Northern Illinois University

The Department of Mathematical Sciences offers
**the Master of Science degree in Mathematics ** with specialization in
Pure Mathematics, Mathematics Education, Applied Mathematics, Computational Mathematics;
** the Master of Science degree in Teaching; **
**the Master of Science degree in Applied Probability and Statistics;**
and
**the Doctor of Philosophy degree in Mathematical Sciences.**
The requirements for each degree are described in the latest
Graduate catalog.
This document is to give you some additional information on
our master's program in mathematics and our doctoral program in mathematical
sciences. For additional information on the M.S. degree in applied probability
and statistics, please contact the
Division of Statistics.

Students in this degree program choose one of the following four specializations: Applied Mathematics, Computational Mathematics, Mathematics Education, or Pure Mathematics. Our master's program is designed so that students can complete the degree requirements in 2 years of full-time study. Superior full-time students can often fulfill the degree requirements in one academic year, combined with the preceding and following summer terms.

The basic requirements are to complete thirty semester hours (10 3-hour courses)
as described in the * Graduate Catalog*, and to pass a written
comprehensive examination. With departmental approval, master's students
can also complete the degree under the * master's thesis option*.
The student prepares a thesis under the direction of a member of the graduate
faculty, and gives an oral defense of the thesis. In most cases, three hours
of MATH 699 can be applied to the 30 hours required for the master's degree.
The oral thesis defense also serves as the student's comprehensive examination,
which replaces the written comprehensive examination that is required for
master's students in the non-thesis option.

** M.S. requirements in Graduate Catalog** |
Sample M.S. Study Plans

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. Working closely with graduate advisers, this allows you to plan
the early part of 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. There is
another transitional course, MATH 523, a second course in linear algebra.
Perhaps your first linear algebra course was taken as a sophomore and focused
on matrix theory. The second course is more theoretical, and provides important
background for subsequent graduate courses in virtually all areas of
mathematics.

**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. MATH 532 (Advanced Calculus III) also fits in this
category; it is intended as preparation for MATH 642 (Partial Differential
Equations).

**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). Before
taking MATH 642, it is recommended that you have appropriate background in
line integrals, surface integrals, and Fourier series. This is provided by
another transitional course, MATH 532 (Advanced Calculus III).

**Mathematics Education: ** Graduate students who are also
seeking certification to teach at the middle and secondary school level,
in addition to a graduate degree, can be accommodated through courses in
methods of teaching (MATH 410 and MATH 412) and the student teaching experience.
However, these courses do not carry credit for graduate degrees in mathematical
sciences.

**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. However, graduate mathematics students
who 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.

MATH 662 is an introductory numerical analysis class, and is required for all doctoral students. This course covers many of the same topics as MATH 534 and MATH 535, but from a more advanced mathematical perspective. Doctoral students who desire a transition to MATH 662 can take MATH 534 or MATH 535, but not both of these. (Students may receive credit for only two of MATH 534, MATH 535, and MATH 662). After completing MATH 662, or MATH 534 and MATH 535, students are ready to take subsequent graduate courses in numerical analysis: MATH 664 (numerical linear algebra), and MATH 666 (numerical differential equations).

In the related area of optimization theory, the course MATH 544 (linear
programming) is sub-transitional, and does not carry graduate credit. The
first graduate course in this area is MATH 668 (nonlinear programming).

**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 M.S. Study Plans and
Sample Ph.D. Study Plans
provide **examples** of programs of study in the 4 specializations for
the M.S. in mathematics (10 courses, 30 hours) and the Ph.D. in mathematical
sciences (90 hours). ** Many other combinations of courses are
possible**. Your adviser will have up-to-date information on the semesters
when particular courses are normally offered.

Professor Zhuan (John) Ye

Director of Graduate Studies

Department of Mathematical Sciences

Northern Illinois University

DeKalb, IL 60115

(815) 753-6775

gradprog@niu.edu or visit the graduate program web page.

Students interested in doing graduate work in statistics should contact the Division of Statistics 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.

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