UCLA’s Bioinformatics Core Curriculum has been offered continuously since 1999. It functions not as a monolithic, comprehensive bioinformatics curriculum, but instead defines the hard core of what you must know to invent new kinds of bioinformatics. It teaches the shared concepts, language and skills which bioinformaticists must have to operate in a collaborative, inter-disciplinary mode. Our goal is to train students who can speak the language of statistical inference, computational complexity, network analysis and data mining. The core curriculum teaches a common vocabulary and set of concepts so people can communicate and collaborate. Beyond this, our main goal is to leave flexibility for students to create a bioinformatics training tailored to their individual interests and background.

Course Choices: Intro course vs. Bioinformatics core sequence

For biology students interested in an introduction to genomics and bioinformatics tools, there is a course offered by Prof. Matteo Pellegrini that does not require programming or statistics prerequisites: MCDB 172 “Genomics and Systems Biology”.

Students who want an in-depth introduction to bioinformatics theory and methods should take the bioinformatics core course sequence. Chem 160A/260A “Introduction to Bioinformatics,” Statistics 254 “Statistical Methods in Computational Biology”, and Chem 160B/260B “Advanced Algorithms in Bioinformatics”. They require statistics and programming prerequisites:

- Statistics 100A or Math 170A or Biostatistics 100A or 110A
- AND one of PIC 10C or Computer Science 32. Beginning 2007-8, the bioinformatics core courses require understanding algorithms and data structures, and involve programming projects.

Note: these prerequisites are required. Stats 100A is offered during Summer session and both Fall and Spring quarters.

Two other newer courses include Computer Science 124/224 “Computational Genetics” (offered by E. Eskin) and Computer Science 229 “Current Topics in Bioinformatics” (offered by E. Eskin). These courses have the same prerequisites as the core bioinformatics courses.

**Core Course Descriptions:**

**Chemistry CM260A. Introduction to Bioinformatics and Genomics. (4)**

(Formerly numbered CM260.) (Same as Human Genetics M260A and Computer Science CM221.) Lecture, four hours; discussion, two hours. Recommended requisites: CS32 or Program in Computing 10C, and Biostatistics 100Aor 110A or Mathematics 170A or Statistics 100A. Introductionto bioinformatics and methodologies, with emphasis on concepts andinventing new computational and statistical techniques to analyzebiological data. Focus on sequence analysis and alignment algorithms.The course is intended for both students in engineering as well asstudents from the biological sciences and medical school. No priorknowledge of biology is required. Concurrently scheduled with course Computer Science CM121. P/NP or letter grading.

**Chemistry C260B. Algorithms in Bioinformatics and Systems. (4)**

(Same as Bioinformatics M260B and Computer Science CM222) . Lecture, four hours; discussion, two hours. Recommended requisite: Computer Science 32 or Program in Computing 10C, and and Biostatistics 100A or 110A or Mathematics 170A or Statistics 100A. Development andapplication of computational approaches to biological questions. Focuson formulating interdisciplinary problems as computational problemsand then solving these problems using algorithmic techniques. Thecomputational techniques discussed include techniques from statisticsand computer science. The course is intended for both students inengineering as well as students from the biological sciences andmedical school. Concurrently scheduled with course Computer Science CM122. Letter grading.

**Statistics M254. Statistical Methods in Computational Biology. (4)**

(Same as Biomathematics M271.) Lecture, three hours; discussion, one hour. Preparation: elementary probability concepts. Requisite: course 100A. Training in probability and statistics for students interested in pursuing research in computational biology, genomics, and bioinformatics. Letter grading.

**Computer Science 224. Computational Genetics (4)**

(Same as Human Genetics CM224.) Lecture, four hours; discussion, two hours. Recommended requisite: Computer Science 32 or Program in Computing 10C, and and Biostatistics 100A or 110A or Mathematics 170A or Statistics 100A. Introduction to computational analysis of genetic variation and computational interdisciplinary research in genetics. Topics include introduction to genetics, identification of genes involved in disease, inferring human population history, technologies for obtaining genetic information and geneticsequencing. Focus on formulating interdisciplinary problems as computational problems and then solving these problems using computational techniques. The computationaltechniques discussed include techniques from statistics and computer science. The course is intended for both students in engineering as well as students from the biological sciences and medical school. Concurrently scheduled with course Computer Science CM124. Letter grading.

