Research in analysis includes real, complex, and functional analysis. Specific research programs carried out by faculty members in our department include harmonic analysis and applications of analysis to fluid dynamics and mathematical physics.<br><br>We offer programs leading to the Master of Science (M.S.) degree, and a doctoral program leading to the Doctor of Philosophy (Ph.D.) degree. The descriptions below of degree requirements for these programs are only summaries, intended to communicate the nature of the programs to potential students. For complete descriptions see the Policies document linked below. <br><br>The Master of Science degree represents two years of course work and an optional thesis. This degree is intended to provide a basic foundation of graduate level work from which the student can pursue multiple options for the future. Many M.S. degree holders move on to a technically oriented job with an employer in the private sector or with a government agency. For others it is the gateway into the more intense and in-depth study of the doctoral program. There are two M.S. degree options: the nonthesis option and the thesis option. As alternatives to the standard requirements for these options, both are available under a special interdisciplinary plan.<br><br>To complete the M.S. degree requirements the student must satisfy some form of final examination requirement. Our current practice is to have the student prepare and give a lecture with written summary on the topic of a short independent study project carried out under the supervision of a faculty member. These Master's Presentations have proven valuable to students in job interviews and in developing professional communication skills, not to mention the interesting mathematical topics they have explored. A standing alternative to the Master's Presentation requirement is the passage of two Ph.D. preliminary examinations. This allows a student to complete the M.S. requirements automatically in the first two years of normal progress toward the Ph.D.<br>The Department of Mathematics at Virginia Tech offers a range of degree programs intended to educate qualified students in the burgeoning world of advanced mathematics, and to prepare them for careers in its use and development. New mathematically related career paths continue to emerge as our technology-based economy evolves, while some traditional ones seem to be declining. Those pursuing careers in teaching will need to prepare their own students to meet the challenges of this changing world. We believe that the best way to prepare for the future is to develop a foundation from which graduates can build careers in many directions, gain some experience with how a specialty is built on those foundations, and learn to use the most up-to-date tools. In what follows you will find an overview of our programs, resources, and faculty. In addition to understanding the opportunities, we also want you to have realistic expectations of the rigors of full-time graduate study and what preparation you should have. If, after reviewing the information below, you have questions or would like to apply for admission, do not hesitate to contact us using the addresses, phone numbers, and electronic addresses which are provided.