Here are some examples of recent topics and syllabi.
| Quoted from "Guidelines for Qualifying Examinations" |
|
The second exam is an oral, 80-minute exam, given by a committee of
four faculty members. It will cover
two topics chosen by the student
in consultation with a prospective dissertation advisor. It will
normally be taken by the beginning of the second semester of the
student's third year; any delays past then will have to be approved
each semester by the program director, and failure to either take the
exam or obtain such permission will result in the student being
dropped from the Ph.D. program.
The student, or faculty giving the second exam, will write a syllabus (or approve a previously written syllabus) for each topic on the exam. A copy of the two individual topic syllabi, along with the membership of the examining committee, must be filed for approval with the program director well in advance of the scheduled date of the exam. The members of the examining committee should normally be chosen from faculty who work in areas related to the proposed topics; a prospective dissertation advisor should be on this committee. It is expected that the student will do some reading independent of course work for this examination. Ideally, the two topics should have some relationship to each other and to a proposed area of dissertation research, but not be so closely related as to be essentially one topic. However, we recognize that a student who decides late on an area of specialization may present two unrelated topics. The examiners may continue as an advisory committee for the student's dissertation. They are also likely to be on the student's dissertation defense committee if they are available. It will continue to be possible for the student to change advisors if so desired, even after this exam is taken. In this case, the program director might consider also appointing a new advisory committee. A student who fails this exam may attempt it a second time within a one year period, potentially with a different proposed dissertation advisor and committee. Students who fail a second time, or whose delay in retaking the exam is excessive (as determined by the program director) will not be allowed to continue in the Ph.D. program. |
| What happens later? Is there life after the oral exam? Here's a link to one useful reference. |
| Comments
Some examples of recent topics and syllabi are given below. It should be strongly emphasized that these are only examples. Each syllabus is specific to a student, the student's committee, the aims of the student's studies, and the time at which the exam is given. Research in mathematics evolves constantly, and suitable syllabi at one time may not be appropriate a year or two later. The examples presented here should help the process be understood better, and also should help students and faculty members create suitable syllabi for future oral exams. Four members! The Graduate School has been enforcing the rule that committees for this exam must have at least four members. To avoid difficulties, students should assemble committees in agreement with that regulation. |
Syllabi will be posted after passing orals. In the table below, "TeX" means some dialect of TeX, which can usually be compiled with a plain TeX or LaTeX command.
| Student | Date | Topics | Formats | ||
|---|---|---|---|---|---|
| Wesley Pegden | April 2007 | Graph Theory, Ramsey Theory,
Graphs and Groups and Combinatorial Game Theory | Postscript | TeX | |
| Nicholas Trainor | April 2007 | Functional Analysis, Partial Differential Equations
and Numerical Analysis | Postscript | TeX | |
| Padmini Mukkamala | February 2007 | Combinatorics, Graph Theory and the Probabilistic
Method
and Discrete and Computational Geometry | Postscript | TeX | |
| Paul Raff | February 2007 | Combinatorics and Graph Theory
and Computational complexity theory and algorithm analysis | Postscript | TeX | |
| Amit Priyadarshi | December 2006 | Fractal Sets and Demensions
and Linear Operator Theory | Postscript | TeX | |
| Linh Tran | December 2006 | Combinatorics and Graph Theory and Probabilistic Methods and Additive Number Theory | Postscript | TeX | |
| Debajyoti Nandi | November 2006 | Lie Algebras and Their Representations