**Computer Science 229. Current Topics In Bioinformatics. (4)**

(Same as Human Genetics M229S.) Seminar, four hours; outside study, eight hours. Designed for graduate engineering students, as well as students from biological sciences and medical school. Introduction to current topics in bioinformatics, genomics, and computational genetics and preparation for computational interdisciplinary research in genetics and genomics. Topics include genome analysis, regulatory genomics, association analysis, association study design, isolated and admixed populations, population substructure, human structural variation, model organisms, and genomic technologies. Computational techniques include those from statistics and computer science. May be repeated for credit with topic change. Letter grading.

**Other Required Courses:
**

**Chemistry 202. Bioinformatics Interdisciplinary Research Seminar. (2)**

Seminar, two hours; discussion, two hours. Concrete examples of how biological questions about genomics data map to and are solved by methodologies from other disciplines, including statistics, computer science, and mathematics. May be repeated for credit. S/U or letter grading.

**Chemistry M252. Seminar: Advanced Methods in Computational Biology. (2)**

(Same as Human Genetics M252.) Seminar, one hour; discussion, one hour. Designed for advanced graduate students. Examination of computational methodology in bioinformatics and computational biology through presentation of current research literature. How to select and apply methods from computational and mathematical disciplines to problems in bioinformatics and computational biology; development of novel methodologies. S/U or letter grading.

**Chemistry 260BL. Advanced Bioinformatics Computational Laboratory. (2)**

Laboratory, 4 hours. Enforced requisite: CM260A. Co-requisite: C260B. This course will focus on the development and application of computational approaches to ask and answer biological questions. Students completing the course should be able to implement a variety of bioinformatics and systems biology algorithms. Correspondingly, they should have an appreciation for the advantages and disadvantages of different algorithmic methods for studying biological questions. Furthermore, students should gain a preliminary understanding of how to compute the statistical significance of their results, a process which may involve writing an estimation or sampling program. The course will focus on development of a conceptual understanding of implementation of bioinformatics algorithms and give students a foundation for how to do innovative work in these fields. Material will be drawn from specific, relevant biological problems and will closely parallel 260B. As a complement to 260, students will gain experience in observing the impact of computational complexity of an algorithm in computing a solution. S/U or letter grading. Bioinformatics Interdepartmental Graduat e Program Proposal Ð page 50

**Elective Course Descritions:**

**Genomics Concentration Area:**

**Biostatistics M272. Theoretical Genetic Modeling . (4)**

(Formerly numbered M237A.) (Same as Biomathematics M207A and Human Genetics M207A.) Lecture, three hours; discussion, one hour. Requisites: Mathematics 115A, 131A, Statistics 100B. Mathematical models in statistical genetics. Topics include population genetics, genetic epidemiology, gene mapping, design of genetics experiments, DNA sequence analysis, and molecular phylogeny. S/U or letter grading.

**Biostatistics M278. M278. Statistical Analysis of DNA Microarray Data. (4)**

(Formerly numbered 278.) (Same as Human Genetics M278.) Lecture, three hours. Requisite: course 200C. Instruction in use of statistical tools used to analyze microarray data. Structure corresponds to analytical protocol an investigator might follow when working with microarray data. S/U or letter grading.

**Chemical Engineering 246. Systems Biology: Intracellular Network Identification and Analysis. (4)**

Lecture, four hours; outside study, eight hours. Requisites: course CM245, Life Sciences 1, 2, 3, 4, Mathematics 31A, 31B, 32A, 33B. Systems approach to intracellular network identification and analysis. Transcriptional regulatory networks, protein networks, and metabolic networks. Data from genome sequencing, large-scale expression analysis, and other high-throughput techniques provide bases for systems identification and analysis. Discussion of gene-metabolic network synthesis. Letter grading.

**Chemistry 269C. Nucleic Acid Structure and Catalysis. (2)**

Lecture, five hours; discussion, two hours. Requisites: courses 153A, 153B, 153C, 156. Threedimensional structure of DNA and RNA. Sequence-specific recognition of DNA and RNA. RNAcatalyzed processes, including self-splicing and peptide bond formation. Letter grading.

