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DEPARTMENT OF MATHEMATICS
PH.D. PROGRAM

[ Ph.D. Program | M.S. Program | Fast-Track Program |Department | UAB ]

Welcome

Are you ready to accept a challenge? We are preparing students interested in an academic career in a college or university as well as students interested in a career in business, industry, or government. These pages will provide you with information about our Ph.D. program and supply you with all necessary information and materials needed for an application. Please see also the information on our Master's program.The table of contents below gives a first overview of the information provided.

Our View of Mathematics

Mathematics has been a human endeavor for millennia. It has always been driven by two sources: the intrinsic beauty of numbers, shapes, structures, and their interrelationships as well as the necessity to solve practical problems in fields as diverse as finance, atomic physics, and computer tomography. Mathematics has therefore always been divided into a pure and an applied branch. However, these have never been strictly separated. Almost all pure mathematics is related to problems which occur in applications, and almost all applied mathematics is based upon pure mathematics. Seismology, the main tool of engineers in oil and gas exploration, is mathematically described as an inverse problem in partial differential equations. Group theory has many applications in quantum mechanics and particle physics. Even number theory, which has long been considered to be the purest area of mathematics, plays nowadays an eminent role in cryptography, the study of codes, and is thus related, for example, to safe data transfer on the internet.

At UAB we are particularly interested in the connections between pure mathematics, mathematical physics, and dynamical systems.

Mathematical physics is the rigorous mathematical study of structures which occur in physics. It cannot be understood without a broad background in mathematics and at least an undergraduate level knowledge of physics. This area deals with such diverse topics as the study of atoms and molecules, the theory of relativity, the study of waves in crystals with impurities, or how to determine the internal structure of something from the way it scatters x-rays or ultrasound waves. These topics among others are studied in our department. Mathematical research areas of our department related to these topics include spectral theory, differential geometry, complex analysis and ordinary and partial differential equations.

A dynamical system is a mathematical description of the time evolution of something, e.g., a system of atoms and molecules, the financial market, the weather, or a population of some biological species. Usually this evolution depends on the previous state of the system (then called a deterministic system) but chance may also be involved. In the presence of nonlinearities even deterministic systems tend to behave in an unpredictable way. Therefore the field of dynamical systems is popularly known as ``chaos theory''. Dynamical systems appear virtually everywhere and a great many of mathematical instruments are used to tackle them. Areas of mathematical research in our department which relate to dynamical systems include ergodic theory, nonlinear partial differential equations, point set topology, complex analysis and topological and complex dynamics.

Naturally, this encourages an interdisciplinary approach in our department. We want our students to know the basics of several different areas of pure and applied mathematics. Also, for Ph.D. students, an important part of our program is the requirement of some coursework in a minor area outside mathematics, e.g., in biology, computer science, engineering, or physics.

M.S. students and beginning Ph.D. students focus mostly on coursework (there is, however, a thesis option for M.S. students, which involves research experience). Ph.D. students, of course, have to contribute a genuine piece of research in form of a dissertation before they earn their degree. We encourage students to be involved in research from the beginning. At first this means concentrated reading with a faculty mentor on a subject or participation in an entry level seminar. But later a student's research becomes more and more independent work guided by the advisor. Research in what? We outlined some areas earlier, but perhaps some case studies would be useful. Students work or have worked recently on relationships between

Admission Requirements

Only students with a firm foundation in Advanced Calculus, Algebra, and Topology are considered for immediate admission to the Ph.D. program. A student lacking this background will be considered for admission to our Master'sprogram first. Upon passing the qualifying exam a student may transfer to the Ph.D. program. We are expecting at least a B average in a student's previous work, and a score above 550 on each section of the Graduate Record Examination General Test. In our assessment of the qualifications of a student the letters of evaluation play an important role. To find more detailed information about the application procedure click here.

Degree Requirements

The following benchmarks have to be passed on a student's way to thePh.D. degree.

The coursework may be finished within two years after the Qualifying Exam and research should be started while coursework is still under way. Typically, work on the thesis itself takes 12 - 18 months. Therefore, depending on a student's background, one has to allow for four to six years to obtain both the M.S. and the Ph.D. degree.

Curriculum

For a typical curriculum and the syllabi ofthe associated courses click here.

Exchange Program

UAB and the University of Munich have initiated an exchange program for Ph.D. students. Students can spend one year in Munich to study Mathematics. For more information click here.

Financial Support

All applicants admitted to our graduate program will be considered for financial support. Teaching assistantships (TAs) and fellowships are available. A tuition award is also made to those holding graduate assistantships and the cost of student health insurance is covered. There remain some fees to be paid by the student. Opportunities are usually available for summer employment. All awards are made on a competitive basis.

As a teaching assistant a student will be assigned up to fifteen hours of service per week. The service (mostly teaching) will be such as to enhance a student's professional development as well as contribute to the operations of UAB.

