2014-2015 Graduate Course Catalog 
    
    May 23, 2022  
2014-2015 Graduate Course Catalog [ARCHIVED CATALOG]

Mathematics Education, PhD


Chair

Uday Banerjee, 215 Carnegie, 315-443-1472.

Faculty

Uday Banerjee, Pinyuen Chen, Dan Coman, J. Theodore Cox, Steven Diaz, Helen M. Doerr, Jack E. Graver, Philip S. Griffin, Peter D. Horn, Tadeusz Iwaniec, Hyune-Ju Kim, Mark Kleiner, Leonid Kovalev, Loredana Lanzani, Graham J. Leuschke, Adam Lutoborski, Joanna O. Masingila, Terry R. McConnell, Claudia Miller, Jani Onninen, Evgeny Poletsky, Declan Quinn, Lixin Shen, John Ucci, Gregory Verchota, Andrew Vogel, William Voltermann, Stephan Wehrli, William Wylie, Yuan Yuan, Dan Zacharia

The Department of Mathematics has 31 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 sponsored by the Graduate School in cooperation with the Department of Mathematics and the School of Education. 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. Generally, a minimum of 48 credits is required in the major area, and a minimum of 33 credits in a minor 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, and 6 credits of internships in K-12 classrooms.

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 professors Joanna Masingila and Helen Doerr, 203 Carnegie Building.

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). Faculty: Banerjee, Lutoborski, 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: Horn, Ucci, Wehrli, Wylie, Yuan.

Math Education


Secondary mathematics education, teacher learning, mathematical modeling, out-of-school mathematics practice, teacher development. Faculty: Doerr, 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, Voltermann.

Graduate Awards


Figures for graduate appointments represent 2014-2015 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 15 hours of work per week; nine months; stipend ranging from $17,244.26 to $21,072.77 in addition to tuition scholarship for 24 credits per year. Additional summer support is generally available.

Syracuse University Graduate Fellowships:

Tax-free stipends ranging from $14,250 to $23,830 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 library currently holds over 57,000 volumes, including 34,000 books and over 350 print and electronic journal subscriptions Online databases include MathSciNet, Current Index to Statistics, Jahrbuch Database, MathEduc, ERIC, Scopus, and Web of Science.

In addition to covering a broad range of pure and applied mathematics, the mathematics library contains print and electronic resources in the history of mathematics, mathematics education, and statistics. The following resources are available for student borrowing: TI graphing calculators, geometry kits, and course reserve books.

The computer lab in Carnegie Library, Room 208, has 16 computers, and a color printer with copying and scanning capability. The lab computers provide extensive software for statistical or data analysis, data base management, programming, and graphics. More information on computing services and the software available for students may be found on the ITS website: https://its.syr.edu/computer-labs/index.html.

The Carnegie Library contains over 210,000 volumes in the sciences, including biology, chemistry, engineering and computer science, library and information science, nutrition science and dietetics, public health, physics & astronomy, photography, technical arts, pure and applied mathematics, probability and statistics, mathematics education, and military and naval sciences. The historic Reading Room provides a quiet place for students to study and use library resources.