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Fall 2018

MATH 771. Matroid Theory 1.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
This course usually follows with a second semester, Math 772, in the spring. Matroid theory emergies from the studies of graph theory, combinatorial optimization, industrial engineeringand studies of certain algebraic structures (linear independence and algebraic independence, for example) and has become an important and attractive branch of mathematics, both in theory and in applications. The objective of this sequence is to introduce to students the basics of matroid theory, including the following topics in the first semester: Independent sets and circuits, other matroid axiom systems, representations, duality theory, matroid minors, connectivity, and constructions. The second semester will be devoted to more advanced topics, including matroid connectivity, algebraic matroids over finite fields, decomposition of matroids, among others. Research front problems will be discussed. Research problem discussions will be focused on supereulerian matroids, and optimal matroid circuit covers

MATH 751. Functional Analysis 1.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
This course is offered in alternate years, alternating with Math 757 Partial Differential Equations. It is intended to be followed in the spring with Math 752 and so would be suitable for either a minor sequence or as part of a major area in analysis for Ph.D. students.

MATH 696. Graduate Seminar.

Credit Hours: 
1
Semester Offered: 
Comments From Graduate Director: 
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, we offer Math 694 Seminar: Professional Tools, which needs to be taken once by each graduate student. During the semester Math 694 is taken, Ph.D. students do not need to enroll in Math 696.

MATH 590. Teaching Practicum.

Credit Hours: 
variable hours
Semester Offered: 
Comments From Graduate Director: 
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 581. Topology 1.

Credit Hours: 
3
Syllabus: 
Semester Offered: 
Comments From Graduate Director: 
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 573. Graph Theory.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
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). 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 follows with Math 571 Combinatorics, and taking both courses will provide a good background in discrete mathematics. Both courses are offered annually.

MATH 567. Advanced Calculus. I.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
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, which primarily covers complex variables and applications from an engineering mathematics perspective.

MATH 563. Mathematics Modeling.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
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 464. Students will need a basic undergraduate background in the areas of differential equations and probability and statistics, and basic knowledge of computing software such as Excel or Matlab.

MATH 555. Complex Variables 1.

Credit Hours: 
3
Semester Offered: 
Comments From Graduate Director: 
This course is offered every other year and provides a graduate-level introduction to complex variables. Math 451 is generally an expected prerequisite. A basic knowledge of complex variables, at least at an undergraduate level, is essential in many areas of pure and applied mathematics so if you have no prior background and you have taken a course similar to Math 451, you might want to consider taking this course. Otherwise, we offer an undergraduate course Math 456 each spring which in most cases does not count toward course work requirements but will give you a working knowledge of the area. Also Math 568 covers basic complex variables from an engineering mathematics viewpoint.

MATH 551. Real Variables 1.

Credit Hours: 
3
Semester Offered: 
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 at least) 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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