For the year 2006/2007 TA stipends start at $18,000 per twelve months. They are available to US citizens as well as to international students. As mentioned above, in addition to the stipend a full tuition scholarship is also provided. Students making satisfactory progress can expect support for four years after the Qualifying Exam, which gives sufficient time to satisfy the degree requirements.

For the best qualified applicants we also offer MCTP and GAANN fellowships. MCTP fellowships, funded by a grant from the US National Science Foundation, provide $21,500 per year. The GAANN fellowships are funded by a grant from the US Department of Education. Depending on financial need they pay up to $30,000 per year. These fellowships are only available to US citizens and permanent residents.

UAB has also university-wide Minority Graduate Fellowships providing a $21,000 per year stipend plus tuition. Minority applicants are strongly encouraged to apply for those fellowships, and should contact the Mathematics Graduate Program Director or the UAB Graduate School for further information early in the application process.

The Department,Research Interests of the Faculty

Our department is a close-knit one, featuring many seminars in which both faculty and graduate students participate. In order to discuss what we do, it makes sense to distinguish between a "core area", in which the faculty has already done substantial research, and a "focus area" which may greatly influence the kind of core research which is done and which may eventually become a core area. Needless to say, the boundaries between these concepts are very fluid.

Core areas are:

Focus areas include:

Each doctoral student learns a fairly broad spectrum of pure and applied mathematics, and also takes an outside minor relating her or his area of interest to an applied area such as computer science or physics. Seminars are very active; students are urged to become involved in these as soon as possible.

The department has extensive outside grant support, funding research, doctoral work, and honors undergraduate fellowships. Students on fellowships have a reduced service load, allowing for a stronger focus on research. They also have funds available for travel to conferences and to buy books relating to their research.

Ph.D. students can expect to have interaction not only with our faculty but with the greater mathematical world. We encourage attendance at professional meetings, and also encourage Ph.D. students to interact with faculty at other universities across the US and abroad.

There are regular seminars in which visitors frequently share theirknowledge on latest developments. Our faculty is quite active in research,publishing widely and lecturing nationally and internationally. We tryto encourage an atmosphere wherein mathematics is of central importanceand is discussed openly and often. We regard graduate students as companionson our mathematical journey; each student is important to us. To learnmore about our department follow the links below.

About UAB and Birmingham

UAB is an urban university in Birmingham, Alabama, a dynamic, progressive urban center of great natural beauty. Birmingham is the largest city in Alabama. Almost a million people live in the metropolitan area, making it large enough to be cosmopolitan, yet small enough to navigate easily. Birmingham is Alabama's cultural and entertainment center, providing a very active intellectual life and a great cultural diversity due partly to its rapid growth in the late 19th and early 20th centuries as an industrial center and partly due to the phenomenal growth of UAB in the last four decades. Birmingham offers beautiful residential neighborhoods and parks, a thriving business climate, a relatively low cost of living, and excellent health care facilities. Among its large variety of arts and music offerings are many jazz clubs, the annual City Stages music festival, and world class events at UAB's Alys Stephens Performing Arts Center. Other local attractions include the Birmingham Civil Rights Institute, McWane Science Center, Birmingham Botanical Garden and Zoo, and Oak Mountain State Park.

Birmingham is in the geographic heart of the Southeast -- two hours from Atlanta, three hours from Nashville, six hours from New Orleans, five hours from the Smoky Mountains, and five hours from the beaches of the Gulf of Mexico.

In just a few decades, UAB has evolved into a world-renowned research university and health care center, Alabama's single largest employer, and an engine of revitalization for the city of Birmingham. UAB has more than 17,000 students (including about 4200 graduate students), 18,600 faculty and staff, and a campus covering more than 80 city blocks. UAB is one of America's premier research universities with a world-famous medical center, ranking among the top 20 in funding from the National Institutes of Health and earning more than $470 million per year in contract and grant support.

The Application Procedure

To apply for admission you have to provide academic records, letters of recommendation, and scores of the Graduate Record Examination (GRE), General Test. There are more requirements for international students. UAB charges also a processing fee. For details please see the admissions page of the Graduate School.The Graduate School requires that all applications are submitted online via the Apply-Yourself Network.If you have any general questions about the online application process, you can contact the Graduate School at the address

The Graduate School
The University of Alabama at Birmingham
1400 University Boulevard, Room 511
Birmingham, AL 35294-1150
USA
E-Mail: gradschool@uab.edu
Phone: 1-800-975-4723

With questions about our mathematics program and financial support, please contact us directly at

Department of Mathematics
University of Alabama at Birmingham
Birmingham, AL 35294-1170
USA
E-Mail: graduate@math.uab.edu
Phone: 1-205-934-2154

Applications for admission to the Graduate Programs in Mathematics are welcome any time. However, it is necessary that your complete application is received by the Graduate School at least six weeks before the beginning of the term in which you wish to begin graduate study. Moreover, to ensure full consideration for financial support for the Academic Year (mid August -- mid May) we should receive your application by March 15.