2008-2009 Bulletin – PDF - SEAS Bulletin - Columbia University

applied physics specialties. The program
may be considered simply as additional
education in areas beyond the bachelor’s
level, or as preparatory to doctoral studies
in the applied physics fields of plasma
physics, laser physics, solid-state physics,
and applied mathematics. Specific
course requirements for the master’s
degree are determined in consultation
with the program adviser.
M.S. Program in Applied Physics /
Concentration in Applied Mathematics
This 30-point program leads to a
professional M.S. degree. Students
must complete five core courses and
five electives. The core courses provide
a student with a foundation in the fundamentals
of applied mathematics and
contribute 15 points of graduate credit
toward the degree. Students must complete
five of the following seven courses:
APMA E4001: Principles of applied mathematics
APMA E4001: Introduction to nonlinear dynamical
systems
APMA E4150: Applied functional analysis
APMA E4200: Partial differential equations
APMA E4204: Functions of a complex variable
APMA E4300: Introduction to numerical methods
APMA E6301: Analytic methods for partial differential
equations
APMA E6302: Numerical methods 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:
CS0R W4231: Analysis of algorithms
C0MS W4236: Introduction to computational
complexity
C0MS W4241: Numerical algorithms and
complexity
C0MS W4252: Computational learning theory
Industrial engineering/operations
research elective courses include:
IEOR E4003: Industrial economics
IEOR E4004: Introduction to operations research:
deterministic models
IEOR E4007: Optimization: models and methods
IEOR E4106: Introduction to operations research:
stochastic models
SIE0 W4150: Introduction to probability and
statistics
IEOR E4403: Advanced engineering and corporate
economics
IEOR E4407: Game theoretic models of operations
SIE0 W4606: Elementary stochastic processes,
IEOR E4700: Introduction to financial engineering
Other elective courses include:
MECE E4100: Mechanics of fluids
MSAE E4215: Mechanical behavior of structural
materials
EEME E6601: Introduction to control theory
M.S. Program in Medical Physics
This 35-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 physics courses, anatomy, lab,
seminar, and two practicums. A passing
grade on a comprehensive examination
is required for graduation. This examination,
on subjects covered in the curriculum,
is taken at the end of the program
of study. Specific course requirements
are APPH E4010, E4710/11, E4500,
E4550, E4600, and APBM E4650, and,
in the Mailman School of Public Health,
EHSC P6330, P9319, P9330, and
P9335. Some opportunities for specialization
exist.
Certificate of Professional
Achievement in Medical Physics
A graduate program of instruction leading
to the Certificate of Professional
Achievement and requiring satisfactory
completion of at least four of the following
courses:
APPH E4500: Health physics
APPH E4600: Dosimetry
EHSC P6330: Radiation science
EHSC P9319: Clinical nuclear medicine physics
EHSC P9330: Diagnostic radiological physics
EHSC P9335: Radiation therapy physics
APBM E4650: Anatomy for physicists and
engineers
This is a two-semester nondegree program.
Students are admitted to the department
as special certificate-track 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.
M.S., Eng.Sc.D., and Ph.D.
Programs in Materials Science and
Engineering
See page 167.
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
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SEAS 2008–2009