Current Graduate Offerings

Current Graduate Offerings

Fall 2012

You are welcome to contact the instructor for more information about any course below. E-mail addresses can be obtained from the Math Department Directory Page.

Roughly speaking, 500-level courses are intended as first-year M.S. courses, 600-level are more advanced M.S. level courses, and 700-level courses are doctoral courses. With the exception of Math 452, most 400-level courses do not count toward program requirements.

Note: Except as noted, all courses below the 600-level that are listed below are now planned on being offered annually.

Links with further information will be added as provided by the instructor. Comments on this page represent brief remarks by the Graduate Director as to how each course fits into the graduate program. Catalog descriptions of the courses are available through the University’s website or at Available Math Courses. Full time students are expected to enroll in three mathematics courses, or other approved courses, each semester, exclusive of seminar hours.

451. Introduction to Real Analysis 1.

Credit Hours: 
3
Course Level: 
400
Prerequisites: 
MATH 283.
Catalog Description: 
A study of sequences, convergence, limits, continuity, definite integral, and derivative, differentials, functional dependence, multiple integrals, sequences, and series of functions.
Semester Offered: 
Fall 2012
Comments From Graduate Director: 
Standard senior-level undergraduate course in advanced calculus. This course is taken by M.S. students who have not had a previous course in advanced calculus. Follows in spring with Math 452. Depending on the outcome of the Basic Exam, if you are a new M.S. student you may be asked or required to take this course. In most cases Math 451 does not count toward M.S. program requirements, but Math 452 does count. Math 451 is a prerequisite for graduate analysis courses, including real variables, Math 551 and complex analysis, Math 555, and provides important background for courses such as Math 564, Differential Equations. All M.S. students must complete, with a B average, either the Math 451/452 sequence, or Math 551.

465. Partial Differential Equations.

Credit Hours: 
3
Course Level: 
400
Prerequisites: 
MATH 261.
Catalog Description: 
Introduces students in mathematics, engineering, and the sciences to methods of applied mathematics. First and second order equations, canonical forms, wave, heat, and Laplace‚s equations, representation of solutions.
Semester Offered: 
Fall 2012
Instructor E-mail: 
Professor Li
Comments From Graduate Director: 
This is an undergraduate course in partial differential equations which in most cases does not count toward M.S. program requirements. However, if you have never seen partial differential equations before, particularly if you are in Option B or are interested in applied mathematics, you might wish to take this course.

521. Numerical Analysis. I.

Credit Hours: 
3
Course Level: 
500
Prerequisites: 
MATH 261 and computer language.
Catalog Description: 
Number systems and errors, interpolation by polynomials, linear systems, scalar algebraic equations and systems, optimization, approximation theory, integration initial, and boundary value problems.
Semester Offered: 
Fall 2012
Comments From Graduate Director: 
This is a standard graduate course covering fundamentals of numerical analysis. A previous numerical analysis course is not required but computer programming is necessary (see instructor if you have questions about prerequisites). If you’re interested in applied mathematics, this is a fundamental course to take. It follows in the spring with Math 522, a course in numerical methods for partial differential equations.

541. Modern Algebra.

Credit Hours: 
3
Course Level: 
500
Prerequisites: 
MATH 341.
Catalog Description: 
Concepts from set theory and the equivalence of the Axiom of Choice. Zorn‚s Lemma and the Well-Ordering Theorem; a study of the structure of groups, rings, fields, and vector spaces; elementary factorization theory; extensions of ring and fields; modules and ideals; and lattices.
Semester Offered: 
Fall 2012
Instructor E-mail: 
Professor Wojciechowski
Comments From Graduate Director: 
This is the basic graduate course in algebra. Note that algebra is one of the areas of the M.S. Advanced Exams/Ph.D. entrance exams. Math 541 follows in the spring with a second semester, Math 641, and both courses are needed if you are taking the exam. Math 541 is a basic prerequisite for advanced courses in combinatorics, graph theory, and number theory. It is a popular course for first year M.S. students and for first year Ph.D. students who expect to take the Entrance Exam in that area.

551. Real Variables 1.

Credit Hours: 
3
Course Level: 
500
Prerequisites: 
MATH 451.
Catalog Description: 
A development of Lebesgue integral, function spaces and Banach spaces, differentiation, complex measures, the Lebesgue-Radon-Nikodym theorem.
Semester Offered: 
Fall 2012
Instructor E-mail: 
Professor Hattori
Comments From Graduate Director: 
This is the first semester of a basic graduate two-semester course (551/651) in real analysis. Real analysis is one of the areas of the M.S. Advanced Exams/Ph.D. entrance exams and the full-year sequence should be taken if preparing for the exam. It is a prerequisite for the doctoral sequence in functional analysis and other doctoral-level courses in analysis and applied mathematics. You should have a good background in advanced calculus (Math 451) before taking this class. The first semester is largely devoted to developing Lebesgue measure. Math 651, Real Variables II, is offered in the spring.

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Courses in other departments

Approved courses in other departments may be used as part of your program of study, under guidelines contained in the Graduate Handbook. In particular, the Department maintains close ties with Statistics, and with Computer Science (part of Computer Science and Electrical Engineering). Also, students in the Mathematics for Secondary Educators option in the M.S. program sometimes include mathematics education courses in their program of study. You are, of course, responsible for any prerequisites, and you may take an undergraduate prerequisite as an "extra" course outside your program of study. Within statistics, the basic course is STAT 561, Theory of Statistics I, which is the first semester of the basic two-semester graduate sequence in probability theory and statistics. Depending on your background, computer science courses in algorithms, complexity, automata, or formal language theory might be suitable, particularly if you are interested in the CCDM program. Courses in computer programming and computer languages normally cannot be counted as part of your program, but can be taken if time allows and are a useful part of a general background in the mathematical sciences. Talk to your advisor or faculty associated with these areas if you are interested in courses outside the department.