# Mathematics and Statistics - 2021-22 Graduate Catalog

**Chair:** Junfeng Shang

**Graduate Coordinator:** Steven Seubert

**Address:** 450 Mathematical Sciences Building

**Phone: **419-372-2636

**Program Web Page:** https://www.bgsu.edu/arts-and-sciences/mathematics-and-statistics/graduate-programs.html

**Degrees Offered**

Master of Arts

Master of Science

Doctor of Philosophy

**Programs Offered**

**The Master of Arts **program can prepare the student for direct entry into careers in business, industry, government, and education, or for study toward a Ph.D. in mathematics, statistics, computer science, or operations research. Areas of specialization in the M.A. program are pure mathematics, statistics, and applied mathematics / scientific computation. The pure mathematics specialization is designed for students interested in obtaining a broad background in pure mathematics or in pursuing a Ph.D. degree in mathematics. The statistics specialization is designed for students interested in theory and applications of statistics and also for those planning to pursue a doctoral degree in statistics. The applied mathematics / scientific computation specialization is designed for students interested in applications of mathematics in science and industry, in particular using differential equations.

**The Master of Science in Applied Statistics** is offered jointly with the Department of Applied Statistics and Operations Research. The program prepares students for careers in business, industry, or government, or for further study toward a Ph.D. degree in statistics.

**The Doctoral Degrees (Ph.D. in Mathematics and Ph.D. in Statistics)** in the Department of Mathematics and Statistics are research degrees. Students in the Ph.D. program are to maintain a balance between the depth of the dissertation work and the breadth provided by the course work. The programs prepare students for academic careers balancing teaching and research, or, especially in the case of the statistics Ph.D., research-oriented jobs in government and industry.

The Master of Science in Data Science and the Ph.D. in Data Science are offered jointly by three departments, the Department of Applied Statistics and Operations Research, the Department of Computer Science, and the Department of Mathematics and Statistics. For more information on the program, please visit the Data Science page in the Graduate Catalog

**The Graduate Certificate in Mathematics for Professionals and Educators** is especially useful for individuals who already possess a Master’s degree and who want to meet the minimum requirements of the State of Ohio to teach survey-level college courses. It can be designed to lead to any of the master’s programs offered by the department.

**Program Learning Outcomes**

Upon completion of the Master's degree, students in the Mathematics program (including Applied Math and Statistics specializations) are expected to be able to:

- Effectively explain, integrate, and apply critical concepts in mathematics/statistics
- Demonstrate proficiency at mathematical/statistical problem solving in novel situations
- Use appropriate technology to successfully make progress on a wide variety of mathematical/statistical tasks
- Clearly communicate mathematical/statistical ideas orally and in writing

Upon completion of the Master's degree, students in the Applied Statistics program are expected to be able to:

- Effectively explain critical concepts and assumptions in applied statistical modeling and analysis
- Effectively analyze data using graphical, exploratory, and statistical modeling approaches to find patterns and assess if these patterns are statistically meaningful
- Effectively use appropriate computer technology to help describe, predict, and prescribe solutions to applied statistical problems
- Clearly communicate - both orally and in writing - conclusions drawn from descriptive, predictive, and prescriptive analysis of applied statistical problems

Upon completion of the PhD degree, students in the Mathematics program are expected to be able to:

- Effectively explain, integrate, and apply critical concepts in mathematics
- Clearly communicate mathematical ideas orally and in writing
- Use appropriate technology to successfully make progress on a wide variety of mathematical tasks
- Read, understand, critique, and extend published articles
- Conduct original research in mathematics and write a dissertation of publishable quality

Upon completion of the PhD degree, students in the Statistics program are expected to be able to:

- Effectively explain, integrate, and apply critical concepts in statistics
- Clearly communicate statistical ideas orally and in writing
- Use appropriate technology to successfully make progress on a wide variety of statistical tasks
- Read, understand, critique, and extend published articles
- Conduct original research in mathematics and write a dissertation of publishable quality

