### DEPARTMENT OF MATHEMATICAL SCIENCES

*PO BOX 172400*

*Wilson Hall 2-214*

*Office Number 406-994-3601*

### Department Head

*Dr. Kenneth Bowers*

### Professors

* • M.M. Barge; dynamical systems. *

* • R.J. Boik; linear models, multivariate analysis. *

* • J.J. Borkowski; experimental design, response surface methodolog sampling, quality control. *

* • K.L. Bowers; applied mathematics, numerical analysis. *

* • M.J. Burke; mathematics education. *

* • J.D. Dockery; applied mathematics. *

* • W.W. Esty; stochastic processes, probability, mathematics education. *

* • T. Gedeon; applied dynamical systems. *

* • I. Klapper; applied mathematics. *

* • J.R. Lund; numerical analysis. *

* • R.C. Swanson; global analysis, dynamical systems. *

* • C.R. Vogel; numerical analysis, inverse problems. *

* • R.B. Walker; dynamical systems. *

### Associate Professors

* • J.D. Banfield; statistical computation, pattern recognition. *

* • J.S. Cherry; ecological and environmental statisitcs. *

* • L.G. Davis; sensitivity analysis, optimal design, numerical analysis. *

* • J. Kwapisz; dynamical systems, ergodic theory. *

* • J. Luebeck; mathematics education. *

* • M.C. Pernarowski; applied mathematics*

* • J.F. Robison-Cox; statistical computing, graphics, mixed effects models. *

### Assistant Professors

*• E. Burroughs; mathematics education.*

*• L. Geyer; dynamical systems, complex analysis.*

*• M. Greenwood; functional data analysis, time series, model selection criteria.*

*• M. Higgs; ecological and environmental statistics, bayesian hierarchial models, spatial statistics, computational statistics.*

*• K. Irvine; bayesian graphical models, spatial statistics, ecological and environmental monitoring.*

*• D. Yopp; mathematics education.*

### Degrees Offered

M.S. in MathematicsM.S. in Mathematics (Mathematics Education option)

M.S. in Statistics

M.S. in Ecological and Environmental Statistics (Please refer to Interdisciplinary Programs)

Ph.D. in Mathematics

Ph.D. in Statistics

The department offers graduate study leading to the degree of Master of Science in either Mathematics, Statistics, or Ecological and Environmental Statistics. The M.S. in Mathematics degree is available with two options: Mathematics and Mathematics Education. The Doctor of Philosophy degree is offered in Mathematics, Statistics, and Mathematics Education.

### Admission

For regular admission to either the M.S. or the Ph.D. degree program, a student should have completed at least eighteen (18) credits of Mathematics beyond calculus or statistics. For mathematics majors, this should include a year of advanced calculus. For statistics majors, it should include a year of statistical theory and a year of probability and statistical methods. Admission to the mathematics education program is determined on an individual basis. Refer to the * Admission Policies* and * Application Requirements* sections for additional information. Successful applicants are accepted into both the department and the Division of Graduate Education.

### Master of Science Requirements

The Master of Science degrees are offered under Plan A ( Thesis) and Plan B (Non-thesis). Of the required thirty (30) credit minimum, at least eighteen (18) credits of 500-level course work must be taken under either plan. Master’s degree programs may be approved with or without a minor or supporting course area. Statistics may be presented as a minor or supporting area for a Mathematics degree, and Mathematics as a minor or supporting area for a statistics degree.

Available under Plan B is a comprehensive master’s degree in either mathematics or statistics. Although no thesis is required in this plan, a sound knowledge of several areas of mathematics and/or statistics is expected. Also available under Plan B is a master’s degree in mathematics with an option in mathematics education. This option is designed primarily for secondary or junior college teachers and is offered as a combination of on-line academic year course work and summer sessions . The requirements for this degree are flexible and an attempt is made to tailor each program to the individual needs of the student. The mathematics education option requires completion of a capstone research project.

For further information, refer to the * For Master's Students* section. Students are expected to be familiar with both the departmental and the Division of Graduate Education degree requirements.

