Mathematics Department - Ph.D. Requirements - Oral Qualifying Exam

Ph.D. Requirements - Oral Qualifying Exam


Mathematics Graduate Program

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.

StudentDateTopics Formats
Wesley Pegden April 2007 Graph Theory, Ramsey Theory,
Graphs and Groups and Combinatorial Game Theory
Postscript PDF TeX
Nicholas Trainor April 2007 Functional Analysis, Partial Differential Equations
and Numerical Analysis
Postscript PDF TeX
Padmini Mukkamala February 2007 Combinatorics, Graph Theory and the Probabilistic Method
and Discrete and Computational Geometry
Postscript PDF TeX
Paul Raff February 2007 Combinatorics and Graph Theory
and Computational complexity theory and algorithm analysis
Postscript PDF TeX
Amit Priyadarshi December 2006 Fractal Sets and Demensions
and Linear Operator Theory
Postscript PDF TeX
Linh Tran December 2006 Combinatorics and Graph Theory and Probabilistic Methods and Additive Number Theory Postscript PDF TeX
Debajyoti Nandi November 2006 Lie Algebras and Their Representations
and Hopf Algebras
Postscript PDF TeX
Reza Rezazadegan November 2006 Symplectic Geometry
and Algebraic Topology
Postscript PDF TeX
Yuan Yuan November 2006 Several Complex Variables
and Riemannian Geometry
Postscript PDF TeX
Eduardo Osorio September 2006 Stochastic Calculus and Financial Mathematics
and Partial Differential Equations
Postscript PDF TeX
Catherine Pfaff September 2006 Manifolds and Morse Theory and Coarse Geometry
and Coarse Geometry
Postscript PDF TeX
Nan Li September 2006 Riemannian Geometry
and Algebraic Topology
Postscript PDF TeX
Phillip Matchett Wood September 2006 Combinatorics, Graph Theory
and The Probabilistic Method
Postscript PDF TeX
Ming Shi April, 2006 Stochastic Calculus & Math Finance
and Numerical Analysis
Postscript PDF TeX
Jawon Koo April, 2006 Financial Mathematics and PDEs Postscript PDF TeX
Jin Wang April, 2006 Math Finance and PDEs Postscript PDF TeX
Goran Djankovic April, 2006 Analytic Number Theory & Algebraic Number Theory Postscript PDF TeX
Luc Nguyen April, 2006 PDEs and Riemannian Geometry Postscript PDF TeX
Mike Neiman March, 2006 Combinatorics and Graph Theory;
Probability Theory and Probabilistic Methods
Postscript PDF TeX
Eric Rowland March 2006 Experimental Mathematics and Diophantine Approximation Postscript PDF TeX
Colleen Duffy March 2006 Noncommutative Algebra and Hopf Algebras Postscript PDF TeX
Lara Pudwell February 2006 Combinatorics and Experimental Mathematics Postscript PDF TeX
Yuan Zhang February 2006 Several Complex Variables and PDE's Postscript PDF TeX
John Bryk January 2006 Analytic Number Theory & Algebraic Number Theory Postscript PDF TeX
Tom Robinson January 2006 Vertex operator algebras and Lie algebras Postscript PDF TeX
Thotsaporn
Thonataponanda
December 2005 Enumerative Combinatorics, Special Functions and Graph Theory Postscript PDF TeX
Ian Levitt December 2005 Combinatorics, Graph Theory & Probabilistic Method, AND Discrete Optimization Postscript PDF TeX
Scott Schneider November 2005 Descriptive Set Theory; Classical Groups Postscript PDF TeX
Ren Guo November 2005 Algebraic Topology and Riemannian Geometry Postscript PDF TeX
Biao Yin October 2005 Elliptic PDE's and Riemannian Geometry Postscript PDF TeX
Jared Speck September 2005 Fourier Analysis, Mathematical Physics
and PDE's
Postscript PDF MS Word
Ben Bunting June 2005 PDE's and Functional Analysis Postscript PDF TeX
Samuel Coskey May 2005 Set Theory and Ergodic Theory Postscript PDF 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 PDF TeX
Sarah Genoway April 2005 Commutative Algebra and
Computational Geometry
Postscript PDF TeX
Chris Stucchio March 2005 Asymptotics and
Semilinear Schro\"odinger Equations
Postscript PDF  
Brian Manning February 2005 Riemannian Geometry;
Algebraic Topology
Postscript PDF TeX
ShiTing Bao February 2005 PDE's and Functional Analysis Postscript PDF TeX
Sujith Vijay November 2004 Combinatorial Number Theory; Diophantine Approximations; Combinatorial Game Theory Postscript PDF TeX
Sikimeti Mau October 2004 Lie Groups, Functional Analysis Postscript PDF TeX
Liming Wang April 2004 Mathematical Biology, PDE's Postscript PDF TeX
Vince Vatter March 2004 Combinatorics, Graph Theory,
and Probability
Postscript PDF TeX
Mohamud Mohammed December 2003 Experimental Mathematics,
Combinatorics and Graph theory
Postscript PDF TeX
Jason Tedor December, 2003 Complex Analysis, Harmonic Analysis Postscript PDF TeX
Brian Lins December, 2003 Functional Analysis, Harmonic Analysis Postscript PDF TeX