**Ecology and Evolutionary Biology C275. Computational Biology. (4)**

Lecture, three hours; laboratory, one hour. Requisites: Life Sciences 1, 4. Introduction to computational biology. Topics include statistical and mathematical analysis, computer simulation, use of Internet for remote databases, and connection to supercomputers, with emphasis on biological applications and individual or group projects. Concurrently scheduled with course C159.

**Human Genetics 236A. Advanced Human Genetics. (4)**

(Formerly numbered 236.) Lecture, three hours. Requisites: courses CM248, CM253. Advanced topics in human genetics related to Mendelian disease, molecular genetics, and relevant technologies. Topics include cytogenetics, genomics, proteomics, positional cloning, bioinformatics, gene therapy, and developmental genetics. Reading materials include original research papers and reviews. Letter grading.

**Human Genetics 236B. Advanced Human Genetics. (4)**

Lecture, three hours. Requisites: courses 236A, CM248, CM253. Advanced topics in human genetics related to complex genetic traits and common diseases, with emphasis on biostatistics and mathematical modeling. Reading materials include original research papers and reviews. Letter grading.

**Human Genetics C244. Genomic Technology. (4)**

Lecture, three hours; discussion, one hour. Requisite: Life Sciences 4. Survey of key technologies that have led to successful application of genomics to biology, with focus on theory behind specific genome-wide technologies and their current applications. Concurrently scheduled with course C144. S/U or letter grading.

**Pathology 255. Mapping and Mining Human Genomes. (3)**

Lecture, three hours. Basic molecular genetic and cytogenetic techniques of gene mapping. Selected regions of human genomic map scrutinized in detail, particularly gene families and clusters of genes that have remained linked from mouse to human. Discussion of localizations of disease genes. S/U or letter grading.

**Statistics 165. Statistical Methods and Data Mining. (4)**

Lecture, three hours. Requisite: course 100A. Introduction and overview of up-to-date statistical methods in microarray analysis designed for students in biostatistics, statistics, and human genetics who are interested in technology and statistical analysis of microarray experiments. Useful for biology students with basic statistical training who are interested in understanding logic underlying many statistical methods. P/NP or letter grading.

**Proteomics Concentration Area:**

**Chemical Engineering 246. Systems Biology: Intracellular Network Identification and Analysis. (4)**

Lecture, four hours; outside study, eight hours. Requisites: course CM245, Life Sciences 1, 2, 3, 4, Mathematics 31A, 31B, 32A, 33B. Systems approach to intracellular network identification and analysis. Transcriptional regulatory networks, protein networks, and metabolic networks. Data from genome sequencing, large-scale expression analysis, and other high-throughput techniques provide bases for systems identification and analysis. Discussion of gene-metabolic network synthesis. Letter grading.

**Chemistry M230B. Structural Molecular Biology. (4)**

Bioinformatics Interdepartmental Graduat e Program Proposal Ð page 52 (Same as Molecular, Cell, and Developmental Biology M230B.) Lecture, three hours; discussion, one hour. Requisites: Mathematics 3C, Physics 6C. Selected topics from principles of biological structure; structures of globular proteins and RNAs; structures of fibrous proteins, nucleic acids, and polysaccharides; harmonic analysis and Fourier transforms; principles of electron, neutron, and X-ray diffraction; optical and computer filtering; three-dimensional reconstruction. S/U or letter grading.

**Chemistry 256N. Seminar: Research in Biochemistry: Advanced Topics in Structural Biology. (2)**

Seminar, three hours. Advanced study and analysis of current topics in biochemistry. Discussion of current research and literature in research specialty of faculty member teaching course. S/U grading.

**Chemistry 256S. Seminar: Research in Biochemistry: Proteome Bioinformatics. (2)**

Seminar, three hours. Advanced study and analysis of current topics in biochemistry. Discussion of current research and literature in research specialty of faculty member teaching course. S/U grading.

**Chemistry 266. Proteomics and Protein Mass Spectrometry. (3)**

Lecture, two hours. Essential technologies and concepts practiced in proteomics-based research, including methods for protein separation and display, protein quantitation, and protein identification. Emphasis on fundamentals of protein mass spectrometry. S/U or letter grading.

