20202021 General 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, business, and industry, as well as prospective college teachers.
Specializations for PhD in Mathematical Sciences
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. This PhD program allows students to specialize in theoretical or applied statistics under the guidance of faculty dedicated to advancing statistical methodology for important and timely realworld problems. Students work with faculty mentors in areas such as Big Data, time series, statistical genetics, bioinformatics, computational statistics, data visualization, experimental design, and biostatistics. Nearly all Statistics dissertations involve collaboration with researchers in other fields, including ecology, agriculture, genetics, cancer, finance, public health, nutrition, education, and engineering.
The Interdisciplinary Studies Specialization gives 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 twothirds of their coursework in the Department of Mathematics and Statistics, and the remaining third in the other discipline. The student's dissertation committee must include 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 College Teaching Specialization is designed for students preparing for careers focused on teaching mathematics and statistics. Students in the College Teaching specialization receive broad training in pure and applied mathematics and statistics and complete six credits of College Teaching Internship under the guidance of their supervisory committee. The dissertation for this specialization is flexible and may include original research in mathematics, statistics or education as well as the exposition of important mathematical and statistical theories and their historical relationships.
All four specializations require a course of study of 45 credits beyond a master's degree or 72 credits beyond a bachelor's degree. Students applying to the PhD program without a master's degree will usually be directed to MS programs in Mathematics, Industrial Mathematics or 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:
 Selecting a supervisory committee with at least one member outside the Department of Mathematics and Statistics and completing a Program of Study.
 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, 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.
 Submitting and defending a written proposal for dissertation research to the supervisory committee.
 Completing a written dissertation.
 Successfully defending the dissertation in a final oral examination scheduled with the School of Graduate Studies.
After completing items 13 and the majority of required coursework a PhD student may be advanced to candidacy.
Specific requirements for each specialization of the PhD in Mathematical Sciences are listed below, assuming that the student already has a master's degree in mathematics or statistics.
The Pure and Applied Mathematics Specialization requires at least 30 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 dissertation should be a publishable, significant contribution to research in an area of mathematics.
The Statistics Specialization requires at least 30 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). The dissertation constitutes a publishable, significant contribution to research in statistics.
The Interdisciplinary Studies Specialization requires at least 30 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 15 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 a publishable contribution.
The College Teaching Specialization requires at least 30 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) with professional development content defined by the student's supervisory committee and coordinated with the Associate Department Head 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/statistics education; or an exposition of important mathematical theories and their historical relationships in an area of the student's choosing.
