APMA E4204: Functions of a complex variable APMA E4300: Intro to numerical methods APMA E4301: N umerical methods for partial differential equations APMA E6301: A nalytic methods for partial differential equations APMA E6302: N umerical analysis for partial differential equations
A student must select five elective courses from those listed below (or any of those not used to satisfy the core requirements from the list above) for a total of 15 points of graduate credit. Additional courses not listed below can be applied toward the elective requirements, subject to the approval of the faculty adviser. Computer science elective courses include: CSOR W4231: Analysis of algorithms, I COMS W4236: I ntro to computational complexity COMS W4241: N umerical algorithms and complexity COMS W4252: Computational learning theory
Industrial engineering/operations research elective courses include: IEOR E4003: Industrial economics IEOR E4004: I ntro to operations research: deterministic models IEOR E4007: Optimization: models and methods IEOR E4106: I ntro to operations research: stochastic models SIE0 W4150: Intro to probability and statistics IEOR E4403: A dvanced engineering and corporate economics IEOR E4407: G ame theoretic models of operations STAT W4606: Elementary stochastic processes IEOR E4700: Intro to financial engineering
Other elective courses include: MECE E4100: Mechanics of fluids MSAE E4215: M echanical behavior of structural materials EEME E6601: Intro to control theory
M.S. Program in Materials Science and Engineering See page 170. M.S. Program in Medical Physics This CAMPEP-approved 36-point program in medical physics leads to the M.S. degree. It is administered by faculty from the School of Engineering and Applied Science in collaboration with faculty from the College of Physicians and Surgeons and the Mailman School of Public Health. It provides preparation toward certification by the American Board of Radiology. The program consists of a core curriculum of medical and nuclear physics courses,
anatomy, lab, seminar, a tutorial, and two practicums. Specific course requirements are APPH E4010, E4330, E4710/11, E4500, E4501, E4550, E4600, E6319, E6330, E6335, and APBM E4650. Some opportunities for specialization exist. A passing grade on a comprehensive examination is required for graduation. This examination, on subjects covered in the curriculum, is taken after two terms of study.
Certificate of Professional Achievement in Medical Physics This graduate program of instruction leads to the Certificate of Professional Achievement and requires satisfactory completion of six of the following courses: APPH E4330: Radiobiology APPH E4500: Health physics APPH E4600: Dosimetry APBM E4650: A natomy for physicists and engineers APPH E6319: Clinical nuclear medicine physics APPH E6330: Diagnostic radiology physics APPH E6335: Radiation therapy physics
This is a nondegree program. Students are admitted to the department as certificatetrack students.
Ph.D. and Eng.Sc.D. Programs After completing the M.S. program in applied physics, doctoral students specialize in one applied physics field. Some programs have specific course requirements for the doctorate; elective courses are determined in consultation with the program adviser. Successful completion of an approved 30-point program of study is required in addition to successful completion of a written qualifying examination taken after two semesters of graduate study. An oral examination, taken within one year after the written qualifying examination, and a thesis proposal examination, taken within two years after the written qualifying examination, are required of all doctoral candidates. Applied Mathematics This academic program, for students registered in the Department of Applied Physics and Applied Mathematics, emphasizes applied mathematics research in nonlinear dynamics, fluid mechanics, and scientific computation, with a current emphasis on geophysical, biophysical, and plasma physics applications.
Applied mathematics deals with the use of mathematical concepts and techniques in various fields of science and engineering. Historically, mathematics was first applied with great success in astronomy and mechanics. Then it developed into a main tool of physics, other physical sciences, and engineering. It is now important in the biological, geological, and social sciences. With the coming of age of the computer, applied mathematics has transcended its traditional style and now assumes an even greater importance and a new vitality. Compared with the pure mathematician, the applied mathematician is more interested in problems coming from other fields. Compared with the engineer and the physical scientist, he or she is more concerned with the formulation of problems and the nature of solutions. Compared with the computer scientist, he or she is more concerned with the accuracy of approximations and the interpretation of results. Needless to say, even in this age of specialization, the work of mathematicians, scientists, and engineers frequently overlaps. Applied mathematics, by its very nature, has occupied a central position in this interplay and has remained a field of fascination and excitement for active minds.
Materials Science and Engineering Program See page 171. Plasma Physics This academic program is designed to emphasize preparation for professional careers in plasma research, controlled fusion, and space research. This includes basic training in relevant areas of applied physics, with emphasis on plasma physics and related areas leading to extensive experimental and theoretical research in the Columbia University Plasma Physics Laboratory. Specific course requirements for the plasma physics doctoral program are APPH E4018, E4200, E4300, E6101, E6102, and E9142 or E9143, or equivalents taken at another university. Optical and Laser Physics This academic program involves a basic training in relevant areas of applied physics with emphasis in quantum mechanics, quantum electronics, and related areas of engineering 2012– 2013
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