**Chemistry 269A. Protein Structure. (2)**

Lecture, five hours; discussion, two hours. Requisites: courses 153A, 153B, 153C, 156. Threedimensional structure of proteins. Forces that stabilize structure of soluble and membrane proteins. Kinetics of protein folding and role of chaperones. Prediction of protein structure from sequence. Letter grading.

**Molecular Evolution and Comparative Genomics Concentration Area:**

**Biomathematics M211. Mathematical and Statistical Phylogenetics. (4)**

(Same as Human Genetics M211.) Lecture, three hours; laboratory, one hour. Requisites: Biostatistics 110A, 110B, Mathematics 170A. Theoretical models in molecular evolution, with focus on phylogenetic techniques. Topics include evolutionary tree reconstruction methods, studies of viral evolution, phylogeography, and coalescent approaches. Examples from evolutionary biology and medicine. Laboratory for hands-on computer analysis of sequence data. S/U or letter grading.

**Biostatistics M272. Theoretical Genetic Modeling . (4)**

(Formerly numbered M237A.) (Same as Biomathematics M207A and Human Genetics M207A.) Lecture, three hours; discussion, one hour. Requisites: Mathematics 115A, 131A, Statistics 100B. Mathematical models in statistical genetics. Topics include population genetics, genetic epidemiology, gene mapping, design of genetics experiments, DNA sequence analysis, and molecular phylogeny. S/U or letter grading.

**Ecology and Evolutionary Biology M231. Molecular Evolution. (4)**

(Same as Earth and Space Sciences M217.) Lecture, two hours; discussion, two hours. Series of advanced topics in molecular evolution, with special emphasis on molecular phylogenetics. Topics may include nature of the genome, neutral evolution, molecular clocks, concerted evolution, molecular systematics, statistical tests, and phylogenetic algorithms. Themes may vary from year to year. May be repeated for credit. S/U or letter grading. Bioinformatics Interdepartmental Graduat e Program Proposal Ð page 53

**Ecology and Evolutionary Biology C235. Population Genetics. (4)**

Lecture, three hours; discussion, one hour. Requisite: Life Sciences 4. Strongly recommended: course 100, Mathematics 31A, 31B. Basic principles of genetics of population, dealing with genetic structure of natural populations and mechanisms of evolution. Equilibrium conditions and forces altering gene frequencies, polygenic inheritance, molecular evolution, and methods of quantitative genetics. Concurrently scheduled with course C135. Letter grading. Molecular, Cell, and Developmental Biology C222A. Advanced Topics in Cell and

**Molecular Biology. Molecular Evolution. (2)**

Lecture, two hours. Requisites: courses 100 or C139 or M140, 144, Life Sciences 4. Current developments in the field of molecular evolution. Constructing evolutionary trees at molecular level; formal testing of evolutionary hypotheses using sequencing data. Original research proposal required. Letter grading.

**Molecular, Cell, and Developmental Biology 292. Seminar: Molecular Evolution. (2)**

Discussion, three hours. Detailed analysis of current understanding of evolution of molecular sequences and structures.

**Neuroinformatics Concentration Area:**

**Biomedical Engineering M217. Biomedical Imaging. (4)**

(Same as Electrical Engineering M217.) Lecture, three hours; laboratory, two hours; outside study, seven hours. Requisite: Electrical Engineering 114D or 211A. Mathematical principles of medical imaging modalities: X-ray, computed tomography, positron-emission tomography, single photon emission computed tomography, magnetic resonance imaging. Topics include basic principles of each imaging system, image reconstruction algorithms, system configurations and their effects on reconstruction algorithms, specialized imaging techniques for specific applications such as flow imaging. Letter grading.

**Biomedical Physics 208A. Medical Physics Laboratory: Medical Imaging. (4)**

Discussion, two hours; laboratory, four hours. Requisite: course 205. Hands-on experience performing acceptance testing and quality control checks of imaging equipment such as fluoroscopy, digital subtraction angiography, mammography, ultrasound, magnetic resonance imaging, computed tomography, and computed radiography.