and Hopf Algebras | Postscript | TeX | |
| Reza Rezazadegan | November 2006 | Symplectic Geometry
and Algebraic Topology | Postscript | TeX | |
| Yuan Yuan | November 2006 | Several Complex Variables
and Riemannian Geometry | Postscript | TeX | |
| Eduardo Osorio | September 2006 | Stochastic Calculus and Financial Mathematics
and Partial Differential Equations | Postscript | TeX | |
| Catherine Pfaff | September 2006 | Manifolds and Morse Theory and Coarse Geometry
and Coarse Geometry | Postscript | TeX | |
| Nan Li | September 2006 | Riemannian Geometry
and Algebraic Topology | Postscript | TeX | |
| Phillip Matchett Wood | September 2006 | Combinatorics, Graph Theory
and The Probabilistic Method | Postscript | TeX | |
| Ming Shi | April, 2006 | Stochastic Calculus & Math Finance
and Numerical Analysis | Postscript | TeX | |
| Jawon Koo | April, 2006 | Financial Mathematics and PDEs | Postscript | TeX | |
| Jin Wang | April, 2006 | Math Finance and PDEs | Postscript | TeX | |
| Goran Djankovic | April, 2006 | Analytic Number Theory & Algebraic Number Theory | Postscript | TeX | |
| Luc Nguyen | April, 2006 | PDEs and Riemannian Geometry | Postscript | TeX | |
| Mike Neiman | March, 2006 | Combinatorics and Graph Theory; Probability Theory and Probabilistic Methods | Postscript | TeX | |
| Eric Rowland | March 2006 | Experimental Mathematics and Diophantine Approximation | Postscript | TeX | |
| Colleen Duffy | March 2006 | Noncommutative Algebra and Hopf Algebras | Postscript | TeX | |
| Lara Pudwell | February 2006 | Combinatorics and Experimental Mathematics | Postscript | TeX | |
| Yuan Zhang | February 2006 | Several Complex Variables and PDE's | Postscript | TeX | |
| John Bryk | January 2006 | Analytic Number Theory & Algebraic Number Theory | Postscript | TeX | |
| Tom Robinson | January 2006 | Vertex operator algebras and Lie algebras | Postscript | TeX | |
| Thotsaporn Thonataponanda | December 2005 | Enumerative Combinatorics, Special Functions and Graph Theory | Postscript | TeX | |
| Ian Levitt | December 2005 | Combinatorics, Graph Theory & Probabilistic Method, AND Discrete Optimization | Postscript | TeX | |
| Scott Schneider | November 2005 | Descriptive Set Theory; Classical Groups | Postscript | TeX | |
| Ren Guo | November 2005 | Algebraic Topology and Riemannian Geometry | Postscript | TeX | |
| Biao Yin | October 2005 | Elliptic PDE's and Riemannian Geometry | Postscript | TeX | |
| Jared Speck | September 2005 | Fourier Analysis, Mathematical Physics and PDE's | Postscript | MS Word | |
| Ben Bunting | June 2005 | PDE's and Functional Analysis | Postscript | TeX | |
| Samuel Coskey | May 2005 | Set Theory and Ergodic Theory | Postscript | TeX | |
| Paul Ellis | May 2005 | Set Theory and Classical Groups | HTML | MS Word | Rich Text |
| Pablo Angulo | April 2005 | Elliptic PDEs and Differential Topology | Postscript | TeX | |
| Sarah Genoway | April 2005 | Commutative Algebra and Computational Geometry | Postscript | TeX | |
| Chris Stucchio | March 2005 | Asymptotics and Semilinear Schro\"odinger Equations | Postscript | ||
| Brian Manning | February 2005 | Riemannian Geometry; Algebraic Topology | Postscript | TeX | |
| ShiTing Bao | February 2005 | PDE's and Functional Analysis | Postscript | TeX | |
| Sujith Vijay | November 2004 | Combinatorial Number Theory; Diophantine Approximations; Combinatorial Game Theory | Postscript | TeX | |
| Sikimeti Mau | October 2004 | Lie Groups, Functional Analysis | Postscript | TeX | |
| Liming Wang | April 2004 | Mathematical Biology, PDE's | Postscript | TeX | |
| Vince Vatter | March 2004 | Combinatorics, Graph Theory, and Probability | Postscript | TeX | |
| Mohamud Mohammed | December 2003 | Experimental Mathematics, Combinatorics and Graph theory | Postscript | TeX | |
| Jason Tedor | December, 2003 | Complex Analysis, Harmonic Analysis | Postscript | TeX | |
| Brian Lins | December, 2003 | Functional Analysis, Harmonic Analysis | Postscript | TeX | |
| Thuy Pham | December, 2003 | Commutative Algebra; Homological Algebra | Postscript | TeX | |
| Ben Kennedy | December, 2003 | Functional Analysis, Riemannian Geometry | Plain text | ||
| Roman Holowinsky | October 2003 | Analytic and Algebraic Number Theory | Postscript | TeX | |
