Master of Science in Biological and

Computational Mathematics

Graduate Handbook-DRAFT

Revision date: June 21, 2019

Index

I. Introduction

II. Admission Requirements and Procedures

A. Admission Criteria

B. Admission Procedures

C. Dismissal and Re-Admittance

D. Fees and Financial Assistance

E. Assistantship Guidelines

F. Training for graduate assistants

III. Degree Requirements and Procedures

A. Advising

B. Required Hours

C. Grade Policy

D. Evaluation of Student Progress

E Residence Requirements

F. Time Limit

G. Research

H. Summer Semester Support

I. Comprehensive Examinations

J. Graduation Policy

K. Forms Summary

IV. Curriculum Summary

A. Course Requirements

B. Sample Program of Study

V. Course Descriptions

VI. Faculty and research interests

VII. Program Learning Objectives

I. Introduction

About the Program:

The M.S. program is a 2-year program consisting of 36 hours of courses. Graduates of the program will

be well-equipped to use a variety of methods to construct mathematical models in order to solve real-

world problems, especially those problems of an interdisciplinary nature. The expertise of the faculty

involved includes many applications in the biomedical fields. The nature and breadth of the curriculum

allows students to enter jobs in industry or to enter Ph.D. programs in Applied Mathematics. The

program includes a strong experiential component in the form of seminars as well as a graduate project

course where students have the opportunity to conduct original research in applied mathematics.

Program highlights:

• Option of engaging in research with a faculty mentor.

• Availability of graduate assistantships and teaching assistantships which include tuition waivers

and financial stipends.

• Provides the background to obtain a quality job in industry or enter a Ph.D. program. Typical

employers are government agencies, manufacturing, biomedical and biotech companies, medical

schools, and pharmaceutical companies. Some specific regional employers are ADP, Savannah River

National Labs, and Unisys.

Deadline for admission:

The program admits students each fall. There are no spring or summer admissions. Applications for the

fall semester must be complete no later than July 1. Students wishing to apply for assistantship support

must complete their application no later than March 1.

Early submission of all application materials is strongly advised, particularly for students applying for

assistantships.

All required application materials and documents must be received in order for an application to be

considered complete and before an admission decision can be made. Applications and supporting

materials received after the program deadline may still be considered.

II. Admission Requirements and Procedures

A. Admission Criteria

Admission to the program is competitive, and students admitted in regular status are likely to have

exceeded the minimum criteria listed below.

1. Completed online application and submitted all requisite fees.

2. Minimum overall undergraduate GPA of 3.0 on a 4.0 scale.

3. Completed a Bachelor's degree from an accredited program and an accredited college or university.

To be used to satisfy degree requirements, evaluation of foreign educational transcripts must show

degree earned that is the U.S. equivalency of degree required by the program.

4. Minimum course requirements in mathematical background are three semesters of calculus

(differential, integral, and multivariable), one semester of linear algebra or equivalent, and one semester

of elementary differential equations.

5. Official transcripts are required from all universities and colleges ever attended.

6. Recommendations (which include a reference form and letter of recommendation) from three

individuals are required.

7. Test scores from the Graduate Record Examination (GRE) taken within 5 years of the date of

application. A minimum score of 290 total (combined Verbal and Quantitative Scores) is required.

8. Official Test of English as a Foreign Language (TOEFL) test scores are required for applicants whose

first language is not English. The institution code for submission of TOEFL scores to Augusta University is

5406. Please do not select a department code.

Exemption from the TOEFL requirement is allowed for graduate students who submit proof of earning a

baccalaureate degree from a regionally accredited U.S. college/university where English is the language

of instruction.

Minimum TOEFL Exam Scores: 550 paper-based, 213 computer-based or 79 internet-based.

9. Proof of Lawful Presence: In accordance with Board of Regents Policy 4.1.6, all applicants for

admission to Augusta University are required to provide validation of lawful presence in the United

States.

B. Admission Procedures

The Office of Admissions will provide the prospective applicant with information concerning admission

procedures. Applications from persons interested in taking graduate courses in mathematics should be

sent to the Augusta University Office of Admissions. All questions about the program should be directed

to the Department of Mathematics.

