### Current MSCS Graduate Courses ( Spring 2018, Fall 2018, Spring 2019 )

### Spring 2018

#### MATH 511

Descriptive Set Theory (Sinapova)- PREREQUISITES:
- Recommended background: MATH 445 or MATH 504 or MATH 533 or MATH 539.
- DESCRIPTION:
- Polish spaces and Baire category; Borel, analytic and coanalytic sets; infinite games and determinacy; coanalytic ranks and scales; dichotomy theorems.

#### MATH 514

Number Theory I (Cojocaru)- PREREQUISITES:
- None
- 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 (Tucker)- 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 (Jones)- PREREQUISITES:
- TBD
- DESCRIPTION:
- TBA

#### MATH 535

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

#### MATH 537

Introduction to Harmonic Analysis I (Greenblatt)- PREREQUISITES:
- Math 533, plus Math 417 or Math 535.
- DESCRIPTION:
- Text: J. Duoandikoetxea "Fourier Analysis", AMS, Grad Stud in Math, Vol 29. Excellent concise text on harmonic analysis with a good selection of exercises. Topics will include Fourier Transform, Hardy-Littlewood maximal function, singular integral operators and Hilbert transform, Littlewood-Paley theory, Sobolev and Besov spaces, BMO, and Hardy spaces, Bernstein inequalities, Carleson measures, applications to PDE.

#### MATH 547

Algebraic Topology I (Antieau)- 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 548

Algebraic Topology II (Antieau)- 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 550

Differentiable Manifolds II (Furman)- 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 (Tucker)- PREREQUISITES:
- Math 552.
- DESCRIPTION:
- Divisors and linear systems, differentials, Riemann-Roch theorem for curves, elliptic curves, geometry of curves and surfaces.

#### MATH 571

Advanced Topics in Algebraic Geometry (Zhang)- PREREQUISITES:
- TBD
- DESCRIPTION:
- TBA

#### 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 582

Linear and Nonlinear Waves (Sparber)- PREREQUISITES:
- MATH 480 and MATH 481; or consent of the instructor.
- DESCRIPTION:
- Topics to be covered include: Fourier transforms; L^2-based Sobolev spaces and Schwartz space distributions; Well-posedness theory for dispersive equations (mainly Nonlinear Schrödinger and Korteweg de Vries); Energy methods; Existence of Solutions to Semi-linear Wave Equations;

#### MATH 586

Computational Finance (David Nicholls)- PREREQUISITES:
- Grade of C or better in MATH 220 and grade of C or better in STAT 381; or consent of the instructor.
- DESCRIPTION:
- Introduction to the mathematics of financial derivatives; options, asset price random walks, Black-Scholes model; partial differential techniques for option valuation, binomial models, numerical methods; exotic options, interest-rate derivatives.

### Fall 2018

Courses for this term have not been posted yet.

### Spring 2019

Courses for this term have not been posted yet.