2019-2020 Graduate Course Catalog 
    
    Dec 10, 2019  
2019-2020 Graduate Course Catalog

Mathematics Education, PhD


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Chair

Uday Banerjee, 215 Carnegie, 315-443-1472

Uday Banerjee, Pinyuen Chen, Dan Coman, J. Theodore Cox, Steven Diaz, Nicole Fonger, Jack E. Graver, Duane Graysay, Philip S. Griffin,Tadeusz Iwaniec, Lee Kennard, Hyune-Ju 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, John Ucci, Gregory Verchota, Andrew Vogel, William Voltermann, Stephan Wehrli, William Wylie, Yuan Yuan, Dan Zacharia

The Department of Mathematics has 35 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.

Ph.D. in Mathematics Education


This degree program is by the School of Education in cooperation with the Department of Mathematics. The program includes not less than 90 credits of graduate work beyond the bachelor’s degree, of which 9 to 24 are allocated for the dissertation. Students must meet the general requirements for the Ph.D. in education. A minimum of 48 credits is required in the major area.

Formal acceptance into this program depends in part on the preliminary examination in the major area, taken no later than the semester in which 45 credits of graduate work have been completed. A research apprenticeship must also be completed.

Qualifying examinations, usually written and covering both the major and minor areas, are taken after the completion of approximately 70 credits of coursework.

All candidates take as a minimum the required courses in the master’s program or transfer comparable credits from other institutions.

Further information is available from Professor Joanna Masingila at jomasing@syr.edu.

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, Cohen-Macaulay modules, characteristic p), non-commutative algebra (representations of finite-dimensional algebras, homological algebra, group actions on non-commutative rings, Hopf algebras, enveloping algebras, non-commutative 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


Low-dimensional topology and knot theory (knot concordance, Heegaard Floer homology, homology theories for knots and links), K-theory (topological K-theory of Eilenberg-Mac Lane spaces, equivariant homotopy theory), Riemannian/Kähler geometry (Ricci curvature and topology, special metrics, geometric flows, rigidity problems). Faculty: Kennard, Ucci, Wehrli, Wylie, Yuan.

Mathematics Education


Secondary mathematics education, teacher learning, mathematical representations, out-of-school 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 two-stage procedures for multinomial problems), change-point problems, sequential analysis, longitudinal analysis, neural networks. Faculty: Chen, Kim, Li, Lui, Volterman.

Graduate Awards


Figures for graduate appointments represent 2019-2020 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:

Tax-free stipends are $25,290 for nine months of full-time 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 non-book 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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