106. Introduction to Cellular Modeling. Lecture, four hours; computer laboratory, two hours. Prerequisites: Mathematics 32A, some computer programming, consent of instructor (undergraduates). Designed for upper division science majors and biomedical graduate students. Introduction to modeling cells and cell systems, including intracellular biochemical networks, applications to cancer research. How to develop one's own computer models using IMSL mathematics subroutines.
108. Introduction to Modeling in Neurobiology. Lecture, four hours; computer laboratory, two hours. Prerequisites: Mathematics 32A, some computer programming, consent of instructor (undergraduates). Designed for upper division science majors and biomedical graduate students. Survey of wide variety of topics in neurobiological modeling, current neuronal modeling systems. Development of skills to formulate and program one's own studies using IMSL mathematics subroutines. P/NP or letter grading.
110. Elements of Biomathematics. Lecture, three hours; laboratory, three hours. Prerequisite: calculus. Analysis of deterministic models. Conditions under which deterministic and probabilistic descriptions of biological phenomena are appropriate. Both approaches are applied to selected examples in physiology and biology.
M153A-M153B. Introduction to Computational Statistics. (Same as Biostatistics M153A-M153B and Statistics M153A-M153B.) Lecture, three hours; discussion, one hour. Prerequisites: Mathematics 115A, Statistics 152B. Linear and nonlinear regression analysis using package programs. Emphasis on relation between statistical theory, numerical results, and analysis of data. M153A. BMDP, SAS, and SPSS regression programs; general linear model theory; linear regression analysis; transforming and weighting; regression diagnostics; model building. M153B. Analysis of variance and covariance; nonlinear regression programs, analysis, and applications; maximum likelihood analysis; robust regression.
160. Introductory Biomathematics for Medical and Biological Research. Lecture, four hours; discussion, 90 minutes. Elementary statistics course that focuses on statistical concepts and critiques the literature, with emphasis on clinical research. Output from statistical computer packages discussed in class, but students do not use the computer themselves. Topics include descriptive statistics, t-tests, confidence intervals, linear regression and correlation, analysis of variance, nonparametric statistics, basic experimental design, sample size determination, article interpretation.
170A. Computer-Based Introductory Biomathematics for Medical and Biological Experimenters. Lecture, four hours; discussion, 90 minutes. Intensive elementary statistics course emphasizing design of experiments and analysis of data using statistical packages. Statistical topics similar to course 160 -- descriptive statistics, t-tests, confidence intervals, linear regression and correlation, analysis of variance, nonparametric statistics, basic experimental design, sample size determination -- but students also shown how to use the computer and run statistical software packages. Practical aspects of data collection and cleaning.
170B. Statistical and Mathematical Modeling in Medical and Biological Research. Lecture, four hours; discussion, 90 minutes. Second course in biomathematical methods. Topics include randomization methods, intermediate experimental design, contingency table analysis, analysis of variance, multiple linear regression, nonlinear regression, methods of classification, model checking, basic mathematical models including compartment models, and statistical computer software. Students have opportunity to design their own experiments and analyze them on the computer, and to analyze previously collected data.
172. Clinical Trials. Lecture, three hours; discussion, two hours. Prerequisite: Biostatistics 100C or 100D or Statistics 152B or equivalent. Topics include steps in bringing a possible therapy to clinical use; design of studies in animals to assess antitumor response; randomization, historical controls, p-values, size of study, stratification, and points; ethics of human experimentation; informed consent; three phases of human studies; indications for various types of controls, prognostic factors, survivorship studies, design of prognostic studies; organization of a clinical trial -- administration, comparability, protocols, nursing and clinical standards, data collection and management.
190HA-190HB. Honors Research in Biomathematics. Prerequisites: upper division standing, consent of instructor and department chair. Individual research in some aspect of biomathematics designed to acquaint students in depth with mathematical models and computer applications in biology. Must be taken for at least two terms and for a total of at least eight units. Thesis required.
