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Stanford Bulletin, Archive 2008-09

Stanford Bulletin, Archive 2008-09

Stanford Bulletin Accreditation Nondiscrimination Policy Additional Information Academic Calendar 2008-09 Welcome to Stanford A Brief History of Stanford University Governance and Organization Directory Organization Admission Undergraduate Admission Graduate Admission Financial Aid Undergraduate Financial Aid Graduate Financial Aid Tuition and Fees Tuition Fees Housing Meal Plans Payments Refunds Housing Undergraduate Residences Graduate Residences Community Housing Undergraduate Degrees and Programs Degree Programs Degree Requirements Degrees, Honors, and Minors Special Registration Statuses (Undergraduate) Graduate Degrees General Requirements Degree-Specific Requirements Advising and Credentials Advising Teaching Credentials Academic Policies and Statements Registration and Records Examinations Grading Systems Academic Standing Statement on Student Academic Grievance Procedures Undergraduate Education Center for Teaching and Learning Freshman and Sophomore Programs Freshman Dean’s Office Introduction to the Humanities Program Overseas Studies Program Structured Liberal Education Program in Writing and Rhetoric Undergraduate Advising and Research Graduate Education Graduate Policy Graduate School of Business School of Earth Sciences Degree Programs in Earth Sciences Earth, Energy, and Environmental Sciences Graduate Program (EEES) Earth Systems Energy Resources Engineering Environmental Earth System Science Geological and Environmental Sciences Geophysics Interdisciplinary Graduate Program in Environment and Resources (IPER) School of Education Undergraduate Programs in Education Graduate Programs in Education School of Engineering Undergraduate Programs in the School of Engineering Graduate Programs in the School of Engineering Aeronautics and Astronautics Bioengineering Chemical Engineering Civil and Environmental Engineering Institute for Computational and Mathematical Engineering Computer Science Electrical Engineering Management Science and Engineering Materials Science and Engineering Mechanical Engineering Mechanical Engineering Course Catalog Numbering System School of Humanities and Sciences African and African American Studies African Studies American Studies Anthropology Applied Physics Archaeology Art and Art History Asian Languages Astronomy Athletics, Physical Education, and Recreation Biology Biology, Hopkins Marine Station Biophysics Chemistry* Classics Communication Comparative Literature Comparative Studies in Race and Ethnicity (CSRE) Drama East Asian Studies Economics English Ethics in Society Program Feminist Studies Financial Mathematics French and Italian German Studies History History and Philosophy of Science and Technology Human Biology Individually Designed Majors Interdisciplinary Studies in Humanities Division of International Comparative and Area Studies International Policy Studies International Relations Jewish Studies Language Center Latin American Studies Linguistics Division of Literatures, Cultures, and Languages Mathematical and Computational Science Mathematics Medieval Studies Modern Thought and Literature Music Philosophy Physics Political Science Psychology Public Policy Religious Studies Russian, East European and Eurasian Studies Science, Technology, and Society Slavic Languages and Literatures Sociology Spanish and Portuguese Statistics Symbolic Systems Urban Studies Stanford in Washington School of Law Joint and Dual Degrees in Law Courses in Law School of Medicine Undergraduate Programs in the School of Medicine Graduate Programs in the School of Medicine Biochemistry Center for Biomedical Ethics Biomedical Informatics Cancer Biology Chemical and Systems Biology Comparative Medicine Developmental Biology Genetics Health Research and Policy Immunology Microbiology and Immunology Molecular and Cellular Physiology Neurobiology Neurosciences Obstetrics and Gynecology Pathology Radiation Oncology Radiology Structural Biology COURSES OF INSTRUCTION Aeronautics and Astronautics (AA) Courses African and African American Studies (AFRICAAM) Courses African and Middle Eastern Languages (AMELANG) Courses African Studies (AFRICAST) Courses American Studies (AMSTUD) Courses Anesthesia (ANES) Courses Anthropology (ANTHRO) Courses Applied Linguistics (APPLLING) Courses Applied Physics (APPPHYS) Courses Archaeology (ARCHLGY) Courses Art History (ARTHIST) Courses Art Studio (ARTSTUDI) Courses Asian American Studies (ASNAMST) Courses Astronomy (ASTRNMY) Courses Athletics, Physical Education, and Recreation (ATHLETIC) Courses Biochemistry (BIOC) Courses Bioengineering (BIOE) Courses Biology (BIO) Courses Biology, Hopkins Marine Station (BIOHOPK) Courses Biomedical Informatics (BIOMEDIN) Courses Biophysics (BIOPHYS) Courses Catalan Language (CATLANG) Courses Cancer Biology (CBIO) Courses Center for Teaching and Learning (CTL) Courses Chemical Engineering (CHEMENG) Courses Chemical and Systems Biology (CSB) Courses Chemistry (CHEM) Courses Chicana/o Studies (CHICANST) Courses Chinese General (CHINGEN) Courses Chinese Language (CHINLANG) Courses Chinese Literature (CHINLIT) Courses Civil and Environmental Engineering (CEE) Courses Classics Art/Archaeology (CLASSART) Courses Classics General (CLASSGEN) Courses Classics Greek (CLASSGRK) Courses Classics History (CLASSHIS) Courses Classics Latin (CLASSLAT) Courses Communication (COMM) Courses Comparative Literature (COMPLIT) Courses Comparative Medicine (COMPMED) Courses Comparative Studies in Race and Ethnicity (CSRE) Courses Computational and Mathematical Engineering (CME) Courses Computer Science (CS) Courses Dance (DANCE) Courses Developmental Biology (DBIO) Courses Division of Literatures, Cultures, and Languages (DLCL) Courses Drama (DRAMA) Courses Earth, Energy, and Environmental Sciences (EEES) Courses Earth Systems (EARTHSYS) Courses East Asian Studies (EASTASN) Courses Economics (ECON) Courses Education (EDUC) Courses Electrical Engineering (EE) Courses Energy Resources Engineering (ENERGY) Courses Engineering (ENGR) Courses English (ENGLISH) Courses English for Foreign Students (EFSLANG) Courses Environmental Earth System Science (EESS) Courses Ethics in Society (ETHICSOC) Courses Feminist Studies (FEMST) Courses Film Studies (FILMSTUD) Courses Film, Practice of (FILMPROD) Courses French General (FRENGEN) Courses French Language (FRENLANG) Courses French Literature (FRENLIT) Courses Genetics (GENE) Courses Geological and Environmental Sciences (GES) Courses Geophysics (GEOPHYS) Courses German General (GERGEN) Courses German Language (GERLANG) Courses German Literature (GERLIT) Courses Graduate School of Business (GSBGEN) Courses Health Research and Policy (HRP) Courses History (HISTORY) Courses History and Philosophy of Science (HPS) Courses Human Biology (HUMBIO) Courses Humanities and Sciences (HUMSCI) Courses Immunology (IMMUNOL) Courses Institute for International Studies (Freeman Spogli) (IIS) Courses Interdisciplinary Program in Environment and Resources (IPER) Courses Interdisciplinary Studies in Humanities (HUMNTIES) Courses International Policy Studies (IPS) Courses International Relations (INTNLREL) Courses Introduction to the Humanities (IHUM) Courses Italian General (ITALGEN) Courses Italian Language (ITALLANG) Courses Italian Literature (ITALLIT) Courses Japanese General (JAPANGEN) Courses Japanese Language (JAPANLNG) Courses Japanese Literature (JAPANLIT) Courses Jewish Studies (JEWISHST) Courses Korean Language (KORLANG) Courses Latin American Studies (LATINAM) Courses Law (LAW) Courses Law, Nonprofessional (LAWGEN) Courses Linguistics (LINGUIST) Courses Management Science and Engineering (MS&E) Courses Master of Liberal Arts (MLA) Courses Materials Science and Engineering (MATSCI) Courses Mathematical and Computational Science (MCS) Courses Mathematics (MATH) Courses Mechanical Engineering (ME) Courses Medicine (MED) Courses Medicine Interdisciplinary (INDE) Courses Medieval Studies (MEDVLST) Courses Microbiology and Immunology (MI) Courses Modern Thought and Literature (MTL) Courses Molecular and Cellular Physiology (MCP) Courses Music (MUSIC) Courses Native American Studies (NATIVEAM) Courses Neurobiology (NBIO) Courses Neurology and Neurological Sciences (NENS) Courses Neurosciences Program (NEPR) Courses Neurosurgery (NSUR) Courses Obstetrics and Gynecology (OBGYN) Courses Ophthalmology (OPHT) Courses Orthopedic Surgery (ORTHO) Courses Overseas Studies Special Programs (OSPGEN) Courses Overseas Studies: Australia (OSPAUSTL) Courses Overseas Studies: Beijing (OSPBEIJ) Courses Overseas Studies: Berlin (OSPBER) Courses Overseas Studies: Florence (OSPFLOR) Courses Overseas Studies: Kyoto—SCTI (OSPKYOTO) Courses Overseas Studies: Madrid (OSPMADRD) Courses Overseas Studies: Moscow (OSPMOSC) Courses Overseas Studies: Oxford (OSPOXFRD) Courses Overseas Studies: Paris (OSPPARIS) Courses Overseas Studies: Santiago (OSPSANTG) Courses Pathology (PATH) Courses Pediatrics (PEDS) Courses Philosophy (PHIL) Courses Physics (PHYSICS) Courses Political Science (POLISCI) Courses Portuguese Language (PORTLANG) Courses Portuguese Literature (PORTLIT) Courses Psychiatry (PSYC) Courses Psychology (PSYCH) Courses Public Policy (PUBLPOL) Courses Radiation Oncology (RADO) Courses Radiology (RAD) Courses Religious Studies (RELIGST) Courses Russian, East European, and Eurasian Studies (REES) Courses Science, Technology, and Society (STS) Courses Slavic General (SLAVGEN) Courses Slavic Language (SLAVLANG) Courses Slavic Literature (SLAVLIT) Courses Sociology (SOC) Courses Sophomore College (SCS) Courses Spanish Language (SPANLANG) Courses Spanish Literature (SPANLIT) Courses Special Language Program (SPECLANG) Courses Stanford Introductory Seminars (IDS, ISF, ISS) Courses Statistics (STATS) Courses Structural Biology (SBIO) Courses Structured Liberal Education (SLE) Courses Surgery (SURG) Courses Symbolic Systems (SYMBSYS) Courses Tibetan Language (TIBETLNG) Courses Urban Studies (URBANST) Courses Writing and Rhetoric, Program in (PWR) Courses Centers, Laboratories, and Institutes Center for Advanced Study in the Behavioral Sciences (CASBS) Center for History and Philosophy of Science Center for Space Science and Astrophysics Edward L. Ginzton Laboratory Freeman Spogli Institute for International Studies (FSI) Geballe Laboratory for Advanced Materials (GLAM) Hoover Institution on War, Revolution and Peace Human Sciences and Technologies Advanced Research Institute (H-STAR) Institute for Research in the Social Sciences (IRiSS) Kavli Institute for Particle Astrophysics and Cosmology (KIPAC) Michelle R. Clayman Institute for Gender Research Morrison Institute for Population and Resource Studies Photon Ultrafast Laser Science and Engineering (PULSE) Precourt Institute for Energy Efficiency (PIEE) Stanford Center on Longevity (SCL) Stanford Humanities Center Stanford Institute for Economic Policy Research (SIEPR) Stanford Institute for Materials and Energy Sciences (SIMES) Stanford Institute for the Quantitative Study of Society Stanford Linear Accelerator Center W. W. Hansen Experimental Physics Laboratory (HEPL) Woods Institute for the Environment Libraries and Computing Resources Stanford University Libraries and Academic Information Resources Coordinate Libraries Hoover Institution on War, Revolution and Peace Information Technology Services (IT Services) The Continuing Studies Program Master of Liberal Arts Program Summer Session Student Affairs Dean of Student Life Dean of Educational Resources Office of Accessible Education (OAE) Career Development Center Community Centers Graduate Life Office Haas Center for Public Service Bechtel International Center Judicial Affairs and Student Conduct Old Union Office of Residential Education Office of Student Activities Tresidder Memorial Union Vaden Health Center Other Services and Programs Bookstore Diversity and Access Office Stanford Conference Services Ombuds Police Services Office for Religious Life Stanford Alumni Association Stanford Events Awards and Honors Exchange Programs and Cross-enrollment Agreements Nonacademic Regulations University Policies Index Alphabetical Index

