Ř Master of Science Program (as of Fall 06): [See also the WIU graduate catalogue description of the program] The recently revised graduate program in the Department of Mathematics at Western Illinois University prepares the students for needed professions in our region or nationwide; and it consists of 7 core courses, 1 mathematics directed elective, and 4 focus area courses that will allow for focus in any single one of various areas of applied or pure mathematics, as well as other areas of study outside the Department of Mathematics, as sanctioned by the Department Graduate Committee. For example, the focus area courses may be in statistics, numerical analysis, teaching of mathematics, Ph.D. pursuit, biology, business, chemistry, computer science, economics, financial mathematics, or physics. The program consists of two steps.
o The first step consists of six courses that lead to a Certificate in Applied Mathematics. [These courses are MATH 551, MATH 552, STAT 553, MATH 554, and MATH 599 (once or twice) or MATH 596 (once or twice), or two courses from another department; where the first four are core courses and the last two are 6 hours of directed electives in a focus area, or credit for professional project, each approved by the Department Graduate Committee. The focus area, therefore, can be in mathematics or in another department.]
o The second step consists also of six courses leading to a Master of Science Degree in Mathematics. [These courses are MATH 651, MATH 652, STAT 653; an approved mathematics directed elective course; and MATH 699 (once or twice), or MATH 600 (once), or MATH 601 (once or twice), or MATH 602 (once or twice), or two courses from another department. The first three courses are core courses, the directed elective is a suitable course adjustable to the student’s background or interest, and the last two are 6 hours of: directed electives in the same focus area as in the first step. The directed electives can be from another department, or a (possible) mix of mathematics courses, a thesis, a project, or a report from an internship; each approved by the Department Graduate Committee and in the same area as in the first step.]
The program provides students with a solid graduate level training in the central and fundamental methods of continuous and discrete mathematics. Both the theoretical framework and the applications of these methods will be covered in the core courses. The 500-level core courses have a significant lean toward applications but theory is present; while the 600-level core courses have a significant lean toward theory and mathematical foundation but applications are not abandoned. For each student, all of the focus area courses will share a common thread, with the first two through MATH 599 (special variable topics course, 3 s.h., which may be repeated for credit) or through a project (MATH 596), or a mix; or from another department; and with the last two from another department, or through MATH 699 (special topics course, 3 s.h., which may be repeated for credit), or a thesis (MATH 600), or a project (MATH 601), or an internship (MATH 602), or a mix (with MATH 600, Thesis, not repeatable).
To earn an MS degree, the student will have successfully completed the following courses
o Core Courses: 21 s.h.
§
MATH 551
(Methods of Classical Analysis): 3 s.h.
Introduction to complex and
multivariable analysis with a significant lean toward applications. Topics include sequences and series,
conformal mappings, complex integration, geometry and topology of R^n,
§
MATH 552
(Scientific Computing with MATLAB): 3 s.h.
Design, analysis, and MATLAB
implementation of algorithms for solving problems of continuous mathematics
involving linear and nonlinear systems of equations, interpolation and
approximation, numerical differentiation and integration, and ordinary
differential equations with a significant lean toward applications. Prerequisites: MATH 311 and MATH 333, or equivalent.
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STAT 553
(Applied Statistical Methods): 3 s.h.
Introduction to probability and
statistics with a significant lean toward applications. Topics include
probability, probability distributions, Central Limit Theorem, sampling
distributions (t, F, Chi-Square), parameter estimation, hypothesis testing,
nonparametric statistics, ANOVA, linear regression. Prerequisites: MATH 231 and STAT 276, or equivalent.
§
MATH 554
(Methods of Symmetry in Alg., Geo., & Topology): 3 s.h.
A study of symmetry in algebra,
geometry, and topology with a significant lean toward applications. Topics of
study include group of Euclidean transformations, symmetries of planar sets,
topological classification of compact surfaces, crystallographic patterns and
classification of their symmetry groups. Prerequisite:
MATH 424 or permission of the instructor.
§
MATH 651
(Elements of Modern Analysis): 3 s.h.
A study of elements of modern
analysis with a lean toward developing the theory. Topics include topology in
normed linear spaces; inner product spaces, Hilbert space, Fourier series;
equicontinuity and Arzela-Ascoli theorem, Banach contraction principle,
Picard’s theorems, Peano's theorem; Gateaux differential and the Euler-Lagrange
equation; compact operators and existence of solutions of Fredholm integral
equations. Prerequisites: MATH 435 and MATH 551,
or equivalent.
§
MATH 652
(Computational Differential Equations): 3 s.h.
A study of elements of
computational mathematics of differential equations with a lean toward developing
the theory. Topics include adaptive one-step and multi-step methods for
ordinary differential equations, finite difference and finite element methods
for partial differential equations, the method of lines for evolutionary
problems, and direct and iterative methods for sparse linear systems. Prerequisites: MATH 551 or MATH 435, and MATH 552 or MATH
481.
§
STAT 653
(Elements of Statistical Inference): 3 s.h.
A study of elements of statistical
inference with a lean toward developing the theory. Topics include probability
theory, random variables, probability distribution functions, limit theorems,
estimation, testing, sufficiency, robust statistical methods, bootstrap, linear
models. Prerequisites: STAT 471 and STAT 553
o Directed Elective Course (A mathematics or
statistics directed elective): 3 s.h.
o Focus Area Courses: 12 s.h.
6 hours through MATH 599 (focus area course), and/or MATH 596 (professional project); or directed electives from any department but in a single focus area; (the combination and the focus to be approved by the Department Graduate Committee).
§
MATH 596
(Project in Applied Mathematics): 3 s.h., repeatable to 6.
A project in applied mathematics
or statistics, or with a professional institution, which will be presented in a
final paper or portfolio, demonstrating entry into an applied mathematics
field. S/U graded by a graduate faculty supervisor. Prerequisite: Permission of the Graduate Committee.
§ MATH 599 (Special Topics): 3 s.h., repeatable to 6. Prerequisite: Permission of the instructor.
6 hours through MATH 699 (focus area course), and/or MATH 600 (thesis, 3 s.h., not repeatable), and/or MATH 601 (project), and/or MATH 602 (internship); or directed electives from any department but in the same single focus area as above; (the combination and the focus to be approved by the Department Graduate Committee).
§
MATH 600
(Thesis): 3 s.h.
The
thesis may be either expository, historical, critical, or original and must be
approved by the student’s advisory committee. The student must present his/her
thesis to the mathematics department faculty in a colloquium. Prerequisite:
Permission of the graduate adviser.
§
MATH 601
(Advanced Project in Applied Mathematics): 3 s.h., repeatable to 6.
Project in an advanced topic of
mathematics or statistics, which will be presented in a final paper or
portfolio, demonstrating advanced proficiency in an applied mathematics field.
S/U graded by a graduate faculty supervisor. Prerequisite:
Permission of the Graduate Committee.
§
MATH 602
(Internship in Applied Mathematics): 3 s.h., repeatable to 6.
Mathematical work or training
conducted at a professional institution, university or government organization,
which will be presented in a final paper or portfolio, demonstrating advanced
proficiency in an applied mathematics field. S/U graded by a graduate faculty
supervisor. Prerequisite: Permission of the
Graduate Committee.
§
MATH 699
(Advanced Special Topics): 3 s.h., repeatable to 6.
Advanced special topics in mathematics or statistics with a lean towards theory. Prerequisite: Permission of the instructor.
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