Graduate Programs in the Mathematical Sciences:

Doctor of Philosophy (Ph.D.)

The Department of Mathematical Sciences offers a Doctor of Philosophy degree in Mathematical Sciences with four different core-course choices. The requirements for the degree are described in the latest Graduate catalog. This document is to give you some additional information on our doctoral program in mathematical sciences.

Ph.D. requirements  |   The Transition to Graduate Study
The Applications Involvement Component  |   Sample Ph.D. Study Plans

Ph.D. in Mathematics

Students who enter the doctoral program with a master's degree or with a very strong undergraduate background may be able to complete the doctoral program in 4 years of full-time study. This cannot be guaranteed, since it depends crucially on the student's progress in research and in writing a dissertation.

Doctoral students focus their work in an area of mathematics ("pure" or "applied"), mathematics education or statistics and probability. While all doctoral students choose five core courses from the same six options, the choice of focus will determine most of the coursework (as shown in the Graduate Catalog under "Group A, B, C and D"). The degree requirements involve a significant amount of mathematics, regardless of the student's focus.

All doctoral students must pass a written Qualifying Examination as stated in the catalog. The exact makeup of this exam is described in the Comprehensive and Qualifying Exam Information document and depends on the student's area of focus. This should be done early on, basically after the core coursework is completed.

Once the student has chosen a dissertation advisor and topic, he or she should soon after take the oral Candidacy Examination. Typically around this point is when the student does their internship in the Applications Involvement Component, or AIC, and subsequently writes a report and delivers a presentation in the AIC colloquium.

The Applications Involvement Component

The design of our doctoral program recognizes the need for new Ph.D. recipients to be exposed to mathematics in non-academic settings by requiring that all doctoral students complete the Applications Involvement Component (AIC) of our Ph.D. degree.

Typically a student's AIC has three parts. In the first, doctoral students attend the AIC colloquia, where speakers external to our department present accounts of how mathematics is used outside of mathematics departments. The external speakers come from industry, government, and education, and are chosen to present a diverse collection of case studies and viewpoints.

The second part of the AIC experience requires each student to undertake an internship in industry, government, or education. Internships usually take place during one of the summers and are arranged by the department's AIC director in consultation with the student. Some of the organizations with which interns have been placed are listed below.

  • Abbott Research Laboratory
  • Allied Signal
  • Ames Research Laboratory
  • Argonne National Laboratory
  • AT&T Bell Labs (Murray Hill, New Jersey)
  • Boeing Computer Services
  • Cray Research Corporation
  • DeKalb Genetics
  • General Electric
  • General Motors
  • IBM (Watson Research Center)
  • Motorola
  • NASA (Langely)
  • Numerical Algorithms Group
  • Oak Ridge National Laboratory
  • United Aircraft
  • Wolfram Research
  • Wright Patterson Air Force Laboratory

The third part of the AIC requires each student to write a report and give a presentation about her/his experience and research results obtained in the internship.

The Transition to Graduate Study

An advantage of our program is that it offers a variety of transitional courses to bridge the gap between undergraduate work and graduate-level courses but still carry graduate credit. This allows you to start your graduate career in a way that is appropriate for your ability and background. Here is a brief description of some of the transitional courses we offer in various areas. Also refer to the course descriptions given in the Graduate Catalog.

Algebra:  If you have already had a one-year sequence of courses in abstract algebra (proof-oriented courses on groups, rings, and fields), then you are probably ready for the initial graduate algebra sequence, MATH 620 and 621. If not, then you may want to start with MATH 520 and 521, transitional courses which discuss groups, rings, and fields, and allow you to develop your skills at writing correct proofs.

Analysis:  If you have already had a one-year sequence of courses in advanced calculus (including differentiation and integration of functions of several variables), with lots of attention paid to writing your own proofs, then you are probably ready for the initial graduate analysis courses, MATH 630 and MATH 632. If not, then you may want to start with MATH 530 and 531, transitional courses in advanced calculus which will give you lots of practice at writing proofs, as well as exposure to the important techniques of the area.

Differential Equations:  You have probably had one course in differential equations as an undergraduate, perhaps with a primary focus on techniques. If not, you should consider taking the NIU course MATH 336. This is a sub-transitional course (an undergraduate course) and would not carry graduate credit. The initial graduate courses are MATH 636 (ordinary differential equations) and MATH 642 (partial differential equations). The prerequisites for these courses are MATH 530 and MATH 531, respectively.

Numerical Analysis:  If you have never written and debugged your own programs in a high-level programming language such as FORTRAN or C, you may wish to take a programming class such as Computer Science 230, which is sub-transitional and does not carry graduate credit, before taking your first numerical analysis class. Graduate mathematics students who do have some programming experience will receive little benefit by taking this course.

Our introductory numerical analysis courses are MATH 534 (numerical linear algebra), MATH 535 (a survey of approximation techniques, numerical integration, and numerical solution of differential equations), and MATH 662 (numerical analysis). These courses involve programming in FORTRAN (or `C'), and they provide an introduction to theoretical issues in numerical analysis.

Topology:  The transitional course is MATH 550, which should be taken after a theoretical course in advanced calculus (such as MATH 530). MATH 550 is almost entirely a course in point-set topology. The initial graduate course is MATH 650, which discusses algebraic as well as point-set topology. MATH 521 is also a prerequisite for MATH 650. Because of the algebraic nature of MATH 650, students may benefit by also taking MATH 620 before taking MATH 650.

The transitional courses described above can be very helpful in facilitating a smooth entry into our program. Keep in mind, however, that a decision to begin at the transitional level will probably delay the completion of your program. If your background has prepared you for the basic graduate courses (this is something your adviser can help you to measure), then you should go ahead and take them.

Examples of Programs of Study

Sample Ph.D. Study Plans provides some examples of programs of study for the Ph.D. in mathematical sciences (90 hours). Please note that many other combinations of courses are possible. Your adviser will have up-to-date information on the semesters when particular courses are normally offered.

For additonal information about our Ph.D. program in mathematical sciences and financial support for students in this degree program, please contact:
Professor Sien Deng
Director of Graduate Studies
Mathematical Sciences Department
Northern Illinois University
DeKalb, IL 60115
(815) 753-6765 or visit the graduate program web page.

Students interested in doing graduate work in statistics should contact the Department of Statistics and Actuarial Science for information about their program. The Division of Statistics also has its own budget for graduate assistantships; contact the Director of the Division for details.

Director of Graduate Studies: Prof. Sien Deng

Last modified: 10/15/2019 (sd)