### Current MSCS Graduate Courses ( Spring 2019, Fall 2019, Spring 2020 )

### Spring 2019

#### MATH 512

Advanced Topics in Logic: Combinatorial Set Theory (Sinapova)- PREREQUISITES:
- DESCRIPTION:
- This course is on applications of forcing and large cardinals to infinitary combinatorics. We will start with an introduction to cardinal arithmetic, especially at singular cardinals, large cardinals, and forcing techniques. Then we will analyze their interactions with combinatorial principles like square, the tree property, and strengthenings of the tree property such as ITP.

#### MATH 515

Number Theory II (Jones)- PREREQUISITES:
- MATH 514.
- DESCRIPTION:
- Introduction to classical, algebraic, and analytic number theory. Algebraic number fields, units, ideals, and P-adic theory. Riemann Zeta-function, Dirichlet's theorem, prime number theorem.

#### MATH 517

Second Course in Abstract Algebra II (Cojocaru)- PREREQUISITES:
- MATH 516.
- DESCRIPTION:
- Rings and algebras, polynomials in several variables, power series rings, tensor products, field extensions, Galois theory, Wedderburn theorems.

#### MATH 525

Advanced Topics in Number Theory: TBD (Takloo-Bighash)- PREREQUISITES:
- TBD
- DESCRIPTION:
- TBD

#### MATH 535

Complex Analysis I (Ross )- PREREQUISITES:
- MATH 411.
- DESCRIPTION:
- Analytic functions as mappings. Cauchy theory. Power Series. Partial fractions. Infinite products.

#### MATH 546

Advanced Topics in Analysis: Advanced Functional Analysis (Sparber)- PREREQUISITES:
- Math 533 and Math 539.
- DESCRIPTION:
- This course will focus on more advanced topics in functional analysis, usually not covered in the MATH 539. Among them are: The spectral theorem for bounded and unbounded self-adjoint operators; semi-groups of operators and applications to PDE; basic properties of locally convex spaces; perturbation theory for Schrödinger operators and application in quantum mechanics.

#### MATH 547

Algebraic Topology I (Whyte)- PREREQUISITES:
- MATH 330 and MATH 445.
- DESCRIPTION:
- The fundamental group and its applications, covering spaces, classification of compact surfaces, introduction to homology, development of singular homology theory, applications of homology.

#### MATH 550

Differentiable Manifolds II (Dumas)- PREREQUISITES:
- Math 549.
- DESCRIPTION:
- Vector bundles and classifying spaces, Lie groups and Lie algebras, tensors, Hodge theory, Poincare duality. Topics from elliptic operators, Morse theory, cobordism theory, de Rahm theory, characteristic classes.

#### MATH 553

Algebraic Geometry II (Coskun)- PREREQUISITES:
- Math 552.
- DESCRIPTION:
- Divisors and linear systems, differentials, Riemann-Roch theorem for curves, elliptic curves, geometry of curves and surfaces.

#### MATH 576

Classical Methods of Partial Differential Equations (Dai)- 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

### Fall 2019

Courses for this term have not been posted yet.

### Spring 2020

Courses for this term have not been posted yet.