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

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B. INDUSTRIAL ENGINEERING AND
OPERATIONS RESEARCH
IEOR E4003x: Industrial economics
IEOR E4201x: The engineering of
management, I
IEOR E4202y: The engineering of
management, II
C. FINANCE
SIEO W4150x,y: Probability and statistics (J)
IEOR E4106y: Introduction to operations
research: stochastic models
(J)
IEOR E4700x: Introduction to financial
engineering
MATH W4071x: Mathematics of finance
ECIE W4280: Corporate finance
• 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.
APMA E4101x: Introduction to dynamical
systems
APMA E4001y: Principles of applied mathematics
APMA E4301x: Numerical methods for partial
differential equations
APMA E4302x: Parallel scientific computing
MATH V3386x: Differential geometry
MATH W4386x-W4387y: Geometrical concepts
in 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.
APMA E4101x: Introduction to dynamical
systems
APMA E4150x: Applied functional analysis
SIEO W4150x,y: Introduction to probability
and statistics (J)
MATH V3386x: Differential geometry
MATH W4386x-W4387y: Geometrical concepts
in physics
MATH W4032x: Fourier analysis
MATH W4062y: Mathematical analysis, II
• 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: Introduction to molecular
and cellular biology,
I & II
APMA E4400y: Introduction to biophysical
modeling
OTHER TECHNICAL ELECTIVES (A COURSE
IN A LEAST TWO AREAS RECOMMENDED):
A. BIOLOGICAL MATERIALS
CHEN E4650x: Biopolymers
BIOL W4070x: The biology and physics
of single molecules
B. BIOMECHANICS
BMEN E3320y: Fluid biomechanics (J)
BMEN E4300y: Solid biomechanics (J)
C. GENOMICS AND BIOINFORMATICS
ECBM E3060x: Introduction to genomic
information science and
technology (J)
BIOL W3037y: Whole genome bioinformatics (J)
CBMF W4761y: Computational genomics
D. NEUROBIOLOGY
BIOL W3004x: Cellular and molecular
neurobiology (J)
BIOL W3005y: Systems neurobiology (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:
APMA E4300y: Introduction to numerical
methods
APMA E4301: Numerical methods for partial
differential equations
AMCS E4302: Parallel scientific computing
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: introduction
to combinatorics
and graph theory (J)
COMS W4203y: Graph theory
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:
MSAE E3103x: Elements of material science (J)
ELEN E3106x: Solid-state devices and
materials (J)
MSAE E4206x: Electronic and magnetic
properties of solids
PHYS G4018y: Solid-state physics
MSAE E4207y: Lattice vibrations and crystal
defects
PHYS W3083y: Electronics laboratory (J)
UNDERGRADUATE PROGRAM
IN MATERIALS SCIENCE AND
ENGINEERING
See page 166.
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
SEAS 2008–2009