| Satadal Ganguly | September 2003 | Analytic and Algebraic Number Theory | Postscript | TeX | |
| William Cuckler | September 2003 | Combinatorics and Graph Theory; Probability Theory | Postscript | TeX | |
| Andrei Zherebtsov | June 2003 | PDE's; Functional Analysis | Postscript | TeX | |
| Alex Zarechnak | May 2003 | Bohmian Mechanics; Differential Geometry | Postscript | TeX | |
| Corina Calinescu | May 2003 | Vertex Operator Algebras; Kac-Moody Algebras | Postscript | TeX | |
| Zhixiang Wang | April 2003 | Vertex Operator Algebras; Riemannian Geometry | Postscript | TeX | |
| Qinian Jin | February 2003 | Elliptic PDE's; Riemannian Geometry | Postscript | TeX | |
| Fernando Louro | December 2002 | Control Theory; Asymptotics | Postscript | TeX | |
| German Enciso | December 2002 | Harmonic analysis; numerical solutions of PDE's | Postscript | TeX | |
| Haoyuan Xu | November 2002 | Functional analysis; PDE's | Postscript | TeX | |
| Nicolas Weininger | September 2002 | Combinatorics and graph theory;
computational complexity | Postscript | TeX | |
| Laura Ciobanu | February 2002 | Combinatorial group theory; computational group theory | Postscript | TeX | |
| Pieter Blue | February 2002 | Functional analysis; differential geometry | Postscript | TeX | |
| Michael Weingart | February 2002 | Representation theory; Lie algebras | Postscript | TeX | |
| Derek Hansen | January 2002 | Functional analysis; Sobolev spaces;
second order elliptic PDE's | Postscript | TeX | |
| Aaron Lauve | January 2002 | Noncommutative rings; Hopf algebras | Postscript | TeX | |
| Liang Kong | December 2001 | Vertex operator algebras; quantum field theory | Postscript | TeX | |
| Stephen Hartke | December 2001 | Graph theory and combinatorics; discrete optimization | Postscript | TeX | |
| Eva Curry | December 2001 | Harmonic analysis and wavelets; probability theory | Postscript | TeX | |
| Sasa Radomirovic | December 2001 | Algebraic number theory; elliptic curves;
modular forms; automorphic forms | Postscript | TeX | |
| Klay Kruczek | November 2001 | Combinatorics; graph theory | Postscript | TeX | |
| Kia Dalili | October 2001 | Algebraic topology; commutative algebra | Postscript | TeX | |
| Matthew Young | October 2001 | Analytic number theory; algebraic number theory;
elliptic curves; modular forms; elliptic functions | Postscript | TeX | |
| Jeffrey Burdges | October 2001 | Stability theory; algebraic geometry | Postscript | TeX | |
| Raju Chelluri | September 2001 | Algebraic number theory; analytic number theory;
elliptic curves; modular forms | Postscript | TeX | |
| Augusto Ponce | September 2001 | Linear second order elliptic PDE's; the semilinear Dirichlet problem | Postscript | TeX | |
| Kai Medville | May 2001 | Functional analysis, Sobolev spaces,
Laplace's equation, second order elliptic equations | Postscript | TeX | |
| Jooyoun Hong | May 2001 | Commutative algebra; homological algebra and Gröbner bases | Postscript | TeX | |
| Liangyi Zhao | April 2001 | Analytic number theory; algebraic number theory;
modular forms; elliptic curves | Postscript | TeX | |
| Waldeck Schültzer | April 2001 | The Littlewood-Richardson rule; the Weyl
character formula; the theory of symmetric functions; Lie algebras and representation theory | Postscript | TeX | |
| Richard Mikula | April 2001 | Linear functional analysis; elliptic partial differential equations | Postscript | TeX | |
| Yongzhong Xu | December 2000 | Partial differential equations; Algebraic topology | Postscript | TeX | |
| Eric Sundberg | December 2000 | Combinatorics and graph theory; probability | Postscript | TeX | |
| David Nacin | December 2000 | Lie algebras and representations; the automorphism tower problem | Postscript | TeX | |
| Carlo Mazza | December 2000 | Homological Algebra; Commutative Algebra and Algebraic Geometry | Postscript | TeX | |
| James Taylor | December 2000 | Functional analysis; differential geometry | Postscript | TeX | |
| David Radnell | June 2000 | Vertex operator algebras; functional analysis | Postscript | TeX | |
| Yuka Umemoto | March 2000 | Algebraic topology; differential geometry | Postscript | TeX | |
| Madalena Chaves | January 2000 | Control theory; numerical analysis | Postscript | TeX | |



