20192020 Graduate Course Catalog
Mathematics, MS


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Department Chair: Uday Banerjee, 215 Carnegie Building, banerjee@syr.edu, 3154431478
Associate Chair for Graduate Studies: Graham Leuschke, 317G Carnegie Building, gileusch@syr.edu, 3154431500
Faculty
Uday Banerjee, Pinyuen Chen, Dan Coman, J. Theodore Cox, Steven Diaz, Nicole M.L. Fonger, Jack E. Graver, Duane Graysay, Philip S. Griffin, Tadeusz Iwaniec, Lee Kennard, HyuneJu Kim, Mark Kleiner, Leonid Kovalev, Loredana Lanzani, Graham J. Leuschke, Wei Li, Jianxuan Liu, Adam Lutoborski, Joanna O. Masingila, Terry R. McConnell, Claudia Miller, Jani Onninen, Evgeny Poletsky, Declan Quinn, Minghao Rostami, Lixin Shen, Gregory Verchota, Andrew Vogel, Stephan Wehrli, William Wylie, Yuan Yuan, Dan Zacharia
The Department of Mathematics has 33 faculty members, with research interests in several areas of mathematics, statistics, and mathematics education, and approximately 55 graduate students. The department is housed in the recently renovated Carnegie Library building on the main campus quadrangle. Programs of study include those for M.S. and Ph.D. degrees in Mathematics, with or without a concentration in Statistics, and for M.S. and Ph.D. degrees in Mathematics Education.

Student Learning Outcomes
1. Demonstrate competency beyond the undergraduate level in the core areas of algebra and analysis by solving problems using advanced techniques
2. Demonstrate competency beyond the undergraduate level in an area of applicable mathematics by solving problems using advanced techniques
3. Read and construct rigorous proofs
4. Effectively communicate mathematical ideas
M.S. in Mathematics
The Department of Mathematics offers two programs leading to the Master’s of Science in Mathematics degree. The programs are (1) Mathematics (including pure and applied mathematics) and (2) Statistics. Master’s programs share MAT 601  Fundamentals of Analysis I and MAT 631  Introduction to Algebra I as common foundations, and there is additional overlap between them.
Thirty credits of graduate work are required, of which at least 18 must be at the 600level or above, and at least 15 of those 18 credits must be in the mathematics department. In the mathematics option the student must also complete MAT 602  Fundamentals of Analysis II , MAT 632  Introduction to Algebra II , and a sequence in applied mathematics from an approved list of sequences. In the statistics option several particular courses are required.
Students must have at least a B average in the 15 credits of 600level or above mathematics department courses and at least a B average in the 30 credits of coursework comprising the degree program. No master’s thesis is required.
Joint and Concurrent Degree ProgramsMathematics and Computer Science
In collaboration with the Department of Electrical Engineering and Computer Science in the College of Engineering, we offer concurrent M.S. degrees in mathematics and computer science. Students complete a total of 51 credits, 30 in mathematics and 21 in computer science. Students who want to pursue this program should have a solid background in undergraduate mathematics, and knowledge of programming in highlevel languages and of algorithms and data structures adequate for graduate study in computer science.
Research Areas
The department’s Colloquium series features weekly lectures by mathematicians from all over the United States and abroad in many of the areas of mathematical research represented in the department. Furthermore several of the research groups organize regular research seminars. Colloquia and seminar schedules, along with other information about our programs, courses, and events, can be found at math.syr.edu.
The following research groups are currently represented in the department.
Algebra
Algebraic geometry (moduli spaces of curves, equations defining finite sets of points), commutative algebra (homological algebra, CohenMacaulay modules, characteristic p), noncommutative algebra (representations of finitedimensional algebras, homological algebra, group actions on noncommutative rings, Hopf algebras, enveloping algebras, noncommutative algebraic geometry). Faculty: Diaz, Kleiner, Leuschke, Miller, Quinn, Zacharia
Analysis
Complex analysis (several complex variables, pluripotential theory, complex dynamics, invariant metrics, holomorphic currents, Kähler geometry, rigidity problems), geometric analysis (PDE on manifolds, geometric flows), harmonic analysis, partial differential equations (linear and nonlinear elliptic PDE, boundary value problems on nonsmooth domains), geometric function theory (quasiconformal mappings, analysis on metric spaces). Faculty: Coman, Iwaniec, Kovalev, Lanzani, Onninen, Poletsky, Verchota, Vogel, Wylie, Yuan
Applied Mathematics
Numerical analysis (approximate solutions of elliptic PDE, generalized finite element methods and meshless methods), nonlinear variational problems (microstructure in nonlinear elasticity), applied and computational harmonic analysis (wavelets, digital image processing), numerical linear algebra, computational fluid dynamics. Faculty: Banerjee, Lutoborski, Rostami, Shen
Combinatorics
Combinatorics, graph theory, rigidity theory, symmetries of planar graphs, automorphism groups of graphs. Faculty: Graver
Geometry/Topology
Lowdimensional topology and knot theory (knot concordance, Heegaard Floer homology, homology theories for knots and links), Ktheory (topological Ktheory of EilenbergMac Lane spaces, equivariant homotopy theory), Riemannian/Kähler geometry (Ricci curvature and topology, special metrics, geometric flows, rigidity problems). Faculty: Kennard, Wehrli, Wylie, Yuan
Mathematics Education
Secondary mathematics education, teacher learning, mathematical representations, outofschool mathematics practice, teacher development. Faculty: Fonger, Graysay, Masingila
Probability
Interacting particle systems, Brownian motion, random walks, probabilistic methods in mathematical finance, martingales. Faculty: Cox, Griffin, McConnell
Statistics
Ranking and selection theory (applications in radar signal processing and twostage procedures for multinomial problems), changepoint problems, sequential analysis, longitudinal analysis, neural networks. Faculty: Chen, Kim, Li, Liu
Graduate Awards
Figures for graduate appointments represent 20192020 stipends.
Graduate Scholarships:
Support graduate study for students with superior qualifications; provide, in most cases, full tuition for the academic year.
Graduate Assistantships:
Offered to most Graduate Scholarship recipients; no more than an average of 20 hours of work per week; nine months; stipend ranging from $19,000 to $22,500 in addition to tuition scholarship for 24 credits per year. Additional summer support is generally available.
Syracuse University Graduate Fellowships:
Taxfree stipends are $25,290 for nine months of fulltime study; tuition scholarship for 15 credits per semester for a total of 30 credits during the academic year.
Facilities
The mathematics collection is held within the Carnegie Library and supports mathematical research over a broad range of pure and applied mathematics, as well as mathematics education, mathematical statistics, and interdisciplinary areas. Most of the nonbook resources are online and includes an extensive collection of databases and journals supporting the mathematical sciences. In addition, the library provides a growing collection of ebooks.
Students may borrow course reserved textbooks, laptops, TI graphing calculators, and geometry kits from the Carnegie Library service desk. Students may also reserve one of three group study rooms located on the first floor of the library. A computer lab in the library provides software for programming, statistical and data analysis, video and multimedia, and access to printers.
Carnegie Library is home to collections in the sciences, including engineering and computer science, the life sciences, and the physical sciences and hosts a strong collection of databases, journals, and ebooks supporting all disciplines. The historic Reading Room gives the library a distinctive ambience and provides a quiet place for students to study.

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