2005-06 - Office of the Registrar - Duke University

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of the Practice Blake and Bookman; Adjunct Professors Bertozzi, Howard, Shearer and Wahl; Professors Emeriti Kitchen, Moore, Scoville, Smith, Warner, and Weisfeld. Graduate work in the Department of Mathematics is offered leading to the Ph.D. degree. Admission to this program is based on the applicant's undergraduate academic record, level of preparation for graduate study, the Graduate Record Examination general and subject tests, and letters of recommendation. The department offers research training in both pure and applied mathematics. Major areas of research specialization include algebra and algebraic geometry, analysis and partial differential equations, applied mathematics and scientific computing, differential geometry, geometry and physics, mathematical biology, probability and stochastic processes, and topology. Interdisciplinary programs with connections to the department include the Center for Geometric Computing, the Center for Hydrologic Science, the Center for Mathematics and Computation in the Life Sciences and Medicine, and the Center for Nonlinear and Complex Systems. All Ph.D. students are required to pass a qualifying examination; most students take this examination shortly after completing their first year of graduate study. While students are normally admitted only to the Ph.D. program, the A.M. degree with a major in mathematics is awarded upon completion of 30 units of graded course work and passing the qualifying examination. Candidacy for the Ph.D. is established by passing an oral preliminary examination. The preliminary examination is normally taken during the third year. By this time the student should have chosen a thesis advisor and demonstrated any computer skills or reading skills in a foreign language judged to be necessary for work in the chosen area. The original research which begins after successful completion of the preliminary examination should culminate in the writing and defense of a dissertation. The dissertation is the most important requirement for the Ph.D. degree. Further details concerning the department, the graduate program, admissions, facilities, the faculty and their research, and financial support may be obtained from our web site http:/ /www.math.duke.edu/. For inquiries, send e-mail to the director of graduate studies at dgsmath@math.duke.edu. For Seniors and Graduates 200. Introduction to Algebraic Structures I. Groups: symmetry, normal subgroups, quotient groups, group actions. Rings: homomorphisms, ideals, principal ideal domains, the Euclidean algorithm, unique factorization. Not open to students who have had Mathematics 121. Prerequisite: Mathematics 104 or equivalent. Instructor: Staff. 3 units. 201. Introduction to Algebraic Structures II. Fields and field extensions, modules over rings, further topics in groups, rings, fields, and their applications. Prerequisite: Mathematics 200, or 121 and consent of instructor. Instructor: Staff. 3 units. 203. Basic Analysis I. Topology of Rn, continuous functions, uniform convergence, compactness, infinite series, theory of differentiation, and integration. Not open to students who have had Mathematics 139. Prerequisite: Mathematics 104. Instructor: Staff. 3 units. 204. Basic Analysis II. Differential and integral calculus in Rn. Inverse and implicit function theorems. Further topics in multivariable analysis. Prerequisite: Mathematics 104; Mathematics 203, or 139 and consent of instructor. Instructor: Staff. 3 units. 205. Topology. Elementary topology, surfaces, covering spaces, Euler characteristic, fundamental group, homology theory, exact sequences. Prerequisite: Mathematics 104. Instructor: Staff. 3 units. 206. Differential Geometry. Geometry of curves and surfaces, the Serret-Frenet frame of a space curve, the Gauss curvature, Cadazzi-Mainardi equations, the Gauss-Bonnet formula. Prerequisite: Mathematics 104. Instructor: Staff. 3 units. 215. Mathematical Finance. An introduction to the basic concepts of mathematical finance. Topics include modeling security price behavior, Brownian and geometric 192 Courses and Academic Programs
Brownian motion, mean variance analysis and the efficient frontier, expected utility maximization, Ito's formula and stochastic differential equations, the Black-Scholes equation and option pricing formula. Prerequisites: Mathematics 103, 104, 135 or equivalent, or consent of instructor. Instructor: Staff. 3 units. C-L: Economics 225 216. Applied Stochastic Processes. An introduction to stochastic processes without measure theory. Topics selected from: Markov chains in discrete and continuous time, queuing theory, branching processes, martingales, Brownian motion, stochastic calculus. Prerequisite: Mathematics 135 or equivalent. Instructor: Staff. 3 units. C-L: Statistics and Decision Sciences 253 217. Linear Models. 3 units. C-L: see Statistics and Decision Sciences 244 221. Numerical Analysis. 3 units. C-L: see Computer Science 250; also C-L: Statistics and Decision Sciences 250 224. Scientific Computing I. Structured scientific programming in C/C++ and FORTRAN. Floating point arithmetic and interactive graphics for data visualization. Numerical linear algebra, direct and iterative methods for solving linear systems, matrix factorizations, least squares problems and eigenvalue problems. Iterative methods for nonlinear equations and nonlinear systems, Newton's method. Prerequisite: Mathematics 103 and 104. Instructor: Staff. 3 units. 225. Scientific Computing II. Approximation theory: Fourier series, orthogonal polynomials, interpolating polynomials and splines. Numerical differentiation and integration. Numerical methods for ordinary differential equations: finite difference methods for initial and boundary value problems, and stability analysis. Introduction to finite element methods. Prerequisite: Mathematics 224 and familiarity with ODEs at the level of Mathematics 111 or 131. Instructor: Staff. 