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.
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