**Biomedical Physics 210. Principles of Medical Image Processing. (4)**

Lecture, three hours; discussion, one hour. Requisite: course 209. Study of image representation, computational structures for imaging, linear systems theory, image enhancement and restoration, image compression, segmentation, and morphology. Special topics include visualization techniques, three-dimensional modeling, computer graphics, and neural net applications. Laboratory projects apply concepts developed in class.

**Biomedical Physics 214. Medical Image Processing Systems. (4)**

Lecture, three hours; discussion, one hour. Requisites: courses 209, 210. Advanced image processing and image analysis techniques applied to medical images. Discussion of approaches to computer-aided diagnosis and image quantitation, as well as application of pattern classification techniques (neural networks and discriminant analysis). Examination of problems from several imaging modalities (CT, MR, CR, and mammography).

**Biomedical Physics M266. Advanced Magnetic Resonance Imaging. (4)**

Bioinformatics Interdepartmental Graduat e Program Proposal Ð page 54 (Same as Neuroscience M267 and Psychiatry M266.) Lecture, four hours. Starting with basic principles, presentation of physical basis of magnetic resonance imaging (MRI), with emphasis on developing advanced applications in biomedical imaging, including both structural and functional studies. Instruction more intuitive than mathematical. Letter grading.

**Biomedical Physics M285. Functional Neuroimaging: Techniques and Applications. (4)**

(Same as Psychiatry M285.) In-depth examination of activation imaging, including PET and MRI methods, data acquisition and analysis, experimental design, and results obtained thus far in human systems. Strong focus on understanding technologies, how to design activation imaging paradigms, and how to interpret results. Laboratory visits and design and implementation of a functional MRI experiment. S/U or letter grading.

**Neuroscience CM272. Neuroimaging and Brain Mapping. (4)**

(Same as Physiological Science M272 and Psychology M213.) Lecture, three hours. Requisites: courses M201, M202. Theory, methods, applications, assumptions, and limitations of neuroimaging. Techniques, biological questions, and results. Brain structure, brain function, and their relationship discussed with regard to imaging. Concurrently scheduled with course C172. Letter grading.

**Statistics 233. Statistical Methods in Biomedical Imaging. (4)**

Lecture, three hours. Requisite: course 100A. Brief review of common general statistical techniques. Advanced statistical methods for analysis of medical imaging, integration, visualization, interrogation, and interpretation of imaging and nonimaging metadata. S/U or letter grading.

**Computer Science Concentration Area:**

**Computer Science 229. Current Topics In Bioinformatics. (4)**

(Same as Human Genetics M229S.) Seminar, four hours; outside study, eight hours. Designed for graduate engineering students, as well as students from biological sciences and medical school. Introduction to current topics in bioinformatics, genomics, and computational genetics and preparation for computational interdisciplinary research in genetics and genomics. Topics include genome analysis, regulatory genomics, association analysis, association study design, isolated and admixed populations, population substructure, human structural variation, model organisms, and genomic technologies. Computational techniques include those from statistics and computer science. May be repeated for credit with topic change. Letter grading.

**Biomedical Engineering 220. Introduction to Medical Informatics. (2)**

Lecture, two hours; outside study, four hours. Designed for graduate students. Introduction to research topics and issues in medical informatics for students new to field. Definition of this emerging field of study, current research efforts, and future directions in research. Key issues in medical informatics to expose students to different application domains, such as information system architectures, data and process modeling, information extraction and representations, information retrieval and visualization, health services research, telemedicine. Emphasis on current research endeavors and applications. S/U grading.

**Biomedical Engineering 223A-223B-223C. Programming Laboratories for Medical Informatics I, II, III. (4-4-4)**

Lecture, two hours; laboratory, two hours. Designed for graduate students. Programming laboratories to support coursework in other medical informatics core curriculum courses. Exposure to programming concepts for medical applications, with focus on basic abstraction techniques used in image processing and medical information system infrastructures (HL7, DICOM). Letter grading. 223A. Integrated with course 226 to reinforce concepts presented with practical experience. Projects focus on understanding medical networking issues and implementation of basic protocols for health care environment, with emphasis on use of DICOM. 223B. Requisite: course 223A. Integrated with courses 224A and 227 to reinforce concepts presented with practical experience. Projects focus on medical image manipulation and decision support systems. 223C. Requisite: course 223B. Integrated with courses 224B and 225 to reinforce concepts presented with practical experience. Projects focus on medical image storage and retrieval.