After all required information has been received, the Graduate Admissions Committee, consisting of the

Director of Graduate Studies in Mathematics and at least two other members of the faculty of

Mathematics appointed by the Department Chair, will make an admission decision. Admission decisions

are subject to final approval of the Department Chair, Dean of Science and Mathematics and the Dean of

The Graduate School. The official final notification regarding admission will come from the Office of

Admissions.

The Director of Graduate Studies in Mathematics will contact the applicant after the official acceptance

has been transmitted by the Office of Admissions. Any appeals of this decision should be addressed to

the Dean of The Graduate School.

C. Dismissal

Students must maintain a cumulative 3.0 GPA in all graduate coursework. Any student whose

cumulative GPA falls below 3.0 will be placed on academic probation, and students on probation who do

not earn a semester GPA of at least 3.0 during each semester on probation will be considered for

dismissal.

Dismissal may also occur when students in provisional status earn any course grade lower than a B while

on provisional status. Students who are dismissed from the program can appeal the decision by

following the procedure outlined in the dismissal policy of The Graduate School.

D. Fees and Financial Assistance

Fees are determined by the University System of Georgia and are posted on the Augusta University

website each year.

The department offers a limited number of graduate assistantships which pay for tuition and provide a

stipend in return for services to the department (see section E). All assistantships must be approved by

The Graduate School each semester.

Graduate assistants are required to carry an academic load of at least 9 semester hours per semester.

The Board of Regents of the University System of Georgia requires that all graduate assistants provide

proof of adequate health insurance coverage.

E. Assistantship Guidelines

Graduate Assistantships and Graduate Teaching Assistantships are the primary means of financial

support for students pursuing graduate study in Mathematics. These awards are limited in number and

are awarded on a competitive basis. Each category of assistantship carries a tuition waiver and a 10-

month stipend. These assistantships do not typically provide any summer support.

First-year students in the program who are on an assistantship will be assigned duties under the direct

supervision of a faculty member. Responsibilities may include working as a tutor in the Mathematics

Assistance Center or assisting a faculty member with a particular course (grading assignments,

conducting supplemental review/problem sessions). At the end of each semester, the faculty member

supervising the student will assess the student’s performance and send their assessment to the Director

of Graduate Studies.

Highly qualified students in the second year of the program who have completed 18 graduate-level

credit hours may be eligible to teach introductory courses. The typical course assignment will be two

sections of a core mathematics course (generally College Algebra, Precalculus, or Elementary Statistics)

per semester. These students will be assigned a teaching mentor who will oversee their training, and

they will report to their mentor and to the Director of Graduate Studies who will provide additional

guidance and oversight. Each semester, the student’s assigned mentor will observe them teaching and

provide a report of their assessment to the Director of Graduate Studies.

Students assigned to teach courses have a number of primary responsibilities, including:

1. Preparing a course syllabus consistent with departmental standards.

2. Preparing for their classes and meeting all classes as scheduled.

3. Preparing assignments and examinations for their courses.

4. Holding a minimum of two office hours per week.

5. Assigning final course grades.

6. Following all university and departmental procedures and guidelines.

Renewal of any assistantship requires satisfactory academic performance (cumulative graduate GPA of

at least 3.0) as well as a satisfactory evaluation of all assistantship duties. Students will be notified by

April 1 concerning the renewal of assistantships.

Students with assistantship support will be expected to report to campus in early August (typically the

Monday of the first full week of August) for either orientation (new students), training, or (for students

in their second year who are selected to teach) to prepare for their classes. Students receiving

assistantships will be expected to be on campus until the end of final examinations. Exact employment

dates associated with the assistantship will be specified.

F. Training for graduate assistants

All students receiving assistantship support may be required to attend training sponsored by either the

department, the college, or Augusta University.

III. Degree Requirements and Procedures

A. Advising

An advisor will meet with each student to discuss course selections and complete plans of study. An

initial plan of study must be completed by the end of the first semester of full-time course work or its

equivalent. Graduate students will be matched with a tenure track faculty member by the end of the

first semester in the graduate program. This faculty member is available to discuss topics such as career

directions, progress in courses, and adjustment to graduate school. This faculty member also provides

feedback from the first and second year reviews.

