2011-2012 Bulletin – PDF - SEAS Bulletin - Columbia University

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 E4101: Intro to dynamical systems
APMA E4150: Applied functional analysis
APMA E4200: Partial differential equations
APMA E4204: Functions of a complex variable
APMA E4300: Intro to numerical methods
APMA E4301: Numerical methods for partial
differential equations
APMA E6301: Analytic methods for partial
differential equations
APMA E6302: Numerical 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: Intro to computational complexity
COMS W4241: Numerical algorithms and
complexity
COMS W4252: Computational learning theory
Industrial engineering/operations
research elective courses include:
IEOR E4003: Industrial economics
IEOR E4004: Intro to operations research:
deterministic models
IEOR E4007: Optimization: models and methods
IEOR E4106: Intro to operations research:
stochastic models
SIE0 W4150: Intro to probability and statistics
IEOR E4403: Advanced engineering and corporate
economics
IEOR E4407: Game 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: Mechanical 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, E4710/11, E4500, E4501,
E4550, E4600, and APBM E4650,
and, in the Mailman School of Public
Health, EHSC P6330, P9319, P9330,
and P9335. 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 at least four of the
following courses:
APPH E4500: Health physics
APPH E4600: Dosimetry
APBM E4650: Anatomy for physicists and engineers
EHSC P6330: Radiation science
EHSC P9319: Clinical nuclear medicine physics
EHSC P9330: Diagnostic radiology physics
EHSC P9335: Radiation therapy physics
This is a two-semester nondegree
program. Students are admitted to the
department as 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.
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.
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