**Biomedical Engineering 226. Medical Knowledge Representation. (4)**

Bioinformatics Interdepartmental Graduat e Program Proposal Ð page 55 Seminar, four hours; outside study, eight hours. Designed for graduate students. Issues related to medical knowledge representation and its application in health care processes. Topics include data structures used for representing knowledge (conceptual graphs, frame-based models), different data models for representing spatio-temporal information, rule-based implementations, current statistical methods for discovery of knowledge (data mining, statistical classifiers, and hierarchical classification), and basic information retrieval. Review of work in constructing ontologies, with focus on problems in implementation and definition. Common medical ontologies, coding schemes, and standardized indices/terminologies (SNOMEF, UMLS, MeSH, LOINC). Letter grading.

**Biomedical Engineering 228. Medical Decision Making. (4)**

Lecture, four hours; outside study, eight hours. Designed for graduate students. Overview of issues related to medical decision making. Introduction to concept of evidence-based medicine and decision processes related to process of care and outcomes. Basic probability and statistics to understand research results and evaluations, and algorithmic methods for decision-making processes (Bayes theorem, decision trees). Study design, hypothesis testing, and estimation. Focus on technical advances in medical decision support systems and expert systems, with review of classic and current research. Introduction to common statistical and decision-making software packages to familiarize students with current tools. S/U grading.

**Computer Science 224. Computational Genetics (4)**

(Same as Human Genetics CM224.) Lecture, three hours; discussion, one hour; outside study, eight hours. Preparation: one statistics course and familiarity with any programming language. Designed for undergraduate and graduate engineering students, as well as students from biological sciences and medical school. Introduction to current quantitative understanding of human genetics and computational interdisciplinary research in genetics. Topics include introduction to genetics, human population history, linkage analysis, association analysis, association study design, isolated and admixed populations, population substructure, human structural variation, model organisms, and genotyping technologies. Computational techniques include those from statistics and computer science. Concurrently scheduled with course CM124. Letter grading.

**Computer Science 249. Current Topics in Data Structures. (2 to 12)**

Lecture, four hours; outside study, eight hours. Review of current literature in an area of data structures in which instructor has developed special proficiency as a consequence of research interests. Students report on selected topics. May be repeated for credit with consent of instructor. Letter grading.

**Computer Science M276A. Pattern Recognition and Machine Learning. (4)**

(Formerly numbered 276A.) (Same as Statistics M231.) Lecture, three hours. Designed for graduate students. Fundamental concepts, theories, and algorithms for pattern recognition and machine learning that are used in computer vision, image processing, speech recognition, data mining, statistics, and computational biology. Topics include Bayesian decision theory, parametric and nonparametric learning, clustering, complexity (VC-dimension, MDL, AIC), PCA/ICA/TCA, MDS, SVM, boosting. S/U or letter grading.

**Computer Science M296A. Advanced Modeling Methodology for Dynamic Biomedical Systems. (4)**

(Same as Biomedical Engineering M296A and Medicine M270C.) Lecture, four hours; outside study, eight hours. Requisite: Electrical Engineering 141 or 142 or Mathematics 115A or Mechanical and Aerospace Engineering 171A. Development of dynamic systems modeling Bioinformatics Interdepartmental Graduat e Program Proposal Ð page 56 methodology for physiological, biomedical, pharmacological, chemical, and related systems. Control system, multicompartmental, noncompartmental, and input/output models, linear and nonlinear. Emphasis on model applications, limitations, and relevance in biomedical sciences and other limited data environments. Problem solving in PC laboratory. Letter grading.

**Computer Science M296D. Introduction to Computational Cardiology. (4)**

(Same as Biomedical Engineering M296D.) Lecture, four hours; outside study, eight hours. Requisite: course M186B. Introduction to mathematical modeling and computer simulation of cardiac electrophysiological process. Ionic models of action potential (AP). Theory of AP propagation in one-dimensional and two-dimensional cardiac tissue. Simulation on sequential and parallel supercomputers, choice of numerical algorithms, to optimize accuracy and to provide computational stability. Letter grading.