3 units. 226. Numerical Partial Differential Equations I. Numerical solution of hyperbolic conservation laws. Conservative difference schemes, modified equation analysis and Fourier analysis, Lax-Wendroff process. Gas dynamics and Riemann problems. Upwind schemes for hyperbolic systems. Nonlinear stability, monotonicity and entropy; TVD, MUSCL, and ENO schemes for scalar laws. Approximate Riemann solvers and schemes for hyperbolic systems. Multidimensional schemes. Adaptive mesh refinement. Prerequisite: Mathematics 224, 225, or consent of instructor. Instructor: Staff. 3 units. 227. Numerical Partial Differential Equations II. Numerical solution of parabolic and elliptic equations. Diffusion equations and stiffness, finite difference methods and operator splitting (ADI). Convection-diffusion equations. Finite element methods for elliptic equations. Conforming elements, nodal basis functions, finite element matrix assembly and numerical quadrature. Iterative linear algebra; conjugate gradients, Gauss-Seidel, incomplete factorizations and multigrid. Mixed and hybrid methods. Mortar elements. Reaction-diffusion problems, localized phenomena, and adaptive mesh refinement. Prerequisite: Mathematics 224, 225, or consent of instructor. Instructor: Staff. 3 units. 228. Mathematical Fluid Dynamics. Properties and solutions of the Euler and Navier- Stokes equations, including particle trajectories, vorticity, conserved quantities, shear, deformation and rotation in two and three dimensions, the Biot-Savart law, and singular integrals. Additional topics determined by the instructor. Prerequisite: Mathematics 133 or 211 or an equivalent course. Instructor: Staff. 3 units. 229. Mathematical Modeling. Formulation and analysis of mathematical models in science and engineering. Emphasis on case studies; may include individual or team research projects. Instructor: Staff. 3 units. 231. Ordinary Differential Equations. Existence and uniqueness theorems for nonlinear systems, well-posedness, two-point boundary value problems, phase plane diagrams, stability, dynamical systems, and strange attractors. Prerequisite: Mathematics 104, 111 or 131, and 203 or 139. Instructor: Staff. 3 units. Mathematics (MATH) 193
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ulletin of Duke University 2005-200
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Contents Academic Calendar—2005-2
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Public Policy Studies (PUBPOL) 240
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Spring 2006 January 11 Wednesday, 8
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Graduate School Faculty (As of July
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James F. Bonk (1959), Ph.D., Profes
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Cathy N. Davidson (1989), Ph.D., Pr
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Bryan Gilliam (1986), Ph.D., Profes
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Randy L. Jirtle (1977), Ph.D., Prof
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Ralph Litzinger (1994), Ph.D., Asso
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Robert F. Nau (1985), Ph.D., Associ
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Michael K. Reedy (1969), M.D., Prof
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Joshua Sosin (2000), Ph.D., Assista
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Miriam L. Wahl (2002), Ph.D., Assis
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Clark R. Cahow (1960), Ph.D., Arts
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Orrin Pilkey (1965), Ph.D., James B
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TO THE PROSPECTIVE GRADUATE STUDENT
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Degree and Non-degree Admission Stu
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Application files are assembled in
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Fellowships and Scholarships The co
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conjunction with the admitting depa
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must be indicated on the form. Stud
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of withdrawal from the university,
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Registration All students who enrol
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and (2) the dropped course(s) resul
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General Academic Regulations Credit
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the instructor, list the course as
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the Graduate School at least one we
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working on their dissertations, it
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The Duke Community Standard Duke Un
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pursued using the steps followed fo
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Pending verdict on charges (includi
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Course Enrollment Courses numbered
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as in a variety of media, from arch
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297S. Topics in Art since 1945. His
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373. The Paris Salon; Artists, Crit
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Biochemistry (BIOCHEM) Professor Ra
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The BGT core curriculum emphasises
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types of cell signaling models can
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esearch problems in anatomy will be
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macroevolution), Mathematics (theor
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259S. The Life and Work of Darwin.