Upon completion of the 18-hour Graduate Certificate degree, students in the Mathematics for Professionals and Educators program are expected to be able to:

- Effectively explain and apply critical concepts in mathematics
- Describe how other students understand, misunderstand, and learn about critical concepts in mathematics
- Develop and refine methods for teaching critical concepts in mathematics
- Clearly communicate mathematical ideas orally and in writing

**Prerequisites to Graduate Work**

The preferred foundation for master’s graduate work is an undergraduate major in mathematics or in a closely related area. Applicants with less than this level of prerequisite background may be accepted if they appear to be adequately prepared for graduate work. Minimum preparation consists of a full year in differential and integral calculus and two courses for which calculus is a prerequisite. Applicants planning to specialize in applied mathematics / scientific computation should have completed courses in linear algebra, advanced calculus, ordinary differential equations, and programming in a high-level language such as C++, Java, or Python before or soon after admission.

Students may enter the Ph.D. program if they have a master’s degree in mathematics, statistics, or a closely related area from an accredited university and meet admission requirements at Bowling Green State University. Applicants planning to specialize in statistics would benefit from having completed courses in advanced linear algebra, real analysis, and regression analysis.

**Admission Procedure**

Applicants seeking admission to a graduate program in mathematics and statistics should follow the instructions outlined in the Graduate Admission webpage.

In addition to the application required by the Graduate College, applicants must submit a statement of intent delineating the purpose for enrolling in the program and career goals. Three original, signed letters of recommendation must be provided. Please also see the Mathematics and Statistics and Graduate College websites.

**Degree Requirements**

**Master of Arts**

Candidates must complete at least 30 semester hours of approved graduate credit, including at least 18 hours in mathematics/statistics courses numbered 6000 or above, excluding MATH 5850, 5900, 5910, 5920, 6850, 6940, 6950, and seminar courses. In addition, students must satisfy all the requirements in one of the three groups described below.

Pure Mathematics: Required courses are MATH 6330, 6340, 6650, and 6660.

Statistics: Required courses are MATH 5650 or 6650, 6410, 6420, and two additional courses in specialized areas of statistics selected from among MATH 6440, 6450, 6460, 6470, 6480, 6710, 6720, 7400, 7410, 7420, 7450, 7460, 7570, 7580 and any approved 6820 course in statistics.

Applied Mathematics / Scientific Computation: Required courses are MATH 5390, 6180, 6200, 6650, and 6680.

Each of the three programs is offered under the following two plans:

Plan I: Candidates must write a thesis and pass an oral and/or written examination on the thesis.

Plan II: Candidates must pass a written comprehensive examination based on the required courses.

Related courses from other fields may be included in the student's plan, subject to the approval of the Graduate Coordinator. The actual course of studies is designed by the student in consultation with, and with the consent of, the Graduate Coordinator on an individual basis.

**Master of Science**

The Master of Science in Applied Statistics program is offered jointly with the Department of Applied Statistics and Operations Research. Candidates must complete at least 33 semester hours of approved graduate credit, including at least 18 hours in mathematics and/or statistics courses numbered 6000 or above, excluding MATH 5850, 5900, 5910, 5920, 6850, 6940, 6950, and seminar courses. Students may pursue the M.S. degree under either Plan I or Plan II described below.

Requirements under either plan are: MATH 6410 and 6420, STAT 5020, 5060, and 5080; At least five elective courses (15 credit hours) in Statistics (at least three at 6000 level). Of these elective courses, at least six hours must be from the Department of Mathematics and Statistics, including MATH 5260, 5270, 5450, 5470, 5650, 5660, 6440, 6450, 6460, 6470, 6480, 6710, 6720, 7400, 7570 or 7580, and at least six hours must be from the Department of Applied Statistics and Operations Research, including OR 6610, 6620, STAT 5120, 5140, 5160, 6200, 6300, 6340 or 6440. The remaining three hours may be from offerings of either the Department of Mathematics and Statistics or the Department of Applied Statistics and Operations Research, or may be any graduate course approved by the advisor.

