Pure mathematics is one of the four graduate mathematics program areas at FSU.

The expertise of the faculty in the department of mathematics includes substantial representation in many areas of pure mathematics, and the department offers programs of studies leading to master's and doctoral degrees in pure mathematics.

The program in pure mathematics at FSU is designed to provide both a solid, broad-range preparation in the main general areas of pure mathematics (traditionally: algebra, analysis, and geometry/topology), and specific expertise in one or more current areas of research. Current research in pure mathematics is extremely active; it may be estimated that close to 100,000 new articles in pure mathematics are published every year. The ideal goal of the program in pure mathematics at FSU is to prepare a student to participate actively in this world-wide effort to advance our state of knowledge in the field. Students seeking a degree in pure mathematics are driven by the study of mathematics as a field in itself, rather than as a tool at the service of applications to other sciences.

On the other hand, a degree in pure mathematics may lead students to apply their expertise as mathematical scientists in the industry, or as educators at teaching institutions. Recent graduates of the program have been successful both in following more research-oriented academic careers, and careers in industry or education.

The following is a list of faculty in the department more actively involved in pure mathematics, with a scant description of specific interests.

FACULTY MEMBER, RESEARCH AREA, TITLE, OFFICE, PHONE

Amod Agashe (Number Theory, Arithmetic Geometry), Assistant Professor, 216 LOV, 644-8704

Ettore Aldrovandi (Algebraic Geometry, Homological and Homotopical Algebra, Category Theory), Associate Professor, 215 LOV, 644-9717

Paolo Aluffi (Algebraic Geometry, Singularities), Professor, 226 LOV, 644-8717

Steve Bellenot (Analysis), Professor & Associate Chair, 223 LOV, 644-7405

Philip Bowers (Geometric Topology, Complex Analysis), Professor & Chair, 227 LOV, 644-3338

Bettye Anne Case (Complex Analysis, History of Mathematics), Professor & Associate Chair for graduate studies, 210 LOV, 644-1586

Sergio Fenley (Geometric Topology, Dynamical Systems), Professor, 105-D LOV, 644-8711

Wolfgang Heil (Geometric Topology), Professor, 115 LOV, 644-8706

Eriko Hironaka (Algebraic Geometry, Geometric Topology), Associate Professor & Director of pure math, 210A LOV, 644-1587

Mark van Hoeij (Algebraic Geometry, Symbolic Computation), Professor, 105B LOV, 644-3879

Sam Huckaba (Algebraic Geometry, Commutative Algebra), Professor & Associate Dean, 213 LOV, 644-1479

Eric Klassen (Geometric Topology, Complex Analysis, Algebraic Geometry), Professor, 109 LOV, 644-6071

Matilde Marcolli (Noncommutative Geometry and Arithmetic, Gauge Theory), Courtesy appointment

Washington Mio (Geometric Topology), Professor, 218 LOV, 644-5596

Craig A. Nolder (Complex Analysis), Associate Professor, 205-C LOV, 644-7586

Behrang Noohi (Algebraic Geometry, Homotopy Theory), Postdoctoral fellow, MCH 403B

Daniel M. Oberlin (Harmonic Analysis, Partial Differential Equations), Professor, 321 LOV, 644-2523

Jack Quine (Complex Analysis), Professor & Director of biomedical math, 110 LOV, 644-6050

Mika Seppälä (Algebraic Geometry, Complex Analysis, Symbolic Computation), Professor, 214-A LOV, 644-6718

Mathematics should not be viewed as compartmentalized into distinct sectors, and many of the faculty listed here share an interest in other aspects of mathematics. For example, several (Aldrovandi, Bowers, Marcolli, and others) have a strong interest in different facets of mathematical physics; Agashe and Huckaba have an interest in cryptography; Bowers has worked on the problem of mapping the cerebral cortex; Case writes in the history, biography, and sociology of mathematics; Klassen and Mio are active in computer visualization; Nolder conducts research in financial mathematics; Quine's expertise extends to biophysics; and Seppälä directs major European projects on technology-aided learning. At the same time, several faculty not listed above have substantial expertise in pure mathematics.

More details about the research activities of each faculty member can be found by visiting that faculty's webpage; this link collects a complete listing of the department's faculty.

The pure mathematics faculty meet regularly in several weekly seminars, grouped under the general headings of Algebra, Geometry/Topology, Real and Complex Analysis, but with substantial overlap in the audience and themes.

The pure mathematics graduate program

Admission to the graduate program in pure mathematics is subject to department-wide requirements. While not technically necessary, undergraduate exposure to basic abstract algebra, real and complex analysis, and topology is recommended. From time to time undergraduate courses in these subjects are offered during the summer term. For example, in recent years, undergraduate complex analysis has been available to graduate students during summer C session. Entering students without complex analysis background are strongly advised to apply for admission in summer, and enroll in that course.

What follows is a description of the general plan of study of a Ph.D.-seeking student joining the pure mathematics program. Students with exceptionally strong background or particularly developed research interests may opt for a more flexible plan of study reflecting their specific needs; such alternative plans of study are decided in consultation with an individual supervisory committee. Some of what follows also applies to students only seeking a Master's degree.

In general, a student begins graduate studies in pure mathematics at FSU by acquiring competence in the four basic areas of Algebra, Complex Analysis, Topology, and Real Analysis. This is accomplished by taking corresponding sequences of courses offered by the department in these disciplines, in the first two years of graduate work. It is expected that students demonstrate competence in these areas by the end of the fourth of fifth semester of graduate work, by excellent coursework or by passing corresponding `qualifying exams'. Completion of this requirement generally confers upon the student the Master's degree in pure mathematics.

Once this basic stage is completed, the student begins taking more advanced topics courses, and participating in seminars close to his or her interests. The subjects covered in the topics courses are decided each year by the faculty in consultation with current graduate students, in order to reflect their research goals.

As well as taking topics courses and participating to seminars, students begin at this stage to prepare for an `Advanced Topics Exam' (ATE), typically by working with an individual faculty on a specific area of specialization. The content covered by the ATE is tailored to the student by that student's committee; the ATE may include a written component in the form of a paper or prospectus, and usually an oral component consisting of one or more presentations for the committee, in which the student demonstrates a more advanced mastery of his or her chosen area of study.

Passing the ATE completes the `preliminary' part of the student's graduate study, conferring upon the student the status of `Ph.D. candidate'. It is expected that students reach this stage by the end of their seventh semester of graduate study.

As a Ph.D. candidate, the student has chosen a major professor and should focus on work leading to the writing of a doctoral dissertation. The student may still enroll in topics courses and will actively participate in the seminar or seminars close to his or her research interest; some of the student's coursework may be in the form of DIS (`Directed Individual Study') courses and dissertation credits. At this stage, the student makes the delicate transition from absorbing knowledge to producing new research in his or her chosen field, under the close supervision of his or her major professor and supervisory committee. The student's dissertation records the result of this research work, which is expected to be original and substantial.

When this work is completed, the student presents it to the committee (which includes at least one member from outside the mathematics department) and the faculty at large, in a dissertation defense. Approval of the dissertation concludes graduate work, and confers upon the student the degree of Ph.D. in pure mathematics.

First- and second-year courses.

Qualification process.

Advanced Topics Exam.

Expectations.