**Departments & Programs**

**Department of Mathematical Sciences**

**Graduate Programs**

The Department of Mathematical Sciences offers graduate training leading to the Purdue University Master of Science degree in Mathematics, with concentrations in pure mathematics, applied mathematics, math education, and applied statistics. By arrangement with Purdue University, West Lafayette, qualified students may also pursue a Ph.D. in Mathematics. Together with the Department of Biostatistics in the Indiana University School of Medicine and the Indiana University Fairbanks School of Public Health at IUPUI, the department also administers and offers an Indiana University Ph.D. in Biostatistics. Requirements for both Ph.D. programs are completed entirely on the IUPUI campus. The M.S. degree requires two years of full-time study, and the Ph.D. typically requires two to three additional years of full-time study.
##### Admission Requirements

Students entering a graduate program in mathematics should have completed an undergraduate program containing as many courses as possible in abstract algebra, linear algebra, advanced calculus, differential equations, logic and foundations, and probability.

Students entering the graduate program in pure or applied mathematics should hold at least a bachelor's degree (or equivalent) from an accredited institution of higher learning in mathematics, or in the physical sciences or engineering with a strong mathematics background. A minimal cumulative GPA of 3.0 is required. The minimal mathematics background includes at least 13 credit hours of mathematics courses past the calculus sequence (single and multivariate calculus and differential equations).

Students entering the graduate program in applied statistics must have at least a bachelor's degree (or equivalent) from an accredited institution. A minimum cumulative GPA of 3.0 is required. The minimal mathematics background is an undergraduate course sequence in univariate and multivariate calculus (equivalent to MATH 16500, 16600, 17100, and 26100 at IUPUI), plus a linear algebra course (equivalent to MATH 35100 or 51100 at IUPUI). Applicants who lack only the linear algebra course may be admitted conditionally and then must complete such a course as soon as practicable.

Students entering the master's program in mathematics education must have at least a bachelor's degree (or equivalent) from an accredited institution. A minimum cumulative GPA of 3.0 is required. The minimal mathematics background includes undergraduate coursework in univariate and multivariate calculus (at IUPUI, MATH 16500, 16600, 17100, and 26100), differential equations, (at IUPUI, MATH 26600), linear algebra (at IUPUI, MATH 35100 or 51100), and abstract algebra (at IUPUI, MATH 45300).

Students entering the Ph.D. program in mathematics must have either an M.S. in mathematics or have successfully completed a bachelor's degree (or equivalent), from an accredited university, with advanced courses in mathematics. A minimum cumulative GPA of 3.0 is required. Competitive applicants will have successfully completed the following course work: linear algebra, abstract algebra, complex analysis, partial differential equations (PDE), ordinary differential equations (ODE), mathematical statistics, probability.

Students entering the graduate program in biostatistics must have a suitable bachelor’s or master’s degree from an accredited institution and show promise for successfully completing all the degree requirements. In addition to satisfying general Indiana University Graduate School requirements for admission, applicants must have at least a B (3.00 GPA) average in course taken during the last two years of their earlier degree studies, and a grade of B+ (3.50 GPA) in courses required as prerequisites for the program. The minimal mathematics background consists of an undergraduate course sequence in univariate and multivariate calculus (equivalent to MATH 16500, MATH 16600 and MATH 26100 at IUPUI) and a course in linear algebra (equivalent to MATH 35100). In addition, applicants should have had a calculus-based undergraduate level course in probability or statistics. Prospective applicants who do not have this background must acquire it prior to admission to the program.

#### Application for Admission

Students who wish to pursue an advanced degree in the Department of Mathematical Sciences should complete an online application available from the department’s web site at http://math.iupui.edu. For Ph.D. mathematics applicants, the GRE general score is required. For Ph.D. biostatistics applicants, the GRE general test is required. Students for whom English is not their native language and who have not completed a post-secondary degree program from an English-speaking university within the past two years must submit TOEFL scores. While this application is being processed, the student may enter IUPUI as a graduate non-degree student. No more than 12 hours of credit earned under this classification may be applied toward an advanced degree. Those who do not want to pursue an advanced degree, but who desire to take graduate courses for personal improvement, may also take courses under the graduate non-degree classification.