Mathematics

Emeriti: Kai Lai Chung, Solomon Feferman, Robert Finn, Joseph Keller, Georg Kreisel, Harold Levine, Tai-Ping Liu, R. James Milgram, Donald Ornstein, Robert Osserman

Chair: Rafe Mazzeo

Professors: Simon Brendle, Gregory Brumfiel, Daniel Bump, Gunnar Carlsson, Ralph L. Cohen, Brian Conrad, Amir Dembo, Persi Diaconis, Yakov Eliashberg, Eleny Ionel, Yitzhak Katznelson, Steven Kerckhoff, Jun Li, Rafe Mazzeo, Maryam Mirzakhani, George Papanicolaou, Richard Schoen, Leon Simon, Kannan Soundararajan, Ravi Vakil, Andras Vasy, Akshay Venkatesh, Brian White

Associate Professor: Soren Galatius

Szegö Assistant Professors: Laurent Demanet, Fei Han, Gautam Iyer, Vladislav Kargin, Joan Licata, Antoine Toussaint, Denis Trotabas, Leo Tzou

Lecturers: Adrian Butscher, Mark Lucianovic, Laurence Nedelec, Wojciech Wieczorek

Courtesy Professors: Renata Kallosh, Grigori Mints

Consulting Professors: Brian Conrey, Keith Devlin, David Hoffman, Wu-chung Hsiang

Samelson Fellows: Matthew Kahle, Anthony Licata, Samuel Lisi

Web site: http://math.stanford.edu

Courses offered by the Department of Mathematics have the subject code MATH, and are listed in the "Mathematics [MATH] Courses" section of this bulletin.

The Department of Mathematics offers programs leading to the degrees of Bachelor of Science, Master of Science, and Doctor of Philosophy in Mathematics, and participates in the program leading to the B.S. in Mathematical and Computational Science. The department also participates in the M.S. and Ph.D. degree programs in Scientific Computing and Computational Mathematics and the M.S. degree program in Financial Mathematics.