CURRENT REQUIREMENTS FOR GRADUATE DEGREES IN PHYSICS
No student may become a candidate for the Doctor of
Philosophy (Ph.D.) degree without first fulfilling the requirements for the
Master of Arts (M.A.) and Master of Philosophy (M.Phil.) degrees at
Columbia. A satisfactory rate of progress is required at all
times. A student whose progress is insufficient may at any time be
requested to withdraw.
The following represents the obligation and requirements for students who
wish to obtain the Ph.D. degree at Columbia. Please retain these
guidelines for reference throughout your program of studies.
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MASTER OF ARTS DEGREE (M.A.)
This degree is a prerequisite for the
M.Phil. and Ph.D. degrees, unless a student has been awarded two Residence
Units of advanced standing.
POINTS OF LETTER-GRADE CREDIT: 30; at least
24 within the department. No credit is granted for work completed
at other universities.
PROGRAM OF STUDY: 15 points of
physics courses numbered 6000 or higher, with an overall performance
satisfactory to the Committee on Graduate Work. The courses are to
be chosen in consultation with the student’s academic advisor, to insure
knowledge of classical and quantum physics.
RESIDENCE UNITS: 2 (minimum).
Any student who fails to complete the requirements for the MA degree
within four consecutive terms (not counting summer terms) must obtain permission
from the department chair in order to continue work into fifth term.
LANGUAGE EXAMINATION: None
AN APPLICATION IS REQUIRED FOR THE AWARD OF THE M.A. DEGREE.
See Lalla Grimes for the MA Application form.
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MASTER OF PHILOSOPHY DEGREE (M.Phil.)
This degree is a prerequisite for the Ph.D. degree and will
be conferred upon certification by the department.
Typical length of
program:
|
Three years, including the time spent for the
M.A.degree.
|
Examination:
|
Qualifying Examination. |
Languages:
|
None.
|
Residence Units:
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Six full-time, including the two earned for the
M.A. degree. |
Points of credit:
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30 earned for the M.A. degree; none if the student has been
awarded two Residence Units of advanced standing. |
Required Courses:
|
See the list of required courses below.
|
Qualifying Examination
The qualifying examination is taken by all students without
exception, after no more than one term of residence. The
examination consists of two parts: the written part is given in three sections
in early January – Section I covers Classical Physics, Section 11 covers Modern
Physics and Section III covers General Physics including contemporary research
and order of magnitude estimate. The written exams are followed
after approximately one week with an oral interview in which each student meets
with three faculty members to go over the questions done on the written exams
and to discuss research plans.
The material covered in the Physics Qualifying Examination is
at the level of advanced undergraduate courses. It is intended
that students will use their first semester in the program to review their
overall knowledge of undergraduate physics and to fill in any gaps in their
knowledge. The Qualifying Examination is intended as a diagnostic
tool to help the faculty and the students know where there may be preparation
gaps and allow these to be addressed before moving on to research.
The Department relies on filtering that is done pre-admission by the
Graduate Admissions Committee. Our experience is that the
admissions process successfully identifies students with appropriate preparation
so that the Qualifying Examination can be relied on as a fine-tuning diagnostic
tool NOT a filter.
Following the oral exams, the faculty meets to consider for
each student the results of the qualifying examination, the student’s academic
record to date and other available information. These criteria
determine whether to permit a student to continue work toward the doctorate.
Each student will then be placed in a category:
Pass……………… qualified
to continue in doctoral program
Conditional Pass …decision withheld pending
completion of specific course work
Retake Exam ……must repeat the examination
again when it is next given
Fail………………. cannot repeat the
examination and must terminate
The results of the meeting are made available to the students
shortly after the meeting by the Physics Director of Graduate Studies. Generally
about 80% of the students pass the exam on the first try.
For students that do not pass on their first try, they are
automatically allowed to take the exam the following year. Based
on the results of the qualifying exam, in some cases students may
be asked to either: (a) retake specific portions of the written exam, (b) retake
the entire exam or (c) take advanced undergraduate courses in areas where the
faculty have found weaknesses in preparation.
Generally, if a student fails to pass the exam on a second
try, they will not be allowed to continue on to a PhD. They will be allowed to
complete the spring semester, giving them the opportunity to consider their
future options. In exceptional cases a student may be allowed to take the exam
for a third time.
Copies of examinations given in previous years can be
obtained in Room 704. From these, students may judge the scope of
knowledge expected.
Required Courses for the M.Phil. Degree
All entering students are required to take the following
basic sequence of courses during the first two academic 
years (minimum passing grade is B-):
I ) Five core courses - All four of the following core
courses:
Electromagnetic Theory (PHYS G6092)
Quantum Mechanics I and II (PHYS G6037, G6038)
Statistical Mechanics (G6036)
and one of the following:
Quantum Field Theory (PHYS G6047) or
Classical Waves (PHYS G6094) new
II) Two field-specific courses, chosen from the list below
with the assistance of a faculty adviser. Normally, both courses
will be in the same field. Note that some course are listed both here and in i)
above. In case of overlap, one course may fill both requirements
but does not count twice toward the total number of courses required for the
M.Phil.
Astrophysics I (PHYS G6011)
Astrophysics II (PHYS G6012)
Physical Cosmology (PHYS G6010)
Condensed Matter Physics I (PHYS G6082)
Condensed Matter Physics II (PHYS G8083)
Quantum Field Theory I (PHYS G6047)
Particle Physics I (PHYS G8069)
General Relativity (PHYS G8040)
Classical Theory of Waves (PHYS G6094)
Students who have previously mastered the equivalent material
in G6092 and/or G6037-G6038 may elect to fulfill these requirements through
course examination alone. Placement examinations to exempt out of
these courses are offered at the beginning of the Fall term.