#### Transfer Credit

The Department of Mathematical Sciences will accept by transfer a maximum of 12 hours of graduate credit, in excess of undergraduate degree requirements, from approved institutions. Transfer credit must be approved by the student’s faculty advisor.

#### Assistantships and Fellowships

Financial support is available to qualified full-time thesis students in the form of university fellowships, school fellowships, graduate teaching assistantships, and research assistantships. Additional summer appointments may be available for students whose performance in course work and assistantship duties is satisfactory.

#### English Requirements

All advanced degree candidates are required to demonstrate acceptable proficiency in English composition.

Students for whom English is not their native language must take the EAP exam administered by the IUPUI English for Academic Purposes program. Students not scoring high enough will be required to take designated courses in English while pursuing their graduate studies.

#### Master of Science (Pure and Applied Mathematics Concentrations)

The Master of Science with focus in pure or applied mathematics consists of a minimum of 30 credit hours. Course grades must be A or B with the possible exception of at most two grades of C. Neither a thesis nor a comprehensive examination is required. Several core courses are specific to an M.S. plan of study and vary according to the student’s interest in (a) pure mathematics with a Ph.D. objective, (b) pure mathematics without a Ph.D. objective, (c) applied mathematics with a Ph.D. objective, or (d) applied mathematics without a Ph.D. objective. The remaining courses are selected by the student and his or her advisory committee.

#### Master of Science (Applied Statistics Concentration)

The Master of Science degree with a concentration in Applied Statistics consists of a minimum of 30 credit hours. Course grades must be A or B with the possible exception of at most two grades of C. A combined written and oral final examination is required. Candidates for this degree may choose either the thesis option or the non-thesis option. Both options require 15 credit hours in the core curriculum consisting of STAT 51200, STAT 51400, STAT 51900, STAT 52400, and STAT 52800.

The non-thesis option consists of 15 credit hours beyond the core curriculum, at least 9 of which must be statistics (STAT) courses. The remaining courses may be taken in mathematics or in areas relevant to statistical applications, subject to approval of the academic advisor.

The thesis option requires a thesis worth 6 credit hours on a topic approved by the student's academic advisor. At least 6 of the remaining 9 credit hours must be taken in statistics coursework beyond the core curriculum. The remaining 3 credit hours of coursework may be taken in Mathematics or in a subject related to statistical applications that has been approved by the advisor. An oral defense of the thesis is required.

#### Master of Science (Mathematics Education Concentration)

The Master of Science with focus in mathematics education consists of a minimum of 30 credit hours and is tailored for secondary school teachers and students who are preparing to become secondary school teachers. Course grades must be A or B with the possible exception of at most two grades of C. Core requirements include a course in abstract algebra (MATH 50500), a course in analysis (MATH 54700 or MATH 50400), a course in geometry (MATH 56100 or MATH 56300), a course in probability (STAT 51600), and a course in statistics (STAT 51700).

#### Master of Science in Computational Data Science

This degree program is offered through the Departments of Computer & Information Science and Mathematical Sciences of the IUPUI School of Science. The objective of the program is to prepare students to enter the workforce in the rapidly advancing field of data science, an interdisciplinary domain that cuts across computer science and statistics, by providing a solid, comprehensive background in the related topics of theory and their applications.

This program will provide the skills necessary that will enable students to be flexible and competitive in today's job market by gaining deep understanding of theory, implementation (e.g., algorithms and appropriate computing languages), as well as the inherent "nature" of different data modalities, such as classification and prediction challenges on specific data (e.g., sparse and/or incomplete data).

