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

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E4134, E4135, and E4136
f. All 3000-level or higher courses
in the Earth and Environmental
Engineering program
2. Courses from the following
departments are not allowed to
count toward the required 48 units of
engineering courses:
a. Department of Applied Physics and
Applied Mathematics
b. Department of Computer Science
c. Department of Industrial
Engineering and Operations
Research
d. Program of Materials Science and
Engineering
The cell and tissue engineering
track requires 4.5 of the required 9
points of technical electives to be
from engineering courses; in the
biomechanics track, 2.5 points of
technical electives must be from
engineering courses; in the imaging
track, the requirements satisfy the 48
points of engineering content. Once 48
points of engineering-content technical
electives are satisfied, students may
choose any course above the 3000
level in Columbia Engineering as well as
biology, chemistry, and biochemistry as
technical electives.
The accompanying charts describe
the eight-semester degree program
schedule of courses leading to the
bachelor’s degree in biomedical
engineering.
Graduate Programs
The graduate curriculum in biomedical
engineering employs the same three
tracks that compose the undergraduate
curriculum: biomechanics, cell and
tissue engineering, and biosignals and
biomedical imaging. Initial graduate study
in biomedical engineering is designed
to expand the student’s undergraduate
preparation in the direction of the track
chosen. In addition, sufficient knowledge
is acquired in other areas to facilitate
broad appreciation of problems and
effective collaboration with specialists
from other scientific, medical, and
engineering disciplines. The Department
of Biomedical Engineering offers a
graduate program leading to the Master
of Science degree (M.S.), the Doctor
of Philosophy degree (Ph.D.), and the
Doctor of Engineering Science degree
(Eng.Sc.D.). Applicants who have a
Master of Science degree or equivalent
may apply directly to the doctoral degree
program. All applicants are expected
to have earned the bachelor’s degree
in engineering or in a cognate scientific
program. The Graduate Record Examination
(General Test only) is required of
all applicants. Students whose bachelor’s
degree was not earned in a country
where English is the dominant spoken
language are required to take the TOEFL
test. M.S. degree candidates must reach
level 8 on the English Placement Test
(EPT) offered by Columbia’s American
Language Program (ALP). Doctoral
degree candidates must attain level 10
on the English Placement Test (EPT).
The ALP examination must be taken
at orientation upon arrival. It is strongly
recommended the students enroll in
an appropriate ALP course if they have
not achieved the required proficiency
after the first examination. In addition,
the individual tracks require applicants
to have taken the following foundation
courses:
• Biomechanics: One year of biology
and/or physiology, solid mechanics,
statics and dynamics, fluid mechanics,
ordinary differential equations.
• Cell and Tissue Engineering: One
year of biology and/or physiology,
one year of organic chemistry or
biochemistry with laboratory, fluid
mechanics, rate processes, ordinary
differential equations.
• Biosignals and Biomedical Imaging:
One year of biology and/or physiology
and/or biochemistry. Linear algebra,
ordinary differential equations, Fourier
analysis, digital signal processing.
Applicants lacking some of these
courses may be considered for
admission with stipulated deficiencies
that must be satisfied in addition to the
requirements of the degree program.
Columbia Engineering does not admit
students holding the bachelor’s degree
directly to doctoral studies; admission
is offered either to the M.S. program or
to the M.S. program/doctoral track. The
Department of Biomedical Engineering
also admits students into the 4-2
program, which provides the opportunity
for students holding a bachelor’s degree
from certain physical sciences to receive
the M.S. degree after two years of study
at Columbia.
Curriculum and Exam
Requirements
Master’s Degree
In consultation with an appointed faculty
adviser, M.S. students should select
a program of 30 points of credit of
graduate courses (4000 level or above)
appropriate to their career goals. This
program must include the course in
computational modeling of physiological
systems (BMEN E6003); two semesters
of BMEN E9700: Biomedical engineering
seminar; at least four other biomedical
engineering courses; and at least one
graduate-level mathematics course.
Students with deficiency in physiology
course work are required to take the
BMEN E4001-E4002 sequence before
taking BMEN E6003. Candidates must
achieve a minimum grade-point average
of 2.5. A thesis based on experimental,
computational, or analytical research
is optional and may be counted in lieu
of 6 points of course work. Students
wishing to pursue the Master’s Thesis
option should register for BMEN E9100
Master’s Research and consult with
their BME faculty adviser.
Doctoral Degree
Students admitted to the doctoral
degree program should select courses
to prepare for the doctoral qualifying
examination and register for research
rotations during the first two semesters
of graduate study. To facilitate future
collaboration with clinicians and
biomedical scientists, students are
encouraged to consider courses at
the Health Sciences campus or in the
Department of Biological Sciences.
Doctoral students must complete
a program of 30 points of credits
beyond the M.S. degree. The course in
computational modeling of physiological
systems (BMEN E6003) is required
for the doctoral program. At least
two graduate mathematics courses
must be taken, which may include the
mathematics course required for the
M.S. degree. Students must register for
BMEN E9700: Biomedical engineering
seminar and for research rotations during
the first two semesters of graduate study.
Remaining courses should be selected
in consultation with the student’s faculty
adviser to prepare for the doctoral
qualifying examination and to develop
expertise in a clearly identified area of
engineering 2011–2012