**Math and Statistics Concentration Area:**

**Biomathematics M203. Stochastic Models in Biology. (4)**

(Same as Human Genetics M203.) Lecture, four hours. Requisite: Mathematics 170A 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. S/U or letter grading.

**Biomathematics 210. Optimization Methods in Biology. (4)**

Lecture, four hours. Preparation: undergraduate mathematical analysis and linear algebra; familiarity with programming language such as Fortran or C. Modern computational biology relies heavily on finite-dimensional optimization. Survey of theory and numerical methods for discrete and continuous optimization, with applications from genetics, medical imaging, pharmacokinetics, and statistics. S/U or letter grading.

**Biomathematics M211. Mathematical and Statistical Phylogenetics. (4)**

(Same as Human Genetics M211.) Lecture, three hours; laboratory, one hour. Requisites: Biostatistics 110A, 110B, Mathematics 170A. Theoretical models in molecular evolution, with focus on phylogenetic techniques. Topics include evolutionary tree reconstruction methods, studies of viral evolution, phylogeography, and coalescent approaches. Examples from evolutionary biology and medicine. Laboratory for hands-on computer analysis of sequence data. S/U or letter grading.

**Biostatistics M234. Applied Bayesian Inference. (4)**

(Same as Biomathematics M234.) Lecture, three hours; discussion, one hour; laboratory, one hour. Requisites: courses 115 (or Statistics 100C), 200A. 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.

**Biostatistics M272. Theoretical Genetic Modeling . (4)**

(Formerly numbered M237A.) (Same as Biomathematics M207A and Human Genetics M207A.) Lecture, three hours; discussion, one hour. Requisites: Mathematics 115A, 131A, Statistics 100B. Mathematical models in statistical genetics. Topics include population genetics, genetic epidemiology, gene mapping, design of genetics experiments, DNA sequence analysis, and molecular phylogeny. S/U or letter grading. Bioinformatics Interdepartmental Graduat e Program Proposal Ð page 57

**Biostatistics M278. M278. Statistical Analysis of DNA Microarray Data. (4)**

(Formerly numbered 278.) (Same as Human Genetics M278.) Lecture, three hours. Requisite: course 200C. Instruction in use of statistical tools used to analyze microarray data. Structure corresponds to analytical protocol an investigator might follow when working with microarray data. S/U or letter grading.

**Statistics 165. Statistical Methods and Data Mining. (4)**

Lecture, three hours. Requisite: course 100A. Introduction and overview of up-to-date statistical methods in microarray analysis designed for students in biostatistics, statistics, and human genetics who are interested in technology and statistical analysis of microarray experiments. Useful for biology students with basic statistical training who are interested in understanding logic underlying many statistical methods. P/NP or letter grading.

**Statistics M231. Pattern Recognition and Machine Learning. (4)**

(Formerly numbered 231.) (Same as Computer Science M276A.) Lecture, three hours. Designed for graduate students. Fundamental concepts, theories, and algorithms for pattern recognition and machine learning that are used in computer vision, image processing, speech recognition, data mining, statistics, and computational biology. Topics include Bayesian decision theory, parametric and nonparametric learning, clustering, complexity (VC-dimension, MDL, AIC), PCA/ICA/TCA, MDS, SVM, boosting. S/U or letter grading.

**Statistics 234. Statistics and Information Theory. (4)**

Lecture, three hours. Preparation: introductory probability theory course. While data compression and transmission are fundamental problems in information theory, field provides insights into fundamentally statistical problems of estimation, prediction, and model selection. Even new concepts of randomness emerge from this line of research. S/U or letter grading.

Students with gaps in their previous training are allowed to take, with the approval of their academic adviser, appropriate undergraduate courses. However, these undergraduate courses may not be applied toward course requirements for a graduate degree in the program.

The following supporting courses are offered in related fields: Statistics 100A (or equivalent preparation) is required as a prerequisite for Chemistry CM260A. CS 31 (or equivalent programming skills) is required for Chemistry C260BL (Bioinformatics Algorithms Laboratory). The Program in Computing offers a range of courses (PIC 10ABC, PIC 20AB, PIC 60, PIC 110) that are also very useful for bioinformatics students. The many departments of the Medical School and Life Sciences offer a wide range of coursework on biology that is highly relevant to bioinformatics students.