(Biomedical Mathematics, Mathematical Biology)
Department of Mathematics
Florida State University
The Mathematics Department offers Doctoral (PhD) and Master of Science (MS) degrees in Biomathematics as one of its four program areas. This is an interdisciplinary program including topics from mathematical and computational biology, biomathematics, bioinformatics, and statistics, Students 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 in Biomathematics (code 116814)
Master of Science. This is a two-year program with 36 semester hours of courses and seminars. Students develop skills in a number of areas for working on applications of mathematics to basic research in biology and medicine and biotechnology.
Ph.D. Students do research work in a variety of fields represented by the biomathematics faculty. Students participate in programs of the Institute of Molecular Biophysics, work on research at the National High Magnetic Field Laboratory, or collaborate with medical researchers at other universities. Ph. D. students should complete all requirements for a Master's degree then pass the preliminary examinations. The preliminary examination for Biomathematics consists of written examinations on fours semesters of coursework, and a candidacy examination. Exemptions from the written examinations can be made on the basis of grades. See Guidelines for Admission to PhD Candidacy.
Our students have been very successful in finding faculty positions and post-docs. Some of our former students
Occasionaly students receive recognition for their work as graduate students. Recognized research of our current student Juan Gutierrez
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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.
Program director: Jack Quine
Mathematics faculty:
Richard Bertram (mathematical physiology, protein structure determination)
Nick Cogan (Fluid dynamics, biofilms)
Monica Hurdal (human brain mapping)
Mike Mesterton-Gibbons (Models of animal behavior and social structure)
Washington Mio (pattern analysis, computer vision, biomedical applications)
Jack Quine (protein structure from solid-state NMR data)
De Witt Sumners (Professor Emeritus) (DNA topology, human brain mapping)
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Admission.
The Department of Mathematics requirements for exam scores, recommendations and statements are necessary for admission. 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.
Students intending to get the PhD degree should have taken more advanced courses in mathematics, such as advanced calculus (or real analysis), complex variables, abstract algebra, or topology.
Biology and programming prerequisites for the program.
It is helpful, but not necessary, to have some background and coursework in Biology. Also some programming experience is desirable. Undergraduate courses can be taken to refresh skills in these subjects, as described below.
During their course of study, students may take for S/U credit an undergraduate genetics course, PCB 3063, and read up on basic concepts in genetics and molecular biology. The genetics course is given in the summer B term (first half of the summer) and in the Fall semester.
Also students may take for S/U credit an undergraduate course in C++ programming. These courses are available in the Summer and Fall.
Do not register for undergraduate courses directly, but see the Academic Support Coordinator, currently Esther Diaguila. The registration for C++ is for one hour credit. These refresher courses do not count for the requirements of the degree.
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Financial aid. Most graduate students in mathematics have support from teaching assistantships. An early application is critical for the best chance of financial aid. Also, the orientation program for new TAs is offered in Summer C-term, and those awarded teaching assistantships may be paid a small stipend beginning at that time.
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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 3 courses to be satisfied by all students, and a weekly seminar. Remaining courses are chosen from a list of options, depending on the student's interest and faculty advice. PhD and Master's students in Biomathematics 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.
Students are expected to have the mathematics prerequisites for all mathematics courses. For Introduction to Mathematical Biophysics and for Computational Biology student should know basic calculus through differential equations, linear algebra, and some computer programming language. More advanced undergraduate courses are prerequisite for advanced mathematics course sequences such as Complex Variables, Topology, Real Analysis and Groups Rings and Vector Spaces.
Required courses: (For course descriptions not found below, see the Graduate Bulletin, Mathematics, Graduate Bulletin Chemistry and Biochemistry, Graduate Bulletin Biological Sciences, or Graduate Bulletin Statistics. For the course schedules in upcoming semesters, see the FSU Course lookup.)
Core courses taken by all students:
MAP 5485 Introduction to Mathematical Biophysics (Biomathematics I) (Fall)
MAP 5486 Computational Biology (Biomathematics II) (Spring)
MAP 6437 Biomedical Mathematics Projects Course (Spring) (student projects)
MAT 6939 Advanced Seminar in Biomathematics (1 hour credit each semester)
Interdisciplinary component: Three courses from Biology, Chemistry, Statistics, Computer Science, or Scientific Computing.
Typical choices are listed below. Other choices can be approved by the director of the program.
BCH 5205 Structure and Function of Enzymes (Fall)
PCB 5525 Molecular Biology (Fall)
BSC 5936 Membrane Biophysics (Spring)
BCH 5887 Macromolecular X-ray Crystallography
BCH 5887 Biomolecular NMR Spectroscopy
MAD 5932 Methods in Interdisciplinary Applications (Spring)
STA 5236 Distribution Theory (Fall)
STA 5327 Statistical Inference (Spring)
STA 5807 Topics in Stochastic Processes (Summer)
Mathematics courses, additional courses from the following, all together to total 36 hours of listed courses (not including seminar) of which at least 5 courses are in the Department of Mathematics. (Students for the PhD degree should begin taking one of the two semester sequences indicated below. These are the basis for written preliminary examinations, of which the student will take two.)
MTG 5326, 5327 Topology I, II (Fall, Spring)
MAS 5307, 5308 Groups Rings Vector Spaces I, II (Fall, Spring)
MAA 5406, 5407 Complex Variables I, II (Fall, Spring)
MAA 5616, 5617 Measure and Integration I, II (Fall, Spring)
MAD 5403, 5404 Foundations of Computational Mathematics I, II (Fall, Spring)
MAP 5345, 5346 Elementary Partial Differential Equations I, II (Fall, Spring)
MAD 5738, 5739 Numerical Solution of Partial Differential Equations I, II (Fall, Spring)
MAP 5165 Methods in Applied Mathematics I (Fall)
MAD 5305 Graph Theory
MAA 6416 Topics in Stochastic Calculus (odd-year Springs)
other approved graduate mathematics course
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Course descriptions and prerequisites
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Introduction to Mathematical Biophysics (Biomathematics I), MAP 5485 (Fall, see Fall 2005 course online)
Most students will take this course in their first semester.
