Applications of mathematics to biology will be discussed. Knowledge of a computer programming language. This course introduces biological topics where mathematical and computational methods are applicable, including discrete and continuous models of biological systems, nonlinear differential equations, and stochastic methods.

MAP 5165, or equivalent knowledge of dynamical systems.

Biological models described using partial differential equations. Topics may include chemotaxis, Turing pattern, biofluids, biofilms, cancer, and calcium signaling.

MAP5345 (Elementary PDEs I).

Mathematical methods for studying networks. Topics may include description of real networks, directed and undirected networks, diffusion on a network, network centrality, and random networks.

MAS3105, or equivalent knowledge of linear algebra.

Topics include separation of variables, Fourier series, Sturm-Liouville problems, multidimensional initial boundary value problems, nonhomogeneous problems, Bessel functions, and Legendre polynomials.

Calculus 3 and ordinary differential equations

Topics include the solution of first order quasi-linear partial differential equations, classification and reduction to normal form of linear second order equations, Green's function, infinite domain problems, the wave equation, radiation condition, and spherical harmonics.

MAP 5345 (Elementary PDEs I).

Algebra and geometry of complex numbers; elementary functions and their mappings. Analytic functions; integration in the complex plane; Cauchy's integral theorem and related theorems. Representation theorems including the Taylor and Laurent expansions. Calculus of residues. Entire and meromorphic functions.

MAA 4227 or 5307; alternatively MAA 4226 and 4402.

Continuation of MAA 5406.

MAA 5406 (Complex Analysis I).

Analysis and implementation of numerical algorithms. Conditioning, numerical errors, interpolation, quadrature, approximation theory, numerical methods for ordinary differential equations.

Linear algebra, competence in a programming language suitable for numeric computation.

Direct and iterative solution of linear systems and least squares problems, root finding, systems of nonlinear equations, numerical optimization.

MAD 5403 (Foundations of Computational Mathematics I).

Finite difference methods for parabolic, elliptic, and hyperbolic problems; consistency, convergence, stability.

MAD 5404 (Foundations of Computational Mathematics II); MAP 4342 or 5346 (Elementary PDEs II).

Continuation of MAD 5738.

MAD 5738 (Numerical Solution of Partial Differential Equations I).

Continuous and discrete models from physics, chemistry, biology, and engineering are analyzed using perturbation methods, analytical and geometrical tools and dynamical systems theory.

MAP 2302, MAC 2313, and MAS 3105.

Ordinary differential equations in the complex plane, special functions, asymptotic methods, integral transforms.

MAP 4341 or MAP 5345.

This courses give students an opportunity to apply and supplement knowledge gained from coursework to real problems in biology or medicine. Students will give class presentations and will present a written report at the end of the semester.

This is the projects course for the Master's degree. Students should have three semesters of coursework in biomathematics.

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.

Three semesters of calculus and an undergraduate course in probability (or some exposure to probability plus a sufficiently strong math background).

Methods of estimation, Bayesian models, Fisher information, large sample theory, introduction to hypothesis testing.

STA 5326 (Distribution Theory).

Identification of risk factors for disease, including exposure-disease association, design of cohort, matched and randomized studies, cross-sectional and longitudinal studies, statistical analysis of data arising from such studies, confounding, adjustment and causality, and evaluation of diagnostic and screening tests.

STA 2171

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.

PCB 3063, or the equivalent, or permission of the instructor.

Students are introduced to basic principles of neurophysiology, including intracellular signaling, membrane potentials, synaptic communication, sensory and motor systems and neural development and plasticity.

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.

Principles of cell organization; membrane structure and transport; cyto skeleton; signaling; organelle structure and function; energy metabolism; cellular aspects of cancer and immunity.

A course in Molecular Biology.

This is an interdisciplinary course, focusing on application of statistical and computational methods to biological problems.

Methods covered are Expectation Maximization (EM), Hidden Markov Model (HMM), Bayesian Network (BN), Monte Carlo (MC) methods and Markov Chain Monte Carlo (MCMC), maximum likelihood estimation (MLE), regression, logistic regression, bootstrapping, machine learning methods such as clustering, classification, and variable selection (feature selection).

The biological problems used to illustrate the methods include DNA sequence analysis/alignment, microarray and genomic data analysis, protein sequence alignment, protein structure prediction, and gene regulations.

An undergraduate course in probability.

Sufficiency, point estimation, confidence intervals, hypothesis testing, regression, linear models, Bayesian models.

An undergraduate course in probability.

This course introduces the statistical methods developed for and used in epidemiology. Statistical design issues in epidemiological studies, measures of disease occurrence, measures of association, and adjusting for confounding without and with multivariate models.

This course provides a focused introduction to methods for describing, analyzing, and modeling survival data in medical studies.