B. Required Hours

The program requires 36 hours of graduate coursework, typically completed over 4 semesters. See

chapter IV for the exact course requirements and a sample course plan.

C. Grade Policy

Students must maintain a cumulative 3.0 GPA in all graduate coursework.

D. Evaluation of Student Progress

In each of the first three semesters of the program, each student will meet with the Director of

Graduate Studies to evaluate the student’s progress in the program. The student will prepare a

tentative course schedule for the upcoming term to be approved by the Director of Graduate Studies.

Feedback from all faculty who have taught the student will be obtained to provide an overall assessment

of the student’s performance in their courses and their assistantship duties, if applicable.

E. Residence Requirements

No more than 9 semester hours of credits may be transferred into the course of study from either

another institution or Augusta University. Transfer of credit should be initiated as soon as possible after

admission and must be reviewed by the Director of Graduate Studies and approved by the Department

Chair. Students must be registered in the university during the semester in which requirements for

graduation are completed, including the semester in which comprehensive examinations are taken.

F. Time Limit

Only that course work completed within the six calendar years prior to completion of degree

requirements will apply toward graduation. The age of a course will be calculated from the date when

the course would be expected to have been completed, normally the last day of class of the term in

which registration for the course occurred.

G. Research

A current list of faculty with potential research projects for the MATH 6990 (Graduate Project) course

can be found on the department’s website. Students interested in doing the Graduate Project should

begin the process of finding an advisor early in their third semester.

H. Summer Semester Support

Students on assistantships are paid their stipend over the 10 month period between August and May.

On-campus summer employment during June and July may be possible, but is not guaranteed, subject

to availability of funding.

I. Comprehensive Examinations

Students may take their comprehensive examination any time after completing 27 hours of graduate

coursework and enrolling in MATH 6960 (Research Seminar). Prior to the end of the final exam period in

the third semester of study, the student must submit to the Director of Graduate Studies a list of three

courses to form the basis for the comprehensive exam. MATH 6960, MATH 6965, and MATH 6990 may

not be used as a comprehensive exam course, nor may any course without a MATH prefix be used for

the comprehensive exam.

Once these courses are approved, the student’s comprehensive exam committee will be populated with

the faculty members who taught the approved courses. This committee should contain no fewer than

three faculty members, and if necessary (for example, if one faculty member has taught multiple

courses) additional faculty members in the appropriate areas of expertise will be selected by the

Director of Graduate Studies to populate the committee.

The comprehensive exam will typically be scheduled in early January of the final semester. Three

individual one-hour exams will comprise the comprehensive exam. Each of the three individual exams

will be evaluated as “pass” or “fail”, and to pass the comprehensive exam, all areas must be passed. The

student may retake a partial examination in any failed areas. If necessary, this partial exam will be

administered in early March (typically during Augusta University’s Spring Pause). If necessary, a final

attempt would be administered in May during final exam week.

Failure to pass the comprehensive exam after three attempts may result in dismissal from the program.

J. Graduation Policy

The department follows the graduation policy published by The Graduate School.

K. Forms Summary

Current forms should be obtained from the department website and/or the Director of Graduate

Studies. The following forms are to be initiated by the student, completed and filed with the

department:

1. Preliminary Plan of Study. No later than the end of the first full-time semester or its equivalent.

2. Proposed Final Plan of Study. Completed after first year review and feedback meeting with the

student’s mentor. This form is to be completed with the Director of Graduate studies.

3. Application for Graduation. No later than the midterm of the semester preceding the semester

in which all course work will be completed. Thus, the application for graduation will normally be

completed by midterm in the fall semester for spring graduation. This form must be filed with the

Registrar.

4. Exit Survey. Submitted online at the end of the final semester and prior to graduation. An exit

interview with the Director of Graduate Studies or Department Chair is required.