### M.S. in Statistics - Program Guidelines

The Master of Science degree in statistics at Montana State University gives students a solid background in the applications as well as the theory of statistics. Students in this program prepare either for further graduate work or for academic, industrial, business, or government employment. Upon entrance, each student meets with the department's Graduate Program Committee to discuss career objectives and first year course work. During the second semester in the program each student forms a Graduate Committee and together, they outline the student's degree program. The prerequisites for the master's degree program in statistics consist of the following semester courses or their equivalent: Multivariable Calculus (M 273), Linear or Matrix Algebra , Probability (STAT 420), and Mathematical Statistics (STAT 424). Students who have not completed these courses may still enter the master's program. It is suggested that these courses then be taken after enrolling.

Either **Plan A** (thesis and 20 credits of course work) or **Plan B** (30 credits of course work) can be chosen. In either case, all courses on a graduate program must be numbered 400 or higher, and STAT courses must be numbered 410 or higher. The specific program of study depends on the student's previous training and experience. Regardless of the plan chosen, (i) at least half of the required non-thesis credits must be STAT courses, (ii) at least two-thirds of the required non-thesis credits must be numbered 500 or higher, and (iii) the following 14 semester core course credits are required:

### Statistics M.S. Required Courses (15 semester credits)

- STAT 501-502 Intermediate Prob and M Stat - 6 credits
- STAT 505-506 Linear Stat Models, Adv Regression - 6 credits
- STAT 510 Statistical Consulting - 2 credits
- STAT 575 (Plan B below) 1 or 2 credits

#### Additional requirements

- The M.S. degree requires completion of either a thesis or a writing project.
- Thesis (
**Plan A**): The**Plan A**thesis typically requires 450-500 hours of work. The student must register for at least 10 thesis credits (STAT 590) in addition to the required 20 credits of course work. The student must give an oral defense of his/her thesis. - Writing Project (
**Plan B**): The**Plan B**writing project typically requires at least 90 hours of work, for which the student earns 2 credits of STAT 575. With permission from the student's committee, additional credits of STAT 575 (no more than 4 total) may be earned. Students should enroll in Stat 575 in their final Spring semester, and must give a seminar on the writing project before graduating.

- Experience in data collection – either through a course such as Sampling or Design of Experiments, or a course taken in a former degree program, or real-life experience.
- For either
**Plan A**or**Plan B**, the student must pass a comprehensive examination.

### M.S. Comprehensive Exam

The M.S. comprehensive exam is a four-hour *written* exam over material from (1) the M.S. core courses listed below and (2) electives selected by the student and approved by the student's graduate committee.

- M.S. Core Courses for the M.S. Comprehensive Exam (12 semester credits)
- STAT 501-502 Intermediate Probability & Statistics
- STAT 505 Linear Models
- Stat 506 Advanced Regression (retakes only)
- Elective Courses for the M.S. Comprehensive Exam (6 semester credits from Stat 446, Stat 431, or 500 level electives)

The exam is given each January with the specific date determined by the department. The exam is graded as PhD pass, M.S. pass, or fail. Examinees will be informed of the results within three working days of taking the exam. The M.S. comprehensive exam may be repeated once. If reexamination is needed, the student's committee will indicate which topics are to be repeated.

### Ph.D. Requirements-Mathematics

Students in Mathematics are expected to develop competence in real and complex analysis and at least two areas chosen from applied Mathematics, dynamical systems, functional analysis, numerical analysis, partial differential equations, probability, topology or other topics the student’s committee may approve.

Students in statistics must demonstrate proficiency in the Ph.D. core (linear models, probability, and mathematical statistics) as well as in two areas of additional study approved by the student’s committee. Potential areas include the following: modeling, multivariate statistics, spatial statistics, sampling, experimental design, time series, statistical computing, and nonparametric statistics. Proficiency is demonstrated by passing a PhD qualifying exam.

