room:
Status: Open
Seats Available: 5/5
PosTag(s): n/a

Independent Study-Graduates
AS.110.800 (05)

This is an independent study course for students interested in a working with a professor on a specific topic.

Credits: 3.00 - 9.00
Level: Graduate Independent Academic Work
Days/Times:
Instructor: Gepner, David James
Room:
Status: Open
Seats Available: 5/5
PosTag(s): n/a

Independent Study-Graduates
AS.110.800 (06)

This is an independent study course for students interested in a working with a professor on a specific topic.

Credits: 3.00 - 9.00
Level: Graduate Independent Academic Work
Days/Times:
Instructor: Sire, Yannick
Room:
Status: Open
Seats Available: 5/5
PosTag(s): n/a

Thesis Research
AS.110.801 (01)