IV. Curriculum Summary

A. Course requirements

Required Courses Semester Hours

MATH 6011: Real Analysis I Fall 3

MATH 6580: Computational Linear Algebra Fall 3 MATH 6200: Applied Partial Differential Equations Spring 3

MATH 6350: Numerical Analysis

Fall 3

MATH 6610: Mathematical Models Spring 3 MATH 6120: Statistical Theory I Fall 3

MATH 6960: Graduate Seminar Fall 3 MATH 6630: Topics in Mathematical Biology Spring 3

MATH 6965: Research Seminar or MATH 6990: Graduate Project or An approved interdisciplinary course from the list below:

MPHI 8001: Public Health Informatics QUAN 6610: Operations Research STAT 7010: Biostatistics I STAT 7020: Biostatistics II STAT 7070: Biomedical Statistics STAT 8110: Introduction to Biostatistics STAT 8130: Introduction to Epidemiology

STAT 8650: Introduction to Stochastic Processes

Spring

Spring/Fall

Variable

(Interdisciplinary

elective)

3

Electives: 9 hours selected from the list below.

Fall/Spring 9

MATH 6130: Statistical Theory II (3 hours) MATH 6220: Dynamical Systems (3 hours) MATH 6400: Combinatorial Mathematics (3 hours) MATH 6420 Graph Theory: (3 hours) MATH 6620: Mathematical Optimization (3 hours) MATH 6980: Special Topics (3 hours) MATH 6990: Graduate Project (3 hours)*

*MATH 6990 may be repeated a second time for an additional three hours if there is ongoing work which is likely to yield a peer-reviewed publication.

Total Semester Credit Hours 36

B. Sample program of study

Semester 1 Semester 2

Course Hours Course Hours

MATH 6011 Real Analysis I 3 MATH 6200 Applied Partial Differential Equations 3

MATH 6580 Computational Linear Algebra 3 MATH 6610 Mathematical Models 3

MATH 6350 Numerical Analysis 3 Elective 3

Subtotal 9 Subtotal 9

Semester 3 Semester 4

Course Hours Course Hours

MATH 6120 Statistical Theory I 3 MATH 6630 Topics in Mathematical Biology 3

Elective 3 Elective 3

MATH 6960 Graduate Seminar 3 MATH 6990 Graduate Project or MATH 6965: Research Seminar

3

Comprehensive Master’s Exam** N/A

Subtotal 9 Subtotal 9

Total Hours in Program: 36

VI. Course Descriptions

MATH 6011 – Real Analysis I (3 hours) 3-0-0-3

A study of the real number system and functions. Topics include sequences, limits, continuity,

differentiation and integration. Prerequisite(s): Permission of instructor.

MATH 6120 – Statistical Theory I (3 hours) 3-0-0-3

Fundamentals of random variables and probability theory, discrete, and continuous distributions, exponential families, joint, marginal, and conditional distributions, functions of random variables, transformation and change of variables, order statistics, convergence concepts, central limit theorem, sampling distributions.

MATH 6130 – Statistical Theory II (3 hours) 3-0-0-3

Point and interval estimation, hypothesis testing, maximum likelihood and moment estimators, Bayes

estimators, unbiased estimators, sufficiency and completeness, Fisher information, uniformly most

powerful tests, likelihood ratio tests, asymptotic inference, introduction to Bayesian inference

MATH 6200 - Applied Partial Differential Equations (3 hours) 3-0-0-3 An advanced course in partial differential equations. First order conservation laws and general nonlinear and quasilinear first order partial differential equations are solved. Hyperbolic systems are solved by characteristic variables. Riemann's function, Green's function and similarity variable methods are introduced. MATH 6220 - Dynamical Systems (3 hours) 3-0-0-3 A course in continuous dynamical systems. Includes linear systems and the local, global and bifurcation theory of nonlinear systems. Applications to systems arising in mechanics, biology, ecology, etc. will be discussed. MATH 6400 - Combinatorial Mathematics (3 hours) 3-0-0-3 A course covering both elementary and advanced topics in combinatorial mathematics. Basic concepts such as inclusion-exclusion, recurrence relations and generating functions will be covered and more