199. Special Studies in Biomathematics (2 to 8 units). Prerequisites: upper division standing, consent of instructor. Special studies in biomathematics, including either reading assignments or laboratory work or both, designed for proper training of students.
200. Research Frontiers in Biomathematics (2 units). Prerequisite: consent of instructor. Series of presentations by faculty members on research frontiers in biomathematics. S/U grading.
201. Deterministic Models in Biology. Prerequisite: knowledge of linear algebra and differential equations. Examination of conditions under which deterministic approaches can be employed and conditions where they may be expected to fail. Topics include compartmental analysis, enzyme kinetics, physiological control systems, and cellular/animal population models.
202. Fourier Analysis in Biology. Prerequisite: knowledge of calculus, linear algebra, and probability. Introduction to theory of Fourier transforms and Fourier series from point of view of generalized functions. Elementary applications to differential equations, quantum mechanics, image reconstruction, X-ray crystallography, branching processes, and time series. Brief review of computational techniques based on fast Fourier transform.
203. Stochastic Models in Biology. Prerequisite: Mathematics M150A or equivalent experience in probability. Mathematical description of biological relationships, with particular attention to areas where conditions for deterministic models are inadequate. Examples of stochastic models from genetics, physiology, ecology, and a variety of other biological and medical disciplines.
204. Biomedical Data Analysis. Prerequisite: consent of instructor. Quantity and quality of observations have been greatly affected by present-day extensive use of computers. Problem-oriented study of latest methods in statistical data analysis and use of such arising in laboratory and clinical research.
205. Electric Potential Problems in Membranes, Cells, and Tissues. Prerequisite: knowledge of differential equations and electrostatics, or consent of instructor. Review of electrostatics; potential problems in rectangular, spherical, and cylindrical coordinates; modeling subthreshold electrical properties of cells; microelectrode measurements of intracellular potentials; boundary conditions for current flow across membranes; eigenfunction expansions and singular perturbation analysis of intracellular and extracellular potential distribution in spherical and cylindrical cells and syncytia; computation of potential barriers for ions traversing a membrane pore.
206. Introduction to Mathematical Oncology. Lecture, four hours; computer laboratory, two hours. Prerequisites: ordinary, partial differential equations, and one computer programming course or consent of instructor. Deterministic and stochastic modeling of cell metabolism, colony growth, and responses to radio-, chemo-, and immuno-therapeutic agents applied to carcinogenesis, therapy, emergence of resistance to therapy. Simulation, optimization methods introduced. Current literature review. S/U or letter grading.
207. Models in Genetics. Lecture, three hours; discussion, one hour. Prerequisite: upper division probability and statistics; knowledge of basic genetics principles helpful. Topics include population genetics, genetic epidemiology, gene mapping, design of genetics experiments, DNA sequence analysis, and molecular phylogeny. Content varies from year to year.
208A. Modeling in Neurobiology for Mathematicians. Lecture, four hours; laboratory, two hours. Prerequisites: introductory ordinary, partial differential equations, programming experience. Introduction to electrochemical bases for nerve function and mathematical and computational methods for studying this, appropriate for physicists, engineers, and mathematicians. Survey of current leading research areas and software systems. S/U or letter grading.
208B. Modeling in Neurobiology for Biologists. Lecture, four hours; laboratory, two hours. Prerequisites: lower division calculus, some elementary programming experience. Introduction to neuronal modeling, including how to formulate models and study them with existing computer software (e.g., NODUS) or one's own simple programs that use IMSL subroutines. Survey of current leading research areas. S/U or letter grading.
211. Tissue and Cell Dynamics. Lecture, three hours; discussion, one hour. Preparation: knowledge of differential equations to level of course 201, some mathematical modeling, computer programming. In-depth mathematical modeling of problems in tissue and cell dynamics to level of research literature. Analytical and numerical techniques for solving partial differential equations. S/U or letter grading.
220. Kinetic and Steady State Models in Pharmacology and Physiology. Recommended: knowledge of linear algebra, differential equations, and statistics. Designed for biologists and theoreticians. Modeling and data analysis in pharmacokinetics, enzyme kinetics, and endocrinology. Topics include compartmental and noncompartmental approaches, steady state analysis of transport and binding processes, and optimal experiment design.