**Curriculum Requirements**

The curriculum requires 30 credits in total that can be completed in three semesters. There are 9 credits for core courses in Computer Science, 6 credits for Statistics core courses, 12 credits for elective courses from Computer Science and/or Statistics, and 3 credits for the capstone course. The students must chooe at least two electives from Computer Science and at least two electives from Statistics.

Successful completion of the program requires a minimum plan of study GPA of 3.0, the minimum grade in any course is C and the maximum number of courses with grades of C or C+ is two.

The course sequence is crucial for successful completion of this program. Students should consult with the departmental advisor.

**General Admission Requirements for MS in Computational Data Science**

Prerequisite coursework and/or degrees:

4-year Bachelor's degree in Computer Science, Engineering, Mathematics, Statistics or related fields. 4-year Bachelor's degree in any other area of study will be considered on a case-by-case basis, based on the coursework and corresponding grades in the applicant's transcripts, as well as on the overall potential of successfully completing this program.

GPA: Scores on the Graduate record Exam (GRE) must be submitted for admission consideration.

English Proficiency Requirements: All applicants whose native language is not English are required to submit scores for TOEFL or IELTS. An overall TOEFL IBT score of 80 or higher, or an IELTS band score of 6.5 or higher is required. Applicants submitting TOEFL scores must also meet the following section minimum requirements in addition to the minimum Total requirement: 18 Writing, 18 Speaking, 14 Listening, 19 Reading.

#### Doctor of Philosophy (Mathematics)

By arrangement with Purdue University, West Lafayette, qualified students may pursue a Ph.D. in Mathematics, with all requirements completed on the IUPUI campus. To be admitted to candidacy for the Ph.D. degree, the student must fulfill the following requirements and must be accepted by the graduate committee of the Department of Mathematical Sciences.

##### Requirements

- The student must pass a suite of four qualifying exams. They must select at least two out of four subject areas from the Core 4 with at least one being either Real Analysis (MATH 54400) or Abstract Algebra (MATH 55300). They must also pass two additional exams from either the remaining Core 4 or the Area Exams.
- The student must satisfy, by one of the five options approved by the graduate school, the world language requirement in German, Russian, or French.
- The student must submit to the graduate school through the department a plan of study including at least 42 credit hours of approved Purdue University graduate coursework.
- The student must pass an advanced topics examination. This examination may be taken only by students who have already passed the qualifying examinations.

A candidate will be recommended to the faculty to receive the Ph.D. degree after a dissertation, submitted in final form, has been accepted by the advisory committee and successfully defended before an open colloquium or seminar.

The department has set time limits for completion of the Ph.D. degree.

#### Doctor of Philosophy (Biostatistics)

Together with the Department of Biostatistics in the Indiana University School of Medicine and the Indiana University Fairbanks School of Public Health at IUPUI, the Department of Mathematical Sciences offers graduate training leading to a Ph.D. in Biostatistics from Indiana University, with all requirements completed on the IUPUI campus. To be admitted to candidacy for the Ph.D. degree, the student must fulfill the following requirements.

##### Requirements

- The student must pass an initial qualifying examination on the five core courses: STAT 51900, STAT 52500, STAT 52800, STAT 53600, and PBHL-B546.
- The student must complete at least 45 credit hours of formal coursework, consisting of 33 credit hours of required courses and additional 12 credit hours in elective statistics/biostatistics courses of which six credit hours must be at the 600 level and above. An additional 45 credit hours are required and will consist of coursework in a minor area (minimum of 9 credits), further elective courses, independent studies, and directed Ph.D. dissertation research.
- The student must pass a preliminary oral examination, which consists of an oral presentation on an advanced research topic.

A candidate will be recommended to the faculty to receive the Ph.D. degree after a dissertation, submitted in final form, has been accepted by the advisory committee and successfully defended before an open colloquium or seminar.

The department has set time limits for the completion of the Ph.D. degree.