Plan I: Candidates must complete a minimum of 33 semester hours of graduate course work plus at least three hours of thesis credit. Candidates must submit a thesis on a topic approved by the Statistics Program Committee and must pass an oral examination covering the materials of the thesis and course materials of MATH 6410, 6420, STAT 5020, 5060, and 5080.

Plan II: Candidates must complete a minimum of 33 hours of graduate course work including STAT 6750. Students must pass a written and oral comprehensive examination over MATH 6410 and 6420, and STAT 5020, 5060, and 5080. However, the oral examination can be waived for students with sufficient written examination scores.

**Doctor of Philosophy**

The programs require a minimum of 90 hours of graduate credit (i.e., 60 hours beyond the master’s work).

Course Work.

1. Students who are pursuing a Ph.D. in Mathematics must take eight of the twelve courses listed below. These eight courses must be selected so as to include at least two of these year-long sequences:

a. Algebra: 7330, 7340; Analysis: 7650, 7660; Complex Analysis: 6610, 7620; Topology: 6510, 7520; Partial Differential Equations: 7120, 7130; Probability: 7410, 7420.

2. Students who are pursuing a Ph.D. in Statistics must take the following courses:

a. Statistics: 7450, 7460, 7570, 7580; Analysis: 6650, 6660; Probability: 7410, Six electives from: MATH 6440, 6450, 6460, 6470, 6480, 6710, 6720, 7400, 7420, STAT 6200, 6300, 6340, 6750, and any approved MATH 6000+ or STAT 6000+ letter-grade topic courses.

A doctoral student needs to pass the Qualifying Examination and the Preliminary Examination.

For a student in the Ph.D. in Mathematics program to pass the Qualifying Examination, the student has to pass two four-hour tests, respectively, in two areas of the student’s choice from among the following: algebra (7330, 7340), real analysis (7650, 7660), complex analysis (6610, 7620), topology (6510, 7520), partial differential equations (7120, 7130), and probability (7410, 7420).

For a student in the Ph.D. in Statistics program to pass the Qualifying Examination, the student has to pass two four-hour tests, respectively, in two areas of the student’s choice from among the following: probability (7410, 7420), estimation and testing hypotheses (7450, 7460), and linear models and computational statistics (7570, 7580). Students intending to write a dissertation in the field of statistics are suggested to choose 7450/7460 and 7570/7580; students intending to write a dissertation in the field of probability are suggested to include 7410/7420 in their choices.

The Preliminary Examination is administered by a student’s Preliminary Examination committee. It consists of a written and an oral component. A student must pass the Department’s Qualifying Examination to qualify to take the Preliminary Examination. The Department offers the following general suggestion to students and their Preliminary Examination committees.

1. A topic/field is determined upon mutual agreement between the student and the Preliminary Examination committee. (It is highly recommended that this topic be the topic/field of the student’s future dissertation research.) The Preliminary Examination committee then assigns materials related to the topic/field for the student to study.

2. The student submits a written report on the reading materials to the Preliminary Examination committee and then gives an oral presentation in front of the Preliminary Examination committee. An almost-final version of the reading report should be submitted to and accepted by the Preliminary Examination committee at least one week before the presentation takes place. To pass the Preliminary Examination, the student is expected to show a comprehensive understanding of the topic in the Preliminary Examination committee’s judgment. A final version of the reading report should be filed with the Department before the Department endorses a positive result to the Graduate College.

**Graduate Courses**

Please access graduate courses online at http://www.bgsu.edu/registration-records/courses-and-classes/class-course-information.html. Graduate courses offered by the Department of Mathematics and Statistics use the prefix: MATH.

Updated: 02/03/2023 09:22AM