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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60<br />
programs is a strong base for a career<br />
in business or finance.<br />
A. ECONOMICS<br />
ECON W3211x,y: Intermediate microeconomics<br />
(J)<br />
ECON W3213x,y: Intermediate macroeconomics<br />
(J)<br />
B. INDUSTRIAL ENGINEERING AND<br />
OPERATIONS RESEARCH<br />
IEOR E4003x: Industrial economics<br />
IEOR E4201x: The engineering of<br />
management, I<br />
IEOR E4202y: The engineering of<br />
management, II<br />
C. FINANCE<br />
SIEO W4150x,y: Probability and statistics (J)<br />
IEOR E4106y: Introduction to operations<br />
research: stochastic models<br />
(J)<br />
IEOR E4700x: Introduction to financial<br />
engineering<br />
MATH W4071x: Mathematics of finance<br />
ECIE W4280: Corporate finance<br />
• Mathematics Applicable to Physics<br />
Applied physics students can specialize<br />
in the mathematics that is applicable<br />
to physics. This specialization is<br />
particularly useful for students interested<br />
in theoretical physics.<br />
MATH W4386x-W4387y: Geometrical concepts<br />
in physics<br />
MATH W4032x: Fourier analysis<br />
MATH W4062y: Mathematical analysis, II<br />
• Quantitative Biology<br />
Traditionally biology was considered a<br />
descriptive science in contrast to the<br />
quantitative sciences that are based on<br />
mathematics, such as physics. This<br />
view no longer coincides with reality.<br />
Researchers from biology as well as<br />
from the physical sciences, applied<br />
mathematics, and computer science<br />
are rapidly building a quantitative base<br />
of biological knowledge. Students can<br />
acquire a strong base of knowledge in<br />
quantitative biology, both biophysics<br />
and computational biology, while completing<br />
the applied physics or applied<br />
mathematics programs.<br />
PROFESSIONAL-LEVEL COURSE:<br />
APPH E1300y: Physics of the human body<br />
RECOMMENDED:<br />
BIOL C2005x-C2006y: Introduction to molecular<br />
and cellular biology,<br />
I & II<br />
APMA E4400y: Introduction to biophysical<br />
modeling<br />
OTHER TECHNICAL ELECTIVES (A COURSE<br />
IN A LEAST TWO AREAS RECOMMENDED):<br />
• Scientific Computation and<br />
Computer Science<br />
Advanced computation has become a<br />
core tool in science, engineering, and<br />
mathematics and provides challenges<br />
for both physicists and mathematicians.<br />
Courses that build on both<br />
practical and theoretical aspects of<br />
computing and computation include:<br />
APMA E4300y: Introduction to numerical<br />
methods<br />
APMA E4301x: Numerical methods for partial<br />
differential equations<br />
AMCS E4302: Parallel scientific computing<br />
MATH V3020x: Number theory and cryptography<br />
(J)<br />
COMS W3137x,y: Data structures and algorithms<br />
(or COMS W3139y:<br />
Honors data structures and<br />
algorithms) (J)<br />
COMS W3157x,y: Advanced programming (J)<br />
COMS W3203x,y: Discrete mathematics: introduction<br />
to combinatorics<br />
and graph theory (J)<br />
COMS W4203y: Graph theory<br />
COMS W4701x,y: Artificial intelligence<br />
COMS W4771y: Machine learning<br />
• Solid-State Physics<br />
Much of modern technology is based on<br />
solid-state physics, the study of solids<br />
and liquids. Courses that will build a<br />
strong base for a career in this area are:<br />
APMA E4101x: Introduction to dynamical<br />
systems<br />
APMA E4001y: Principles of applied mathematics<br />
APMA E4301x: Numerical methods for partial<br />
differential equations<br />
APMA E4302x: Parallel scientific computing<br />
MATH V3386x: Differential geometry<br />
MATH W4386x-W4387y: Geometrical concepts<br />
in physics<br />
• Fundamental Mathematics in<br />
Applied Mathematics<br />
This specialization is intended for students<br />
who desire a more solid foundation<br />
in the mathematical methods and<br />
underlying theory. For example, this<br />
specialization could be followed by<br />
students with an interest in graduate<br />
work in applied mathematics.<br />
APMA E4101x: Introduction to dynamical<br />
systems<br />
APMA E4150x: Applied functional analysis<br />
SIEO W4150x,y: Introduction to probability<br />
and statistics (J)<br />
MATH V3386x: Differential geometry<br />
A. BIOLOGICAL MATERIALS<br />
CHEN E4650x: Biopolymers<br />
BIOL W4070x: The biology and physics<br />
of single molecules<br />
B. BIOMECHANICS<br />
BMEN E3320y: Fluid biomechanics (J)<br />
BMEN E4300y: Solid biomechanics (J)<br />
C. GENOMICS AND BIOINFORMATICS<br />
ECBM E3060x: Introduction to genomic<br />
information science and<br />
technology (J)<br />
BIOL W3037y: Whole genome bioinformatics (J)<br />
CBMF W4761y: Computational genomics<br />
D. NEUROBIOLOGY<br />
BIOL W3004x: Cellular and molecular<br />
neurobiology (J)<br />
BIOL W3005y: Systems neurobiology (J)<br />
ELEN G4011x: Computational neuroscience<br />
The second term of biology will be considered<br />
a technical elective if a student<br />
has credits from at least two other of the<br />
recommended courses in quantitative<br />
biology at the 3000 level or above.<br />
MSAE E3103x: Elements of material science (J)<br />
ELEN E3106x: Solid-state devices and<br />
materials (J)<br />
MSAE E4206x: Electronic and magnetic<br />
properties of solids<br />
PHYS G4018y: Solid-state physics<br />
MSAE E4207y: Lattice vibrations and crystal<br />
defects<br />
PHYS W3083y: Electronics laboratory (J)<br />
UNDERGRADUATE PROGRAM<br />
IN MATERIALS SCIENCE AND<br />
ENGINEERING<br />
See page 168.<br />
GRADUATE PROGRAMS<br />
Financial aid is available for students<br />
pursuing a doctorate. Fellowships,<br />
scholarships, teaching assistantships,<br />
and graduate research assistantships<br />
are awarded on a competitive basis. The<br />
Aptitude Test of the Graduate Record<br />
Examination is required of candidates<br />
for admission to the department and for<br />
financial aid; the Advanced Tests are<br />
recommended.<br />
<strong>SEAS</strong> <strong>2009</strong>–<strong>2010</strong>