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Scientific Computing Group
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Department of Computer Science
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University of Illinois at Urbana-Champaign
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Numerical Analysis PhD Qualifying Examination
General Description
The Numerical Analysis PhD Qualifying Examination (NA Qual) is
intended to determine whether a student is qualified to begin
research toward a PhD dissertation in the general area of numerical
analysis. The NA Qual also enforces a breadth requirement in
numerical analysis. The format is a 90-minute oral examination in
which a committee of three faculty members asks the student questions
on any topic listed in the examination
syllabus. The student is expected to be able to supply any
requested details, such as proofs and derivations, on the whiteboard
without consulting any notes or references.
Prior to taking the Qual, the student must submit a written statement
(one to two pages) describing his or her academic background,
technical interests, experience, intended area of research
specialization, and general academic plans. The student begins
the examination with a brief (five to ten minute) oral summary of
his or her research interests. The committee may ask a few questions
specific to the student's stated interests, but by far the bulk of
the examination consists of general questions drawn from the material
listed in the examination syllabus.
There are numerous facts and techniques that should be known by
every PhD graduate who claims a research interest in numerical
analysis. A 90-minute examination is inadequate to test all of
these, but a reasonable subset is to focus on the material typically
covered in the courses CS 450 and CS 455, which serves as the basis
for the detailed examination syllabus.
Note that the student is responsible for all of the topics in
the examination syllabus, even if some may
have been omitted from a particular offering of CS 450 or 455.
Advice to the Student
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You should take both CS 450 and CS 455 unless you have already taken
equivalent courses elsewhere and done well in them.
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You should obtain several intermediate-level books on numerical
analysis and use them to flesh out your knowledge of the topics
listed in the syllabus (specific suggestions are given in the
accompanying reading list). There
is often more than one way to express various definitions, theorems,
and algorithms, and you should find ways of expressing them that
you are comfortable with.
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You should confer with your faculty advisor, who can give you a
realistic assessment of your potential as well as specific advice
on exam preparation.
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You should practice as much as possible by answering the sample
questions and questions from previous NA Qual exams, and by conducting
mock quals with fellow students and/or your advisor. The latter
will give you experience answering questions "on your feet" in a
setting that approximates that of the actual exam, and will help you
become more comfortable with the exam format.
Scientific Computing Group,
Department of Computer Science,
University of Illinois at Urbana-Champaign,
201 N. Goodwin Ave., Urbana, IL 61801, USA.