20112012 General Catalog [ARCHIVED CATALOG Please see current catalog]
Mathematical Sciences, PhD


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Department of Mathematics and Statistics
This is a terminal degree for mathematics and statistics researchers in academe, government, and industry, and for prospective college teachers.
Specializations for PhD in Mathematical Sciences
The College Teaching Specialization is designed to prepare students to teach undergraduate mathematics in two and fouryear colleges and in universities. This program is less specialized than the other two options. Students in the College Teaching specialization receive broad training in pure and applied mathematics. The dissertation for this specialization includes exposition of important mathematical theories and their historical relationships in an area of mathematics of the student’s choosing.
The Interdisciplinary Studies Specialization offers students the opportunity to receive advanced training in mathematics and/or statistics in the context of another field of inquiry, such as biology, ecology, business, economics, engineering, or education. Students in this specialization will usually take about two thirds of their coursework in the Department of Mathematics and Statistics, and the remaining third in the other discipline. The student’s dissertation committee will choose two members from outside the Department of Mathematics and Statistics. The dissertation itself will generally entail the development of advanced mathematical or statistical methods to solve problems in the other subject area.
The Pure and Applied Mathematics Specialization is a traditional doctoral program in mathematics, offering broad training in the foundations of modern mathematics together with specialized training in an area of mathematical research. The dissertation represents a significant contribution to mathematics research in the chosen area of specialization.
The Statistics Specialization offers broad training in theoretical and applied statistics for students seeking careers in academia, industry, or government. The dissertation represents a significant contribution to statistical research.
All four specializations require a course of study of 60 credits beyond a master’s degree or 90 credits beyond a bachelor’s degree. In almost all cases, a student who applies to the PhD program who does not already have a master’s degree will first be directed to the MS programs in mathematics and statistics. Satisfactory performance in one of these programs can lead to admission to the PhD program in mathematical sciences.
The core requirements for the PhD degree in Mathematical Sciences that are common to all four specializations include the following:
 Passing a standard written qualifying examination appropriate for the specialization.
 Passing a comprehensive examination that is constructed specifically for the student by his or her supervisory committee. The form of the examination may be written or oral, or may include a combination of written and oral components. The length and content of the exam are determined by the student’s supervisory committee.
 Successfully complete a test of technical English writing skills. Usually the student’s dissertation proposal will serve this purpose.
 Complete a dissertation.
 Successfully defend the dissertation in a final oral examination.
After completing items 13, a PhD student may be advanced to candidacy.
Requirements that are specific to the specialization of the PhD in Mathematical Sciences are listed below. In all cases, it is assumed that the student already has a master’s degree in mathematics or statistics.
The College Teaching Specialization requires at least 60 credits in mathematics courses numbered 6000 or higher, excluding MATH 7990 and MATH 6990 , of which no more than 20 can be completed in MATH 7970 (Dissertation Research). At least 6 credits should be selected from classes and seminars at the 7000 level, and 6 credits of MATH 7910 (College Teaching Internship) are also required. Students in this specialization take a qualifying examination in Real Analysis. The student’s dissertation in this specialization may take several forms, including a traditional, publishable contribution to some area of mathematics; a significant contribution in the area of mathematics education; or an exposition of important mathematical theories and their historic relationships in an area of the student’s choosing.
The Interdisciplinary Studies Specialization requires at least 60 credits numbered 6000 or higher, excluding MATH 7990 , STAT 7990 , MATH 6990 , and STAT 6990 . No more than 30 of the credits may be completed in MATH 7970 or STAT 7970 (Dissertation Research). At least 20 of the credits should be in mathematics and/or statistics, of which at least 6 should be in seminars and classes at the 7000 level. An additional 10 credits in the student’s chosen interdisciplinary area are also required. Students in this specialization may take a qualifying examination in Real Analysis or in Probability and Mathematical Statistics, depending on whether the majority of their coursework is in mathematics or in statistics. The student’s PhD supervisory committee should include two persons in the student’s selected interdisciplinary area, and the comprehensive examination should have a significant interdisciplinary component. The dissertation for a student in this specialization should involve the development and application of mathematical or statistical methods to solve problems in the chosen interdisciplinary area, and should be publishable in journals in that area.
The Pure and Applied Mathematics Specialization requires at least 60 credits in mathematics numbered 6000 or higher, excluding MATH 6990 and MATH 7990 . At least 6 credits must be selected from seminars or classes numbered 7000 or higher, and no more than 30 of the credits can be completed in MATH 7970 (Dissertation Research). The qualifying examination for this option is in Real Analysis. The dissertation should be a publishable, significant contribution to research in an area of mathematics.
The Statistics Specialization requires at least 60 credits in statistics at the 6000 and 7000 level, excluding STAT 6990 and STAT 7990 . With the permission of the student’s supervisory committee, some of these credits may be in mathematics or in another discipline. At least 6 credits must be selected from seminars and classes numbered 7000 and higher, and a maximum of 30 credits may be completed in STAT 7970 (Dissertation Research). Students in this specialization take a qualifying examination in Probability and Mathematical Statistics. The dissertation constitutes a publishable, significant contribution to research in statistics. 