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. 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, HP model of protein folding.
Prerequisites: Calculus, linear algebra.
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Computational Biology (Biomathematics II) MAP 5486 (Spring)
Several applications of mathematics to biology will be discussed. Computational methods will be used, in conjunction with qualitative tools from dynamical systems theory to analyze the models. Topics include the construction and analysis of neuron models, intracellular calcium dynamics, minimal models of excitable systems, fast and slow time scales, models of circadian gene dynamics, stability properties of delay differential equations, models of the cell cycle, stochastic models of ion channel activity, and stochastic resonance.
Prerequisites: MAP 5485 Introduction to Mathematical Biophysics, MAT 5932, Methods of Applied Math I, or equivalent knowledge of ODEs and dynamical systems. Knowledge of a computer programming language is expected.
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Elementary Partial Differential Equations I, II MAP 5345, 5346 (Fall, Spring)
MAP 5345. Elementary Partial Differential Equations I (3). Prerequisites: MAC 2313; MAP 2302 or 3305. Separation of variables; Fourier series; Sturm-Liouville problems; multidimensional initial boundary value problems; nonhomogeneous problems; Bessel functions and Legendre polynomials.
MAP 5346. Elementary Partial Differential Equations II (3). Prerequisite: MAP 4341 or 5345. Solution of first order quasi-linear partial differential equations; classification and reduction to normal form of linear second order equations; Greens function; infinite domain problems; the wave equation; radiation condition; spherical harmonics.
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Foundations of Computational Mathematics I, II MAD 5304, 5304 (Fall, Spring)
MAD 5403. Foundations of Computational Mathematics I. Analysis and implementation of numerical algorithms. Matrix analysis, conditioning, errors, direct and iterative solution of linear systems, rootfinding, systems of nonlinear equations, numerical optimization.
Prerequisites: Linear algebra, competence in a programming language suitable for numeric computation.
MAD 5404 Foundations of Computational Mathematics. Interpolation, quadrature, approximation theory, numerical methods for ordinary differential equations and partial differential equations.
Prerequisite: MAD 5403.
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Numerical Solution of Partial Differential Equations I, II. MAD 5738, 5739 (Fall, Spring)
Prerequisites: MAD 5708; MAP 4342 or 5346. Finite difference methods for parabolic, elliptic, and hyperbolic problems; consistency, convergence, stability.
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Methods of Applied Mathematics I MAT 5932 (Fall)
Linear systems of ODE, phase plane, limit cycles, bifurcations.
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Biomedical Mathematics Projects Course MAP 6437 (Spring)
The goal of the course give students an opportunity to apply and supplement knowledge gained from coursework to real problems in biology or medicine. Students will give two class presentations concerning their research and will present a written report at the end of the semester.
Prerequisites: This is the projects course for the Master's degree. Students should have three semesters of coursework in Biomathematics.
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Distribution Theory STA 5326 (Fall)
Axioms and basic properties of probability, Combinatorial probability, Conditional probability and independence, Applications of the Law of Total Probability and Bayes Theorem, Random variables, Cumulative distribution, density, and mass functions, Distributions of functions of a random variable, Expected values, Computations using indicator random variables, Moments and moment generating functions, Common families of distributions, Location and scale families. Exponential families, Joint and conditional distributions, Bivariate transformations, Covariance and correlation, Hierarchical Models, Variance and Conditional variance. Introduction to Brownian Motion
Prerequisites. Three semesters of calculus and an undergraduate course in probability (or some exposure to probability plus a sufficiently strong math background).
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Statistical Inference STA 5327 (Spring)
Statistical inference viewed at a measure-theoretic level.
Prerequisites. STA 5326, Distribution Theory
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Molecular Biology, BCH 5425 (Spring)
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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Structure and Function of Enzymes, BCH 5505 (Fall)
Course addresses elements of protein structure and structural motifs, structure determination methods; protein folding and stability; enzyme kinetics and mechanisms; structure-function relationships.
Prerequisites: Pre- or co-requisite: BCH 4053 General Biochemistry I or equivalent.
recent course webpage
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Bioinformatics, BSC 5936 (Spring)
Sequences alignment and analysis, phylogenetics, evolutionary trees.
Prerequisite: A course in genetics
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Molecular Biology, PCB 5525 (Fall)
Introduction to molecular biology and molecular genetics. The emphasis will be on the activities of DNA, RNA, regulation of gene expression, gene cloning, bioinformatics, and biotechnology.
Prerequisites: PCB 3063, or the equivalent, or permission of the instructor.
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Membrane Biophysics, BSC 5936 (Spring)
The primary objective of this course is to train the graduate student with the necessary mathematical, physiological, and molecular background that he or she will need to be able to design competitive research in the field of membrane biophysics. This course is an integrated approach to modern biophysics with an emphasis on neural applications. Modern biophysics requires a strong working knowledge of physical laws, molecular approaches, physiological responses, structural proteins, and the mechanics of the equipment used to measure the physical properties of biological membranes. It is a tandem objective of this course that the student will be able to apply this working knowledge to a deep comprehension of the primary literature. Towards this end, the class will collectively build a literature resource that can be drawn upon for a firm foundation for comprehensive research directives in two fields 1) Ion Channels, and 2) Biophysical Methods.
Methods in Interdisciplinary Applications (new Spring 2005), MAP 5932 (Spring)
Regression, time series. Software: R (free software)
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