Students in mathematics education must demonstrate competence in three areas: (1) at least one topic Ph.D. level mathematics as described above; (2) current theory in mathematics curriculum, assessment, and instruction; and (3) educational statistics and research methods.

Doctor of Philosophy programs in the Department of Mathematical Sciences must include a supporting course area which may be taken within the department. A minor field of study is optional. Comprehensive examinations will cover approved areas. The student's graduate committee determines additional requirements. Refer to the * For Doctoral Students* section for additional information. Degree candidates are expected to be familiar with both departmental and Division of Graduate Education degree requirement.

### Ph.D. in Statistics - Program Requirments

The Ph.D. program in statistics at Montana State University prepares students for academic, industrial, business, or government employment. To earn a Ph.D. in statistics, a student must pass the Ph.D. qualifying exam, pass the Ph.D. comprehensive exam, and write and defend a Ph.D. dissertation. The exams are described below. The dissertation must be an original contribution to statistical science and must include new material worthy of publication. There is no departmental foreign language requirement for the Ph.D.

A Ph.D. student typically takes at least 24 credits of statistics in courses numbered 500 and higher and six credits of mathematics (M 505 & M 586). Additional course work in statistics and/or mathematics may be necessary, depending on the candidate's chosen area of specialization and background. For instance, a Ph.D. student is expected to have completed all courses required for the M.S. degree in statistics and may need to make-up one or more of these courses. Also, it is expected that a Ph.D. student will take directed study courses ( STAT 689) in his/her area of specialty. Stat 690, dissertation credit requirements, are listed in the Graduate Catalog. Two credits of Stat 510, S tatistics Consulting Seminar are required.

### Ph.D. Qualifying Exam

The Ph.D. qualifying exam is identical to the core course portion of the statistics M.S. comprehensive exam except that the exam must be passed at the Ph.D. level (i.e., Ph.D. pass). A student who earned an M.S. in Statistics from MSU need not take the PhD qualifying exam if the M.S. comprehensive exam was passed at the Ph.D. level. Other students are expected to take the Ph.D. qualifying exam during their first post-master's semester at MSU or as soon as course work in the M.S. core has been completed. Two attempts to pass the qualifying exam are allowed.

### Ph.D. Comprehensive Exam

The *written* comprehensive exam for the Ph.D. in Statistics consists of an 8-hour exam. It is given in August at a time determined by the department, and has been split into a session emphasizing methods and another emphasizing theory. At the discretion of the student's committee, the format might be changed, and the exam could be split so that half is taken one year and the remainder taken the following year.

The written Ph.D. comprehensive examination covers material in the student's concentration areas and in the Ph.D. core. The Ph.D. core consists of the following material.

- STAT 532 Bayesian Data Analysis
- STAT 550 Advanced Mematical Statistics
- M 586 Probability

Each student must devise at least two areas of concentrated study that are separate from the PhD core. Each area should include an amount of material (and at an appropriate depth) equivalent to two graduate level statistics or mathematics courses. The concentration areas must be approved by the student's committee and must include, in total, an amount of material equivalent to at least 4 graduate level courses. An area could involve course material from outside the department. Some examples are the following:

- Modeling (STAT 539 & 578)
- Multivariate Statistics (STAT 537 & 538 or STAT 537, 538, & 539)
- Design (STAT 526 & 578)
- Real Analysis (M 547 & 548)
- Biostatistics/Generalized Linear Models (STAT 524 & STAT 539).

Each session of the written comprehensive examination is graded separately as pass or fail. A failed session may be repeated once. Once the written comprehensive examination has been passed, the student must pass the oral comprehensive examination. The student's committee will inform the student of a timeline to take the oral and will

### Financial Assistance

Graduate assistantships are available to qualified graduate students in mathematics, mathematics education, or statistics. Graduate Teaching Assistantships (GTA) usually require teaching one course each semester. Graduate Research Assistantships (GRA) may also available to qualified students in mathematics and statistics. Time requirements are similar to those for teaching assistantships. See the * Graduate Assistantships* section for detailed information on appointment criteria.