### Current MSCS Graduate Courses ( Spring 2017, Fall 2017, Spring 2018 )

### Spring 2017

MATH 507
Model Theory II
(Marker)

- PREREQUISITES:
- Math 506 or Phil 567.
- DESCRIPTION:
- Intermediate stability theory, dependence, prime models, isolation, regular types, dimension, weight.

MATH 512
Advanced Topics in Logic: Forcing and Large Cardinals
(Sinapova)

- PREREQUISITES:
- Approval of the Department.
- DESCRIPTION:
- Large cardinals, iterated forcing, Prikry type forcing. Applications to infinitary combinatorics, singular cardinals, square principles, and the tree property.

MATH 514
Number Theory I
(Takloo-Bighash)

- PREREQUISITES:
- MATH 514
- DESCRIPTION:
- Introduction to classical, algebraic, and analytic, number theory. Euclid's algorithm, unique factorization, quadratic reciprocity, and Gauss sums, quadratic forms, real approximations, arithmetic functions, Diophantine equations.

MATH 517
Second Course in Abstract Algebra II
(Zhang)

- PREREQUISITES:
- MATH 516
- DESCRIPTION:
- Rings and algebras, polynomials in several variables, power series rings, tensor products, field extensions, Galois theory, Wedderburn theorems.

MATH 535
Complex Analysis I
(Furman)

- PREREQUISITES:
- MATH 411.
- DESCRIPTION:
- Analytic functions as mappings. Cauchy theory. Power Series. Partial fractions. Infinite products.

MATH 548
Algebraic Topology II
(Whyte)

- PREREQUISITES:
- MATH 547
- DESCRIPTION:
- Cohomology theory, universal coefficient theorems, cohomology products and their applications, orientation and duality for manifolds, homotopy groups and fibrations, the Hurewicz theorem, selected topics.

MATH 549
Differentiable Manifolds I
(Schaposnik)

- PREREQUISITES:
- Math 445; and Math 310 or Math 320 or the equivalent.
- DESCRIPTION:
- Smooth manifolds and maps, tangent and normal bundles, Sard's theorem and transversality, embedding, differential forms, Stokes' theorem, degree theory, vector fields.

MATH 553
Algebraic Geometry II
(Paun)

- PREREQUISITES:
- Math 552.
- DESCRIPTION:
- Divisors and linear systems, differentials, Riemann-Roch theorem for curves, elliptic curves, geometry of curves and surfaces.

MATH 569
Advanced Topics in Geometric and Differential Topology: Representations of Surface Groups
(Dumas)

- PREREQUISITES:
- Approval of the department
- DESCRIPTION:

MATH 569
Advanced Topics in Geometric and Differential Topology
(Kauffman)

- PREREQUISITES:
- Math 547
- DESCRIPTION:
- Topics in Knot Theory: The course will cover basic knot theory and touch on current research questions.

MATH 571
Advanced Topics in Algebraic Geometry: Frobenius Singularities and Postive Characteristic Methods
(Tucker)

- PREREQUISITES:
- Approval of the department
- DESCRIPTION:

MATH 576
Classical Methods of Partial Differential Equations
(Shvydkoy)

- PREREQUISITES:
- MATH 410 and MATH 481 and MATH 533; or consent of instructor
- DESCRIPTION:
- First and second order equations, method of characteristics, weak solutions, distributions, wave, Laplace, Poisson, heat equations, energy methods, regularity problems, Green functions, maximum principles, Sobolev spaces, imbedding theorems

MATH 580
Mathematics of Fluid Mechanics
(Cheskidov)

- PREREQUISITES:
- Grade of C or better in MATH 410 and grade of C or better in MATH 417 and grade of C or better in MATH 481
- DESCRIPTION:
- Development of concepts and techniques used in mathematical models of fluid motions. Euler and Navier Stokes equations. Vorticity and vortex motion. Waves and instabilities. Viscous fluids and boundary layers. Asymptotic methods

### Fall 2017

Courses for this term have not been posted yet.

### Spring 2018

Courses for this term have not been posted yet.