M230. Computed Tomography: Theory and Applications. (Same as Biomedical Physics M230.) Computed tomography is a three-dimensional imaging technique being widely used in radiology and is becoming an active research area in biomedicine. Basic principles of computed tomography (CT), various reconstruction algorithms, special characteristics of CT, physics in CT, and various biomedical applications.
M231. Statistical Methods for Categorical Data. (Same as Biostatistics M210.) Lecture, three hours; discussion, one hour. Requisites: Biostatistics 100B or 110B, Statistics 152B. Statistical techniques for analysis of categorical data; discussion and illustration of their applications and limitations.
M232. Statistical Analysis of Incomplete Data. (Same as Biostatistics M232.) Lecture, three hours; discussion, one hour. Requisite: Statistics 152B. Discussion of statistical analysis of incomplete data sets, with material from sample survey, econometric, biometric, psychometric, and general statistical literature. Topics include treatment of missing data in statistical packages, missing data in ANOVA and regression imputation, weighting, likelihood-based methods, and nonrandom nonresponse models. Emphasis on application of methods to applied problems, as well as on underlying theory. S/U or letter grading.
M234. Applied Bayesian Inference. (Same as Biostatistics M234.) Lecture, three hours; discussion, one hour. Requisites: Biostatistics 200B, Statistics 152B. Bayesian approach to statistical inference, with emphasis on biomedical applications and concepts rather than mathematical theory. Topics include large sample Bayes inference from likelihoods, noninformative and conjugate priors, empirical Bayes, Bayesian approaches to linear and nonlinear regression, model selection, Bayesian hypothesis testing, and numerical methods. S/U or letter grading.
M270. Optimal Parameter Estimation and Experiment Design for Biomedical Systems. (Same as Computer Science M296B and Medicine M270D.) Lecture, four hours; outside study, eight hours. Prerequisite: Computer Science M296A or consent of instructor. Estimation methodology and model parameter estimation algorithms for quantifying (fitting) dynamic system models to real-world data. Theory and algorithms for designing optimal experiments for developing and quantifying models, with special focus on data sampling schedule design. Exploration in PC laboratory of applications software for model building and optimal experiment design.
273. Stochastic Modeling in Molecular Cellular Biophysics. Lecture, three hours; discussion, one hour. Prerequisite: Mathematics M150A or equivalent experience in probability, lower division physics, or physical chemistry. Most molecular systems are large collections of molecules; behavior of such a system is stochastic. Mathematical descriptions of biochemical reactions with and without energy dissipation, molecular structures, and biophysical techniques which measure various biological processes.
M280. Statistical Computing. (Same as Biostatistics M280 and Mathematics M280.) Lecture, three hours. Prerequisites: Mathematics 115A, Statistics 152C, or equivalent. Introduction to theory and design of statistical programs: computing methods for linear and nonlinear regression, dealing with constraints, robust estimation, and general maximum likelihood methods.
M281. Survival Analysis. (Same as Biostatistics M215). Lecture, three hours; discussion, one hour. Requisites: Biostatistics 110B, Statistics 152B. Statistical methods for analysis of survival data. S/U or letter grading.
M282. Analysis of Repeated Measures Designs. (Same as Biostatistics M236.) Lecture, three hours; discussion, one hour. Requisites: Biostatistics 200A, 200B. Presentation of classical and modern theories for analysis of repeated measures designs, with focus on computation and robustness. S/U or letter grading.
596. Directed Individual Study or Research in Biomathematics (2 to 12 units). Individual study on topics not yet covered by offerings of department. May be repeated for credit with topic change.
597. Preparation for M.S. or Ph.D. Comprehensive Examination or Ph.D. Qualifying Examinations (2 to 8 units). Prerequisite: consent of graduate adviser. Individual study. S/U grading.
599. Research for and Preparation of Ph.D. Dissertation (2 to 12 units). Prerequisite: consent of instructor. S/U grading.