Biomedical Mathematics Program

(Program in Mathematical and Computational Biology)

Department of Mathematics

Florida State University

The Mathematics Department offers a PhD and Master of Science degrees in Biomedical Mathematics. This is an interdisciplinary program including topics from computational biology, computational structural biology, bioinformatics, evolutionary game theory, and mathematical physiology. Students in Biomedical Mathematics develop a mix of biological, mathematical, statistical, and computational skills. Coursework is flexible and tailored toward the needs and goals of individual students.

Contents

Degree options

Faculty

Admission

Advisement and Supervisory Committees

Curriculum and Requirements

Degree Options

Ph.D., Mathematics. An interdisciplinary research area is available in biomedical mathematics. Students can work in a variety of fields represented by the biomedical mathematics faculty. Recent Ph.D graduates in this area have worked with Professors Jack Quine and De Witt Sumners, some with funding through Research Training Grants or the Program in Mathematics and Molecular Biology. Students participate in programs of the Institute for Molecular Biophysics, work on research at the National High Magnetic Field Laboratory, or collaborate with medical researchers at other universities. Guidelines for Admission to PhD Candidacy

Master of Science, Biomedical Mathematics. This is a two-year program with 36 hours of course work and seminars. Students develop necessary skills in a number of areas necessary to obtain employment in government and industry, and to work on applications of mathematics to medicine, drug development and biotechnology.

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Faculty.

FSU faculty members from five departments are involved in this effort. PhD's are directed by one or more of the Mathematics faculty, often in conjunction with faculty from the other departments.

Mathematics faculty:

Richard Bertram (mathematical physiology, protein structure determination)

Monica Hurdal (human brain mapping)

Michael Mesterton-Gibbons (game theoretic modelling)

Jack Quine (protein structure from solid-state NMR)

De Witt Sumners (DNA topology, human brain mapping)

 

Affiliated faculty from other departments:

Biological Science: Lloyd Epstein, George Bates, Tom Keller, Timothy Moerland

Chemistry: Michael Chapman, Tim Cross

Computer Science: Ted Baker, David Gaitros, Michael Mascagni

Statistics: Myles Hollander, Lei Li

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Admission.

The Department of Mathematics requirements for exam scores, recommendations and statements are necessary. The typical first semester courses in the program require knowledge of undergraduate mathematics including at least multivariate calculus, ordinary differential equations and linear algebra. A basic knowledge of statistics, computer programming, genetics is helpful.

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Advisement and Supervisory Committees.

Students have a faculty advisor to recommend and approve coursework. For PhD students, a Supervisory Committee, which determines the program, is appointed consisting of at least three faculty members, with at least one from the Department of Mathematics and at least one from another participating department. Substitutions for courses for which the student has prior credit must be approved by the advisor.

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Curriculum.

The core curriculum includes 5 courses to be satisfied by all students. Remaining courses are chosen from a list of options, depending on the student's interest and faculty advice. Students also participate in seminars and workshops.

The 36 semester hours of required courses leave some time within two years for the student to take undergraduate courses in areas where the student needs extra preparation. The student coming to the program from Mathematics, Computer Science or Statistics undergraduate majors, for example, may need to take the undergraduate genetics course in their first term. Such students are strongly encouraged to begin study in summer "C" term ( about June 25 ).

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Requirements. PhD and Master's students in Biomedical Mathematics complete 36 hours of approved coursework, of which at least five 3-hour courses must be in the Department of Mathematics. Students completing this coursework are awarded a Master's degree. The program is typically structured as follows; all courses must be approved by the advisor.

Required courses:

MAP 5485 Introduction to Mathematical Biophysics

MAD 5xxx Computational Methods in Biology (new Spring 2002)

BCH 5425 Molecular Biology (Spring) or PCB 5525 Molecular Biology (Fall)

STA 5176 Statistical Modeling with applications to biology (New Fall 2001)

MAP 6437 Topics in Biomedical Mathematics (New Spring 2002) student resources and projects course

MAT 6939 Advanced Seminar in Biomedical Mathematics (1 hour credit each semester)

1. Normally the student will be registered in each semester of residence.
2. As part of the seminar program, announcements will be made of available computer and biology laboratory workshops. Participation is required to earn an “S” in Seminar unless scheduling exigencies prohibit.