advanced topics may include the calculus of finite differences, Mobius and binomial inversion, partially ordered sets, and algebraic combinatorics. MATH 6420 – Graph Theory (3 hours) 3-0-0-3 A study of graphs, subgraphs, paths, arcs, trees, circuits, digraphs, colorability. Additonal topics from topological and algebraic graph theory will also be presented. MATH 6580 - Computational Linear Algebra (3 hours) 3-0-0-3 This course provides an introduction to computational linear algebra. Topics include direct and iterative methods for solving linear systems, error analysis, least squares problems, eigenvalue problems, Newton’s and Quasi-Newton methods for systems of nonlinear equations. MATH 6610 - Mathematical Models (3 hours) 3-0-0-3 Introduction to model development for physical and biological applications including analytical and numerical solution techniques and validation and verification techniques. Includes a study of examples of existing models chosen from physical, biological, social, and management sciences (e.g. conservation laws, heat transfer, fluid flow, population and disease models). Written and oral report is required for at least one of the models studied. Knowledge of a high-level programming language strongly recommended. MATH 6620 - Optimization (3 hours) 3-0-0-3 Newton's method and Quasi-Newton methods for nonlinear equations and optimization problems, globally convergent extensions, applications to differential equations, integral equations and general minimization problems. The course may involve use of a high-level programming language. MATH 6630 - Topics in Mathematical Biology (3 hours) 3-0-0-3 Deterministic and stochastic models in biology and the health-related sciences. MATH 6960 - Graduate Seminar (3 hours) 1-1-1-3 A series of seminars on topics in current mathematical research. MATH 6965 - Research Seminar (3 hours) 0-1-2-3 A course in which students gain familiarity with current mathematical research. This course will feature directed readings of topics selected from recent mathematical literature, culminating with each student giving multiple presentations for the Department’s regularly scheduled Applied Mathematics Seminar; attendance at the seminar talks throughout the semester will be required.

MATH 6980 - Special Topics (3 hours) 3-0-0-3 This course is designed to cover special topics in mathematics that are not covered in regular courses. The topics will depend on the research interests of the instructor and the students. MATH 6990 - Graduate Project (3 hours) 0-0-0-3 This course features directed readings in the current mathematical literature, culminating in a research presentation. These presentations may be expository in nature or they may involve original research in collaboration with a faculty member. The course may be repeated when a project is likely to produce a peer-reviewed publication.

VII. Faculty and research interests

Bruce Landman, Ph. D, Professor and Chair Discrete mathematics, combinatorics, Ramsey theory Guangming Jing, Ph. D, Assistant Professor Combinatorial Matrix Theory, Graph Theory Eric Numfor, Ph. D, Assistant Professor Mathematical biology, optimal control Sam Robinson, Ph. D, Professor Mathematical physics, quantum mechanics

Laurentiu Sega, Ph. D, Associate Professor

Mathematical biology, epidemiology and immunology Sankara Sethuraman Ph. D., Professor Applied statistics, statistical consulting Neal Smith, Ph. D., Associate Professor and Director of Graduate Studies Combinatorics, commutative rings Dharma Thiruvaiyaru, Ph. D., Associate Professor Biostatistics, statistical consulting, generalized linear regression models Anastasia Wilson, Ph. D., Assistant Professor Numerical methods, modeling, optimization He Yang, Ph. D, Assistant Professor Medical imaging, numerical analysis, scientific computing

VIII. Program Learning Objectives

An M.S. in Biological and Computational Mathematics will prepare students to solve problems that arise

in various fields of applied mathematics, and a focus of the program will be the creation of

mathematical models that describe real-world phenomena. Further, any advanced degree in

mathematics with a modeling component requires a strong knowledge of certain fundamental areas,

including differential equations and linear algebra.

Outcome 1: Effectively communicate mathematical concepts, problems and their solutions in verbal or

written form as appropriate.

Outcome 2: Design mathematical models and identify and employ other appropriate methods of applied

mathematics needed to solve real-world problems.

Outcome 3: Be able to apply techniques from fundamental areas of applied mathematics, including, but

not limited to, differential equations and linear algebra, to the solution of problems, particularly

problems arising in the health sciences and the biosciences.