III) Additional Courses
Any course chosen from the 6000 and 8000 level offerings of
the Physics, Astronomy, Applied Physics, Electrical Engineering, Chemistry and
Biology Departments may be taken to bring a student’s point total up to at least
the 30 points required by the University. In addition to the
courses listed in categories I and II above, the Physics Department may offer
the following 6000 and 8000 level courses:
-Nuclear Physics (G6040)
-Experimental Methods for Nuclear, Particle and
Astrophysics (G6042)
-Particle Phenomenology (G6050)
- Laser Physics (G6060)
-Biological Physics (G6070)
-Scientific Computing (G6080)
-Solid State Physics (G6081)
-Advanced Statistical Mechanics (G8036)
-Quantum Field Theory II (G8048)
-Quantum Field Theory III (G8049)
-Special Topics: Condensed Matter Physics
(G8066)
Students who have previously mastered the equivalent material
in G6092 and/or G6037-G6038 may elect to fulfill these requirements through
course examination alone. Placement examinations to exempt out of
these courses are offered at the beginning of the Fall term.
Teaching
Teaching is the principal method of support for first and second year
graduate students, who are appointed as Teaching Fellows. Most
assignments are to teach small laboratory sections or problem sessions in
elementary courses. In general, this program concentrates on
teaching in the first two years, while the student is taking graduate
courses. The maximum teaching assignment for a Faculty Teaching
Fellow is approximately four contact hours per week for four terms.
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DOCTOR OF PHILOSOPHY DEGREE (Ph.D)
The requirements for the Ph.D. degree, except for the
dissertation, are given above as M.Phil requirements.
Research
Research for the dissertation is a particularly important
part of a student’s training. Topics for research may be in either
experimental or theoretical physics. Even before taking the
Physics Qualifying Examination, a student should attend department Colloquia and
research group seminars in which new findings by various research groups of the
department are discussed. In this way, an uncommitted student may
learn of problems or areas of research of particular interest and challenge.
Graduate students who have passed the Qualifying Examination
are strongly urged to find a sponsor for doctoral research by the end of their
second year of residence.
A student and his or her sponsor decide upon a suitable
problem, and arrangements are made for space and other necessary physical
facilities. Students are required to find a sponsor by the end of
the fourth term. Any student unable to find a sponsor in this time
may be informed that they will not be admitted to a third year of graduate
study.
Students who wish to do their research in theoretical physics
are urged to complete the basic graduate courses as soon as possible to allow
for the inclusion of advanced and specialized theoretical course work in the
early part of the research program. Only those students with
special talents for theoretical work are encouraged to specialize in
theory. A strong academic record does not by itself insure success
in theoretical physics. Students who wish to undertake theoretical
research must submit their names to the Committee on Theoretical Physics
(notices about this are posted after each administration of the Qualifying
Examination).
Students who wish to undertake research outside the
department must obtain the approval of the Director of Graduate Studies.
Seven Year Limit
Candidates for the Ph.D degree must complete all requirements
including examinations and the defense of the dissertation within no more than
seven years of their first registration in the Graduate School of Arts and
Sciences. If a student receives two Residence Units of advanced
standing, all degree requirements must be completed within six years.
Extension of the time limit will be granted only on the
recommendation of the student’s sponsor and the department chairman to the Dean
when special circumstances warrant. Such extensions are initiated
by submitting to the department chairman a schedule of work in progress and a
schedule for completion.
AN APPLICATION IS REQUIRED FOR THE AWARD OF THE M.PHIL.
DEGREE. See the Administrative Coordinator for the M.Phil. Application
form.
THE DISSERTATION
The doctoral dissertation should provide clear and literate
evidence that the candidate has successfully completed or made a substantial
contribution to some original research. The aim of the research
should be formulated in a manner which clearly indicates its significance and
its relationship to the already existing body of knowledge in the particular
field of research and, where relevant, to the wider field of physics.
In the account of the research, there should be adequate explanation of
the particular problems and difficulties encountered, and of the manner in which
these were overcome. The achievement of the research, both in
relation to the original aims and the possible future developments of the
subject, should be dealt with explicitly. The dissertation should
contain adequate reference to the literature of the subject, but should
nevertheless be intelligible, in principles if not details, to a well-informed
physicist who is not necessarily a specialist in the candidate’s own
field. The dissertation will accordingly be a self-contained,
perhaps rather extended document, which has been written by the student.
Joint papers are not acceptable in fulfillment of the dissertation
requirement.
DEPARTMENTAL DEFENSE FOR THOSE WORKING WITH NON-PHYSICS FACULTY
ADVISORS
If a candidate is working with a research advisor outside the Physics
Department, an additional departmental defense exam is required.
When the dissertation is completed, the candidate will present a copy to
each member of his/her departmental defense committee. In the
department defense the student must demonstrate (a) thorough mastery of the
elementary aspects and fundamental principles of his/her field, (b) possession
of the theoretical background necessary for intelligent evaluation and analysis
of his/her research, and (c) acquaintance with the current status of research in
his/her field. The department defense is also attended by the
student’s faculty advisor. At the time of the oral examination,
the committee will either approve the dissertation or indicate the alterations
it requires. Approval qualifies the student for admission to the University
defense examination.
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