Course Atlas

Graduate MATH Courses

Graduate MATH Courses

MATH512 Analysis II Credits: 3
Content: Topics will include: Measure and integration theory on the real line as well as on a general measure space, Bounded linear functionals on L^p spaces. If time permits, Sobolev spaces and Fourier transforms will be introduced.
Texts: TBA
Assessments: TBA
Prerequisites: Students are expected to have the background of Math 411-412 sequence or the equivalent.
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E406 MW      10:00AM - 11:15AM David Borthwick 15
MATH516 Numerical Analysis II Credits: 3
Content: This course covers fundamental concepts of numerical analysis and scientific computing. Material includes numerical methods for curve fitting (interpolation, splines, least squares), differentiation, integration, and differential equations. It is assumed that students have a strong background in numerical linear algebra.
Texts: TBA
Assessments: TBA
Prerequisites: Math 515, undergraduate course work in multivariable calculus and ordinary differential equations. An undergraduate course in numerical analysis would help, but is not absolutely essential. Prerequisites: This is a "hands on" course and students will be required to demonstrate their understanding of the concepts through programming assignments in MATLAB/Octave (help will be given for the novice programmer).
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E406 MW      11:30AM - 12:45PM Alessandro Veneziani 15
MATH517 Iterative Methods for Linear Systems Credits: 3
Content: The aim of this course is to provide a comprehensive coverage of the solution of large-scale sparse linear systems by iterative methods. Because different algorithms are designed for particular linear systems (e.g, symmetric positive definite, symmetric indefinite, unsymmetric, rectangular), it is essential that students have a strong background in numerical linear algebra and matrix analysis. Therefore, a minimum prerequisite for this course is Math 515 (Numerical Linear Algebra). It is recommended that students take Math 561 (Matrix Analysis) and Math 516 (Numerical Analysis) prior to taking Math 517, but it is not required. The topics to be covered in Math 517 include: • Quick review of basic facts from Matrix Analysis and Numerical Linear Algebra. • Stationary iterative methods (e.g., Jacobi, Gauss-Seidel, SOR, SSOR). • Krylov subspace methods (e.g, CG, MINRES, GMRES, LSQR). • Preconditioning techniques (e.g., Incomplete LU and Cholesky). • Multilevel algorithms (e.g., multigrid, Schwarz). • Selected applications.
Texts: Iterative Methods for Sparse Linear Systems, 2nd Ed., by Y. Saad, SIAM, 2003. (See also: http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf)
Assessments: TBA
Prerequisites: Math 515
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E406 TuTh      10:00AM - 11:15AM Yuanzhe Xi
MATH522 Algebra II Credits: 3
Content: Continuation of 521. Topics: Modules, especially modules over a principal ideal domain, fields, Galois theory, representation of finite groups, Commutative algebra.
Texts: TBA
Assessments: TBA
Prerequisites: Math 521.
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E408 TuTh      1:00PM - 2:15PM David Zureick-Brown 15
MATH536 Combinatorics II Credits: 3
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E406 MW      2:30PM - 3:45PM Hao Huang 15
MATH543 Algebraic Topology I Credits: 3
Content: Homotopy theory, the fundamental group, free products of groups with amalgamation, Van Kampen's Theorem, covering spaces, classification of surfaces, classifying spaces, higher homotopy groups
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC N302 TuTh      11:30AM - 12:45PM David Zureick-Brown
MATH558 Partial Differential Equations Credits: 3
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E406 TuTh      2:30PM - 3:45PM Vladimir Oliker 15
MATH572 Numerical Partial Differential Equations Credits: 3
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E406 MW      4:00PM - 5:15PM Alessandro Veneziani 15
MATH578R Seminar in Algebra Credits: 1-9
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC W201 Tu      4:00PM - 5:00PM David Zureick-Brown 25
MATH579R Seminar in Analysis Credits: 3
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC W301 F      2:00PM - 2:50PM Lars Ruthotto 15
MATH590 Teaching Seminar Credits: 3
Content: This seminar will concentrate on effective teaching techniques in mathematics. Topics included will include: General advice for new TA's. General advice for International TA's. Students will present several practice lectures over different levels of material. They will receive practice on quiz and test preparation. Syllabus information on courses most likely to be taught by new TA's will be supplied. General professional development information will also be included.
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E406 F      11:00AM - 12:00PM Juan Villeta-Garcia
Michael Carr
MATH787R Topics in Combinatorics Credits: 3
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E406 TuTh      11:30AM - 12:45PM Vojtech Rodl 15
MATH789 Topics in Analysis Credits: 3
Content: TBA
Texts: TBA
Assessments: TBA
Prerequisites: TBA
Section Location Meeting Time Instructor Enrollment (max)
1 MSC E408 MW      1:00PM - 2:15PM David Borthwick 15