And one or more of:

BCH 5205 Structure and Function of Proteins

BCH 5887 Macromolecular X-ray Crystallography

BCH 5887 Biomolecular NMR Spectroscopy

PCB 5595 Gene Expression and Development

PCB 5137 Advanced Cell Biology

Other courses must be approved by advisor for program.

And two or more of:

CGS 5428 Relational Database Theory

COP 5710 Database Systems

CAP 5600 Artificial Intelligence

CAP 5615 Artificial Neural Networks

Cxx xxxx Other graduate Computer Science Science (must be approved by advisor for program)

STA 5326 Distribution Theory and Inference

STA 5xxx Other non-dual-numbered statistics as approved by advisor for program

Additional courses from the following, all together to total 36 hours of listed courses of which at least 15 hours is in the Department of Mathematics:

MAD 5708 Numerical Analysis II

MTG 5326 & 5327 Topology I & II

MAS 5307 & 5308 Groups Rings Vector Spaces I & II

MAD 5305 Graph Theory

MAS 5731 Computer Algebra

MAD 5420 Numerical Optimization

MAA 5406 & 5407 Complex Variables I & II

MAA 5616 & 5617 Measure and Integration I & II

MAD 5xxx Scientific Visualization

MAP 5345 & 5346 Elementary Partial Differential Equations I & II

MAT 5945 Internship in Biomedical Mathematics (The student must petition and present appropriate evidence of performance to count hour(s) toward degree credit.)

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Course Descriptions

Introduction to Mathematical Biophysics, MAP 5485 (see Fall 2000 course online)

Most students will take this course in their first semester.

Course Objective: The use of mathematics and computation is becoming increasingly important in biology and medicine as scientists search for better ways to process all the information now available about the molecular structure of living organisms. The goal of the course is to introduce students from a variety of disciplines to some of the many uses of mathematics in modern molecular biology and to the use of symbolic and numerical packages for doing the computations.

Graduate Bulletin Description: Mathematical tools in Biophysics: symbolic and numerical packages for matrix computations, rotation matrices, Euclidean motions, lattices, continuous and discrete curves in space, torsion angles, gram and distance matrices, graphs, trees and strings. Applications such as: protein secondary structure, structure determination by crystallography and NMR, writhing twisting and knotting of DNA, sequence alignment, wavelets.

Prerequisites: Calculus, linear algebra.

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Molecular Biology, BCH 5425

Course Description: Course discusses gene organization and replication; control of gene expression in transcription and translation; application of recombinant DNA techniques.

Prerequisites: Introductory biochemistry or consent of instructor.

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Molecular Biology, PCB 5525

Course Description: This course provides an introduction to modern molecular biology and biotechnology. The central question that we will explore is: how is genetic information encoded in DNA and how do cells control the expression of their genes? Topics covered include the structure and properties of DNA and RNA, DNA replication and repair, recombinant DNA technology, the genetic code and translation, control of transcription and translation, molecular biology of cancer, bioinformatics, human gene therapy, and applications of genetic engineering to agriculture and industry.

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Gene Expression and Development, PCB 5595

Course Description: This course will provide graduate students an in depth study of the molecular mechanisms of gene expression and DNA replication in the contexts of the control of cell development and cell differentiation. In addition to textbook readings the students will read and discuss primary literature sources to identify current issues and problems in the field of molecular biology. Topics covered include chromatin structure and gene activation, DNA replication, DNA maintenance, damage, and repair; RNA synthesis and the transcriptional unit; transcription initiation; transcription regulation in prokaryotes and eukaryotes; translation and posttranslational mechanisms; biotechnology and bioinformatics.

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Data Structures, Algorithms, and Generic Programming, COP 4530.

Course Description: Definition, use, and implementation of generic data types and algorithms using a modern programming language; reusable program components.

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Database Systems, COP 5710

Course Description: Prerequisites: COP 4020, 4530, 4610. Use of a generalized database management system; characteristics of database systems; hierarchical, network, and relational models; file organizations.

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Relational Database Theory, CGS 5428

Course Description: Prerequisites: COP 4531. For graduate non-majors and graduate majors needing foundational work in computer science; credit may not be applied towards a graduate degree in computer science. Basic file organization methods, indexed files, multi-key processing; architecture of database management systems; relational, hierarchical network, and semantic database models; normalization; distributed databases and file systems; practical use of a DBMS and the building of a database application.

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This document is maintained by Melissa Elaine Smith / smith@math.fsu.edu
Last modified: 8 August 2001