Thuy Pham December, 2003 Commutative Algebra; Homological Algebra Postscript PDF TeX
Ben Kennedy December, 2003 Functional Analysis, Riemannian Geometry Plain text    
Roman Holowinsky October 2003 Analytic and Algebraic Number Theory Postscript PDF TeX
Satadal Ganguly September 2003 Analytic and Algebraic Number Theory Postscript PDF TeX
William Cuckler September 2003 Combinatorics and Graph Theory;
Probability Theory
Postscript PDF TeX
Andrei Zherebtsov June 2003 PDE's; Functional Analysis Postscript PDF TeX
Alex Zarechnak May 2003 Bohmian Mechanics; Differential Geometry Postscript PDF TeX
Corina Calinescu May 2003 Vertex Operator Algebras;
Kac-Moody Algebras
Postscript PDF TeX
Zhixiang Wang April 2003 Vertex Operator Algebras;
Riemannian Geometry
Postscript PDF TeX
Qinian Jin February 2003 Elliptic PDE's; Riemannian Geometry Postscript PDF TeX
Fernando Louro December 2002 Control Theory; Asymptotics Postscript PDF TeX
German Enciso December 2002 Harmonic analysis;
numerical solutions of PDE's
Postscript PDF TeX
Haoyuan Xu November 2002 Functional analysis; PDE's Postscript PDF TeX
Nicolas Weininger September 2002 Combinatorics and graph theory;
computational complexity
Postscript PDF TeX
Laura Ciobanu February 2002 Combinatorial group theory;
computational group theory
Postscript PDF TeX
Pieter Blue February 2002 Functional analysis; differential geometry Postscript PDF TeX
Michael Weingart February 2002 Representation theory; Lie algebras Postscript PDF TeX
Derek Hansen January 2002 Functional analysis; Sobolev spaces;
second order elliptic PDE's
Postscript PDF TeX
Aaron Lauve January 2002 Noncommutative rings; Hopf algebras Postscript PDF TeX
Liang Kong December 2001 Vertex operator algebras; quantum field theory Postscript PDF TeX
Stephen Hartke December 2001 Graph theory and combinatorics; discrete optimization Postscript PDF TeX
Eva Curry December 2001 Harmonic analysis and wavelets; probability theory Postscript PDF TeX
Sasa Radomirovic December 2001 Algebraic number theory; elliptic curves;
modular forms; automorphic forms
Postscript PDF TeX
Klay Kruczek November 2001 Combinatorics; graph theory Postscript PDF TeX
Kia Dalili October 2001 Algebraic topology; commutative algebra Postscript PDF TeX
Matthew Young October 2001 Analytic number theory; algebraic number theory;
elliptic curves; modular forms; elliptic functions
Postscript PDF TeX
Jeffrey Burdges October 2001 Stability theory; algebraic geometry Postscript PDF TeX
Raju Chelluri September 2001 Algebraic number theory; analytic number theory;
elliptic curves; modular forms
Postscript PDF TeX
Augusto Ponce September 2001 Linear second order elliptic PDE's;
the semilinear Dirichlet problem
Postscript PDF TeX
Kai Medville May 2001 Functional analysis, Sobolev spaces,
Laplace's equation, second order elliptic equations
Postscript PDF TeX
Jooyoun Hong May 2001 Commutative algebra;
homological algebra and Gröbner bases
Postscript PDF TeX
Liangyi Zhao April 2001 Analytic number theory; algebraic number theory;
modular forms; elliptic curves
Postscript PDF TeX
Waldeck Schültzer April 2001 The Littlewood-Richardson rule; the Weyl character formula; the theory of symmetric functions;
Lie algebras and representation theory
Postscript PDF TeX
Richard Mikula April 2001 Linear functional analysis; elliptic partial differential equations Postscript PDF TeX
Yongzhong Xu December 2000 Partial differential equations; Algebraic topology Postscript PDF TeX
Eric Sundberg December 2000 Combinatorics and graph theory; probability Postscript PDF TeX
David Nacin December 2000 Lie algebras and representations;
the automorphism tower problem
Postscript PDF TeX
Carlo Mazza December 2000 Homological Algebra;
Commutative Algebra and Algebraic Geometry
Postscript PDF TeX
James Taylor December 2000 Functional analysis; differential geometry Postscript PDF TeX
David Radnell June 2000 Vertex operator algebras; functional analysis Postscript PDF TeX
Yuka Umemoto March 2000 Algebraic topology; differential geometry Postscript PDF TeX
Madalena Chaves January 2000 Control theory; numerical analysis Postscript PDF TeX
This page was last updated on April 06, 2009 at 05:36 pm and is maintained by grad-director@math.rutgers.edu.
For questions regarding courses and/or special permission, please contact mclausen@math.rutgers.edu.
For questions or comments about this site, please contact help@math.rutgers.edu.
© 2012 Rutgers, The State University of New Jersey. All rights reserved.