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

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undergraduate minors
Undergraduate minors are
designed to allow engineering
and applied science students
to study, to a limited extent, a discipline
other than their major. Besides
engineering minors offered by Columbia
Engineering departments, liberal arts
minors are available.
A minor requires at least 15 points
of credit, and no more than one course
can be taken outside of Columbia
or met through AP or IB credit. This
includes courses taken through study
abroad. In Engineering departments
with more than one major program,
a minor in the second program may
be permitted, if approved by the
department.
No substitutions or changes of any
kind from the approved minors are
permitted (see lists below). No appeal
for changes will be granted. Please
note that the same courses may not be
used to satisfy the requirements of more
than one minor. No courses taken for
pass/fail may be counted for a minor.
Minimum GPA for the minor is 2.0.
Departments outside the Engineering
School have no responsibility for
nonengineering minors offered by
Engineering.
For a student to receive credit for
a course taken while studying abroad,
the department offering the minor must
approve the course in writing, ahead of
the student’s study abroad.
Students must expect a course load
that is heavier than usual. In addition,
unforeseen course scheduling changes,
problems, and conflicts may occur. The
School cannot guarantee a satisfactory
completion of the minor.
Minor in Applied
Mathematics
Prospective students should consult
the first- and second-year requirements
for applied mathematics majors to
ensure that prerequisites for the applied
mathematics minor are satisfied in the
first two years.
Course work counting toward the
applied mathematics minor may not
include advanced placement credits.
Any substitutions for the courses listed
below require the approval of the applied
mathematics program adviser.
1. APMA E3101: Linear algebra (3)
or MATH V2010: Linear algebra (3)
2. APMA E3102: Partial differential equations (3)
or MATH V3028: Partial differential equations (3)
3–5. Three of the following courses:
APMA E4300: Intro to numerical methods (3)
APMA E4204: Func of complex variable (3)
APMA E4101: Intro to dynamical systems (3)
MATH V2500: Analysis and optimization (3)
SIEO W4105: Intro to probablity and statistics (3)
STAT W4107: Statistical inference (3)
or any other course designated APMA, MATH,
STAT, IEOR, or COMS that is approved by the
applied mathematics program adviser
Minor in Applied Physics
Prospective students should consult the
first- and second-year requirements for
applied physics majors to ensure that
prerequisites for the applied physics
minor are satisfied in the first two years.
Course work counting toward the
applied physics minor may not include
advanced placement credits.
1. APPH E4901: Problems in applied physics (1)
2. PHYS W3003: Mechanics (3)
3. APPH E3100: Intro to quantum mechanics (3)
4. APPH E3300: Applied electromagnetism (3)
5. MSAE E3111: Thermodynamics, kinetic theory,
and statistical mechanics (3)
6. Two of the following courses
APPH E4010: Intro to nuclear science (3)
APPH E4100: Quantum physics of matter (3)
APPH E4110: Modern optics (3)
APPH E4112: Laser physics (3)
APPH E4300: Applied electrodynamics (3)
APPH E4301: Intro to plasma physics (3)
Minor in Architecture
1. Studio: One of the following courses
ARCH V1020: Intro to architectural design and
visual culture (3)
ARCH V3101: Abstraction (4)
ARCH V3103: Perception (4)
2–4. History/theory courses (see Note below)
5. Elective: must be either an approved second
design studio or an additional history/theory
course
Note: A list of the approved history/theory
courses is available at the departmental
office each semester.
Minor in Art History
1–7. Seven courses in art history, covering
four of the following areas: (a) ancient
Mediterranean, (b) medieval Europe,
(c) Renaissance and baroque, (d) 18th,
19th, and 20th century, and (e) non-
Western
Minor in Biomedical
Engineering
The Biomedical Engineering program
offers a minor in one of three tracks: (I)
cellular engineering, (II) biomechanics,
and (III) biosignals and biomedical
imaging. Students who wish to get a
minor in biomedical engineering should
engineering 2011–2012