Fall Courses for graduate students, 2009

You are welcome to contact the instructor for more information about any course below. E-mail addresses can be obtained from the main math department web page, http://www.math.wvu.edu. Instructors will be assigned for graduate courses later in July.

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.

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. Full time students are expected to enroll in three mathematics courses, or other approved courses, each semester, exclusive of seminar hours.
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Math 451 Introduction-Real Analysis I , Riemenschneider

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.

Math 465 Partial Differential Equations, Hattori

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, you might wish to take this course.

Math 521 Numerical Analysis, Christie

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.

Math 541 Modern Algebra I, Wojciechowski

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.

Math 545 Number Theory 1, Mays

This course is offered about every other year and provides a graduate-level introduction to number theory. Usually a second semester, 
Number Theory 2, is offered. Course description: Introduction to classical number theory covering such topics as divisibility, the Euclidean
algorithm, Diophantine equations, congruences, primitive roots, quadratic residues, number-theoretic functions, distribution of primes, 
irrationals, and combinatorial methods. Special numbers such as those of Bernoulli, Euler, and Stirling. Focus in the spring semester sequel, 
Math 645, will be topics from additive number theory (partitions and compositions).

Website with syllabus and scanned first chapter of text: http://www.math.wvu.edu/~mays/545/545.htm

Math 551 Real Variables I, Li

This is the first semester of a basic graduate two-semester course (551/651) in real analysis. It is a required course for M.S. students. 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. Math 551 generally includes a review of basic results in advanced calculus before proceeding on to measure theory. Math 651, Real Variables II, is offered in the spring.

Math 563    Mathematics Modeling, Ganser

This course will give the student some exposure to how mathematics is used to analyze problems arising in real-world applications in industry and science. It is a required course in Option B of the M.S. program. It has been run on a yearly basis, concurrently with Math 367. Students will need a basic undergraduate background in the areas of differential equations and probability and statistics.

Math 567 Advanced Calculus, Clarke

This is a course in mathematical methods, aimed primarily at engineering and science graduate students. Can be used to meet requirements in Option B (Industrial/Applied Mathematics) of the M.S. program, or as an elective in other options. This course continues with Math 568 in the spring.

Math 573 Graph Theory, CQ Zhang

Graph Theory is one of the areas represented in Discrete Mathematics, and has grown over the last thirty years to become an important area in both pure and applied mathematics (e.g. computer science, statistics, and operations research). This course may continue in the spring with a doctoral-level course (Math 773), depending on student interest and enrollment. We regularly offer doctoral-level courses in graph theory, for which this course would be prerequisite and Ph.D. students can make a minor area out of Math 573 and Math 773 or some other 700-level discrete math course. In the spring Math 573 will follow with Math 571 Combinatorics, and taking both courses will provide a good background in discrete mathematics. Both courses are offered annually, with the course order reversing each year.

Math 581 Topology 1, Ciesielski

This is a basic graduate course in topology, useful in both pure and applied mathematics. Topology is one of the areas of the M.S. Advanced Exams/Ph.D. entrance exams, so this course is taken both by M.S. students and by Ph.D. students who want to prepare for the entrance exams. Math 581 follows in the spring with the second semester of topology, Math 681. Students taking the exam in topology will need the background of both semesters.

Math 590    Teaching Practicum, Deshler

All GTA’s enroll for one credit hour of Math 590 each semester. This course will reflect the supervised duties assigned to the GTA each semester, which will change from semester to semester. Most GTA’s will take the Teaching Seminar in the Spring of their first year, followed by a second semester in the Fall of their second year. The Teaching Seminar is included in your Math 590 enrollment.

Math 691 ADTP: Rsrch-Undergrd Math Ed 1

The is the first course in a planned series of four courses covering research in undergraduate mathematics education that is expected ultimately to form the basis of an area of emphasis in our Ph.D. program. For now M.S. students can include this as an elective in their course work and the course is open to M.S. or Ph.D. students, preferably those with the maturity of at least a year of graduate level work. To register, students need to have at least one semester of classroom teaching experience, although not necessarily as the primary instructor for the course.

Math 696     Graduate Seminar
Ph.D. students are required to enroll for one credit of graduate seminar each semester they are in residence. Expectations of this course are contained in the linked document. In the spring, a section of Math 696 is devoted to the Professional Tools Seminar, which needs to be taken once by each graduate student.

Math 757 Theory of PDE’s 1, Hattori

This is an advanced course in partial differential equations. It is intended to be followed in the spring with Math 758 and so would be suitable for either a minor sequence or as part of a major area for Ph.D. students. Math 757-758 alternates on a yearly basis with Math 751-752, Functional Analysis.

Math 777 Advanced Topics in Combinatorics: Finite Extremal Set Theory, Goldwasser

The course will present some background material:  the Erdos-Ko-Rado theorem, the Kruskal-Katona theorem, Turan's theorem, perhaps the Erdos-Stone theorem.  In the second part of the course the class will read papers in a couple of these areas depending on the interests of the students, though certainly including some generalizations of Turan's theorem to r-graphs (graphs where each edge has r vertices). There will be one or two problem sets during the first part of the class, but the bulk of the class will just be to read (and present) the papers. The text is "Combinatorics", by Bollobas (cheap paperback), for background material.
Prerequisite:  an introductory course in combinatorics (including binomial theorem, inclusion-exclusion, basic counting techniques).  Certainly our Math 571 is more than sufficient.  If you are unsure if your background is ok, feel free to contact Professor Goldwasser. You are welcome to come to the first few classes and then decide whether or not you are interested.

Math 777A Advanced Topics in Combinatorics: Combinatorial Optimization, Hong-Jian Lai

This course usually follows with a second semester in the spring. It is aimed at advanced students in discrete mathematics and discrete optimizations. It will cover topics in basic network flow models such as optimal spanning trees, shortest paths, maximum flows,

minimum cost flows, optimal matchings, and standard optimization problems in matroids. This sequence of courses can be used to fulfill PhD course requirements in Discrete Mathematics, in either major or minor areas. Background should include either Math 541 or 543, and

either Math 571 or 573.

Math 791G Advanced Topics: Algebraic Topology, Fuller

The first of a sequence of courses in algebraic topology.

Math 791O Advanced Topics in Graph Theory: Cycle Covering of Graphs, CQ Zhang

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 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. Talk to your advisor or faculty associated with these areas if you are interested in courses outside the department.