2009-2010 Bulletin â PDF - SEAS Bulletin - Columbia University
2009-2010 Bulletin â PDF - SEAS Bulletin - Columbia University
2009-2010 Bulletin â PDF - SEAS Bulletin - Columbia University
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M.S. Program in Applied Physics<br />
The program of study leading to the<br />
degree of Master of Science, while<br />
emphasizing continued work in basic<br />
physics, permits many options in several<br />
applied physics specialties. The program<br />
may be considered simply as additional<br />
education in areas beyond the bachelor’s<br />
level, or as preparatory to doctoral studies<br />
in the applied physics fields of plasma<br />
physics, laser physics, solid-state physics,<br />
and applied mathematics. Specific<br />
course requirements for the master’s<br />
degree are determined in consultation<br />
with the program adviser.<br />
M.S. Program in Applied Physics /<br />
Concentration in Applied Mathematics<br />
This 30-point program leads to a<br />
professional M.S. degree. Students<br />
must complete five core courses and<br />
five electives. The core courses provide<br />
a student with a foundation in the fundamentals<br />
of applied mathematics and<br />
contribute 15 points of graduate credit<br />
toward the degree. Students must complete<br />
five of the following seven courses:<br />
APMA E4001: Principles of applied mathematics<br />
APMA E4101: Introduction to dynamical systems<br />
APMA E4150: Applied functional analysis<br />
APMA E4200: Partial differential equations<br />
APMA E4204: Functions of a complex variable<br />
APMA E4300: Introduction to numerical methods<br />
APMA E4301: Numerical methods for partial<br />
differential equations<br />
APMA E6301: Analytic methods for partial differential<br />
equations<br />
APMA E6302: Numerical analysis for partial<br />
differential equations<br />
A student must select five elective<br />
courses from those listed below (or any<br />
of those not used to satisfy the core<br />
requirements from the list above) for a<br />
total of 15 points of graduate credit.<br />
Additional courses not listed below can<br />
be applied toward the elective requirements,<br />
subject to the approval of the<br />
faculty adviser. Computer science elective<br />
courses include:<br />
CS0R W4231: Analysis of algorithms<br />
C0MS W4236: Introduction to computational<br />
complexity<br />
C0MS W4241: Numerical algorithms and<br />
complexity<br />
C0MS W4252: Computational learning theory<br />
Industrial engineering/operations<br />
research elective courses include:<br />
IEOR E4003: Industrial economics<br />
IEOR E4004: Introduction to operations research:<br />
deterministic models<br />
IEOR E4007: Optimization: models and methods<br />
IEOR E4106: Introduction to operations research:<br />
stochastic models<br />
SIE0 W4150: Introduction to probability and<br />
statistics<br />
IEOR E4403: Advanced engineering and corporate<br />
economics<br />
IEOR E4407: Game theoretic models of operations<br />
SIE0 W4606: Elementary stochastic processes,<br />
IEOR E4700: Introduction to financial engineering<br />
Other elective courses include:<br />
MECE E4100: Mechanics of fluids<br />
MSAE E4215: Mechanical behavior of structural<br />
materials<br />
EEME E6601: Introduction to control theory<br />
M.S. Program in Medical Physics<br />
This CAMPEP-approved 36-point program<br />
in medical physics leads to the<br />
M.S. degree. It is administered by faculty<br />
from the School of Engineering and<br />
Applied Science in collaboration with<br />
faculty from the College of Physicians<br />
and Surgeons and the Mailman School<br />
of Public Health. It provides preparation<br />
toward certification by the American<br />
Board of Radiology. The program consists<br />
of a core curriculum of medical<br />
physics courses, anatomy, lab, seminar,<br />
and two practicums. Specific course<br />
requirements are APPH E4010,<br />
E4710/11, E4500, E4550, E4600, and<br />
APBM E4650, and, in the Mailman<br />
School of Public Health, EHSC P6330,<br />
P9319, P9330, and P9335. Some<br />
opportunities for specialization exist.<br />
A passing grade on a comprehensive<br />
examination is required for graduation.<br />
This examination, on subjects covered<br />
in the curriculum, is taken at the end of<br />
the program of study.<br />
Certificate of Professional<br />
Achievement in Medical Physics<br />
This graduate program of instruction<br />
leads to the Certificate of Professional<br />
Achievement and requires satisfactory<br />
completion of at least four of the following<br />
courses:<br />
APPH E4500: Health physics<br />
APPH E4600: Dosimetry<br />
EHSC P6330: Radiation science<br />
EHSC P9319: Clinical nuclear medicine physics<br />
EHSC P9330: Diagnostic radiological physics<br />
EHSC P9335: Radiation therapy physics<br />
APBM E4650: Anatomy for physicists and<br />
engineers<br />
This is a two-semester nondegree program.<br />
Students are admitted to the department<br />
as certificate-track students.<br />
Ph.D. and Eng.Sc.D. Programs<br />
After completing the M.S. program in<br />
applied physics, doctoral students specialize<br />
in one applied physics field. Some<br />
programs have specific course requirements<br />
for the doctorate; elective courses<br />
are determined in consultation with the<br />
program adviser. Successful completion<br />
of an approved 30-point program of<br />
study is required in addition to successful<br />
completion of a written qualifying<br />
examination taken after two semesters<br />
of graduate study. An oral examination,<br />
taken within one year after the written<br />
qualifying examination, and a thesis proposal<br />
examination, taken within two years<br />
after the written qualifying examination,<br />
are required of all doctoral candidates.<br />
M.S., Eng.Sc.D., and Ph.D.<br />
Programs in Materials Science and<br />
Engineering<br />
See page 169.<br />
Applied Mathematics<br />
This academic program, for students<br />
registered in the Department of Applied<br />
Physics and Applied Mathematics,<br />
emphasizes applied mathematics<br />
research in nonlinear dynamics, fluid<br />
mechanics, and scientific computation<br />
with a current emphasis on geophysical,<br />
biophysical, and plasma physics applications.<br />
Applied mathematics deals with the<br />
use of mathematical concepts and techniques<br />
in various fields of science and<br />
engineering. Historically, mathematics<br />
was first applied with great success<br />
in astronomy and mechanics. Then it<br />
developed into a main tool of physics,<br />
other physical sciences, and engineering.<br />
It is now important in the biological,<br />
geological, and social sciences. With the<br />
coming of age of the computer, applied<br />
mathematics has transcended its traditional<br />
style and now assumes an even<br />
greater importance and a new vitality.<br />
Compared with the pure mathematician,<br />
the applied mathematician is more<br />
interested in problems coming from<br />
other fields. Compared with the engineer<br />
and the physical scientist, he or she is<br />
61<br />
<strong>SEAS</strong> <strong>2009</strong>–<strong>2010</strong>