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

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• Business and Finance
The knowledge of physics and
mathematics that is gained in
the applied physics and applied
mathematics programs is a strong
base for a career in business or
finance.
Economics
ECON W3211x,y: Intermed microeconomics (J)
ECON W3213x,y: Intermed macroeconomics(J)
Industrial Engineering
and Operations Research
IEOR E4003x: Industrial economics
IEOR E4201x: The eng of management, I
IEOR E4202y: The eng of management, II
Finance
MATH W4071x: Mathematics of finance
IEOR E4106y: Intro to operations research:
stochastic models (J)
SIEO W4150x,y: Probability and statistics (J)
ECIE W4280: Corporate finance
IEOR E4700x: Intro to financial engineering
• Mathematics Applicable to Physics
Applied physics students can specialize
in the mathematics that is applicable
to physics. This specialization is
particularly useful for students
interested in theoretical physics.
MATH V3386x: Differential geometry
APMA E4001y: Principles of applied mathematics
APMA E4101x: Intro to dynamical systems
APMA E4301x: Numerical methods for partial
differential equations
APMA E4302x: Parallel scientific computing
PHYS G4019y: Mathematical methods of physics
• Fundamental Mathematics in Applied
Mathematics
This specialization is intended for
students who desire a more solid
foundation in the mathematical
methods and underlying theory. For
example, this specialization could
be followed by students with an
interest in graduate work in applied
mathematics.
MATH V3386x: Differential geometry
APMA E4101x: Intro to dynamical systems
APMA W4150x: Applied functional analysis
MATH W4032x: Fourier analysis
MATH W4062y: Modern analysis, II
SIEO W4150x,y:Intro to probability and
statistics (J)
PHYS W4386x-W4387y: Geometrical concepts
in physics
• Quantitative Biology
Traditionally biology was considered a
descriptive science in contrast to the
quantitative sciences that are based
on mathematics, such as physics. This
view no longer coincides with reality.
Researchers from biology as well as
from the physical sciences, applied
mathematics, and computer science
are rapidly building a quantitative base
of biological knowledge. Students can
acquire a strong base of knowledge in
quantitative biology, both biophysics
and computational biology, while
completing the applied physics or
applied mathematics programs.
Professional-level Course:
APPH E1300y: Physics of the human body
Recommended:
BIOL C2005x-C2006y: Intro biology, I and II
APMA E4400y: Intro to biophysical modeling
Other Technical Electives (a course
in at least two areas recommended):
Biological Materials
BIOL W4070x: The biology and physics of
single molecules
CHEN E4650x: Biopolymers
Biomechanics
BMEN E3320y: Fluid biomechanics (J)
BMEN E4300y: Solid biomechanics (J)
Genomics and Bioinformatics
BIOL W3037y: Whole genome bioinformatics (J)
ECBM E3060x: Intro to genomic information
science and technology (J)
CBMF W4761y: Computational genomics
Neurobiology
BIOL W3004x: Neurobiology, I (J)
BIOL W3005y: Neurobiology, II (J)
ELEN G4011x: Computational neuroscience
The second term of biology will be
considered a technical elective if a
student has credits from at least two
other of the recommended courses in
quantitative biology at the 3000 level
or above.
• Scientific Computation and
Computer Science
Advanced computation has become a
core tool in science, engineering, and
mathematics and provides challenges
for both physicists and mathematicians.
Courses that build on both
practical and theoretical aspects of
computing and computation include:
MATH V3020x: Number theory and cryptography (J)
COMS W3137x,y: Data structures and algorithms
(or COMS W3139y:
Honors data structures and
algorithms) (J)
COMS W3157x,y: Advanced programming (J)
COMS W3203x,y: Discrete mathematics: intro
to combinatorics and graph
theory (J)
COMS W4203y: Graph theory
APMA E4300y: Intro to numerical methods
APMA E4301: Numerical methods for partial
differential equations
AMCS E4302: Parallel scientific computing
COMS W4701x,y: Artificial intelligence
COMS W4771y: Machine learning
• Solid-State Physics
Much of modern technology is based
on solid-state physics, the study of solids
and liquids. Courses that will build a
strong base for a career in this area are:
PHYS W3083y: Electronics laboratory (J)
MSAE E3103x: Elements of material science (J)
ELEN E3106x: Solid-state devices and
materials (J)
PHYS G4018y: Solid-state physics
MSAE E4206x: Electronic and magnetic
properties of solids
MSAE E4207y: Lattice vibrations and crystal
defects
Undergraduate Program
in Materials Science and
Engineering
See page 169.
Graduate Programs
Financial aid is available for students
pursuing a doctorate. Fellowships,
scholarships, teaching assistantships,
and graduate research assistantships
are awarded on a competitive basis. The
Aptitude Test of the Graduate Record
Examination is required of candidates
for admission to the department and for
financial aid; the Advanced Tests are
recommended.
M.S. Program in Applied Physics
The program of study leading to the
degree of Master of Science, while
emphasizing continued work in basic
physics, permits many options in
several 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
engineering 2011–2012