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293. Simulating Ecological and Evol
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Faculty are from the Departments of
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551. Finance I. This course gives r
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of the department addresses cell bi
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COURSES CURRENTLY UNSCHEDULED 204.
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magnetic resonance, and problem-sol
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374. Seminar. One hour a week discu
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For Graduates 301. Seminar in Greek
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Vitter; Adjunct Associate Professor
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derandomization. Prerequisite: Comp
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the areas of research lab organizat
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space, and the relationship between
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departmental training to enable stu
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210S. Paleoenvironmental Analysis.
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ing of phase equilibrium. Prerequis
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courses from an approved list of co
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expertise in the environmental scie
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215S. Research Seminar. Individual
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279. Advanced Microeconomics II. Fo
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320. Macroeconomic Analysis I. Inte
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Contract Theory, Decision Theory, G
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Biomedical Engineering (BME) Profes
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222. Principles of Ultrasound Imagi
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264L. Medical Instrument Design. Ge
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223. Cellular and Integrative Cardi
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characteristics, hydrologic instrum
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Passivity, positivity, and self-dua
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Collins, Kedem, Smith, and Teitswor
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Page 149 and 150: 280. Convective Heat Transfer. Mode
Page 151 and 152: 202S. Narrative Writing. The writin
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Page 155 and 156: 204LS. Field Ecology. 4 units. C-L:
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Page 163 and 164: 353. Advanced Topics in Landscape E
Page 165 and 166: 232. Microclimatology 242. Environm
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Page 169 and 170: Expressionism to poets active since
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Page 175 and 176: 210S. Anthropology and History. 3 u
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Page 181 and 182: University Programs: Cell and Molec
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Page 191: Environment 243. Environmental Bioc
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Page 197 and 198: Professors Dobbins, MacFall, Song,
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Page 203 and 204: Molecular Genetics and Microbiology
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Page 207 and 208: Biology 295S. Physical Approaches t
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Page 219 and 220: 225S. British Empiricism. A critica
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Page 225 and 226: The terminal degree of Master of Ar
Page 227 and 228: 229S. Contemporary Theory of Libera
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Page 231 and 232: Emphasis on using these techniques
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Bomber, a child nutrition program,
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314. The Politics of the Policy Pro
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387. Master's Project in Internatio
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226. A-F. Exegesis of the Greek New
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304. Aramaic. Study tests represent
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362. Readings in Old Testament and
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Dainotto, Hardt, Nouzeilles, Siebur
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COURSES CURRENTLY UNSCHEDULED 211.
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248. Studies in Spanish-American Li
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391. Hispanic Seminar. Each semeste
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206. Russian Modernism. Russian cul
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305. Advanced Russian Conversation
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COURSES CURRENTLY UNSCHEDULED 274S.
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D. Research Design E. Evaluation Re
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controversies in the discipline, ho
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decision functions and their proper
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structural relationships in a chemi
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field's first decades, feminist sch
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391. Tutorial in Special Topics. Di
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Center for Advanced Computing and C
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Center for Cognitive Neuroscience T
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times in scholarly fashion. It asks
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knowledge about the region. Chaired
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locations may also be considered wh
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The Libraries The libraries of the
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THE DIVINITY SCHOOL LIBRARY The Div
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The Phytotron. The Phytotron, a nat
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1) ARL-Fisons Spectraspan 7 direct
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ultraviolet to soft X-ray FEL (this
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X-ray generator and diffractometer,
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Living Accommodations Duke offers t
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general medical care, nutrition cou
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intellectually, is also developing
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its markings. The Center is named i
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E Earth and Ocean Sciences 110 Eart
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S Satisfactory Progress 42 Scholars
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2005-06 - Office of the Registrar - Duke University

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