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

approval is obtained from the department.
A number of approved technical
electives are listed in the section on specialty
areas following. The remaining
points of electives are intended primarily
as an opportunity to complete the fouryear,
27-point nontechnical requirement,
but any type of course work can satisfy
them.
UNDERGRADUATE PROGRAM
IN APPLIED MATHEMATICS
The applied mathematics program is
flexible and intensive. A student must
take the required courses listed below,
or prove equivalent standing, and then
may elect the other courses from mathematics,
computer science, physics,
Earth and environmental sciences,
biophysics, economics, business and
finance, or other application fields. Each
student tailors his or her own program in
close collaboration with an adviser. He
or she must also register for the applied
mathematics seminar during both the
junior and senior years. During the junior
year, the student attends the seminar
lectures for 1 point; during the senior
year, he or she attends the seminar
lectures as well as tutorial problem
sessions for 4 points.
While it is common for students
in the program to go on to graduate
school, many graduating seniors will
find employment directly in industry,
government, education, or other fields.
Of the 33 points of elective content
in the third and fourth years, at least 21
points of technical courses approved by
the adviser must be taken. The remaining
points of electives are intended primarily
as an opportunity to complete the fouryear,
27-point nontechnical requirement,
but any type of course work can satisfy
them.
UNDERGRADUATE DOUBLE
MAJOR IN APPLIED PHYSICS
AND APPLIED MATHEMATICS
Students satisfy all requirements for
both majors, except for the seminar
requirements. They are required to take
both senior seminars, APMA E4903 and
APPH E4903 (taking one in the junior
year and one in the senior year, due to
timing conflicts), but not the junior seminars,
APMA E4901 and APPH E4901.
A single course may be used to fulfill a
requirement in both majors. Students
must maintain a GPA at or above 3.75,
and must graduate with at least 143
points, 15 above the regular 128-point
requirement. These extra 15 points
should be technical electives appropriate
for one or both majors.
To apply, a student first obtains the
approval of both the general undergraduate
AP adviser and the general undergraduate
AM adviser, and then the
approval of the Dean.
SPECIALTY AREAS IN APPLIED
PHYSICS AND APPLIED
MATHEMATICS
Both applied physics and applied mathematics
students can focus their technical
electives and develop a strong base
of knowledge in a specialty area. There
is no requirement to focus electives, so
students may take as many or as few of
the recommended courses in a specialty
area as is appropriate to their schedules
and interests. Some specialties are given
below, but this is not an exclusive list
and others can be worked out in coordination
with the student’s adviser. The
courses that are often taken, or in some
cases need to be taken, in the junior
year are denoted with a “J.”
Technical Electives
• Applications of Physics
Courses that will give a student a
broad background in applications of
physics are:
MSAE E3103x: Elements of materials science (J)
ELEN E3000x: Introduction to circuits, systems,
and electronics (J)
APPH E4010x: Introduction to nuclear science
APPH E4110x: Modern optics
APPH E4112y: Laser physics
APPH E4200x: Physics of fluids
APPH E4301y: Introduction to plasma physics
PHYS G4018y: Solid-state physics
APMA E4101y: Introduction to dynamical
systems
• Earth and Atmospheric Sciences
The Earth sciences provide a wide
range of problems of interest to physicists
and mathematicians ranging
from the dynamics of the Earth’s
climate to earthquake physics to
dynamics of Earth’s deep interior. The
Lamont-Doherty Earth Observatory,
which is part of Columbia University,
provides enormous resources for
students interested in this area.
A. ATMOSPHERE, OCEANS AND CLIMATE
APPH E4200x: Physics of fluids
APPH E4210y: Geophysical fluid dynamics
EESC W4008y: Introduction to atmospheric
science
ESC W4925x: Introduction to physical
oceanography
EES W4930y: Earth’s oceans and atmosphere
B. SOLID EARTH GEOPHYSICS
APPH E4200x: Physics of fluids
EESC W4941y: Principles of geophysics
EESC W4001x: Advanced general geology
EESC W4113x: Introduction to mineralogy
EESC W4701y: Introduction to igneous
petrology
EESC W4950x: Mathematical methods in
the Earth sciences
(See also courses listed under
Scientific Computation and Computer
Science, page 60)
• Basic Physics and Astrophysics
Fundamental physics and astrophysics
can be emphasized. Not only is astrophysics
providing a deeper understanding
of the universe, but it is also
testing the fundamental principles of
physics.
PHYS W3002y: From quarks to the cosmos:
applications of modern physics
ASTR C3601x: General relativity, black holes,
and cosmology (J)
ASTR C3602y: Physical cosmology and extragalactic
astronomy (J)
APMA E4101x: Introduction to dynamical
systems
ASTR G4001y: Astrophysics, I
• 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.
A. ECONOMICS
ECON W3211x,y: Intermediate microeconomics
(J)
ECON W3213x,y: Intermediate macroeconomics
(J)
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SEAS 2008–2009