Ph.D. candidates must complete a minimum of 36 credits (12 courses)
of graduate mathematics at the 500 level (excluding Math 500, 510-519,
599, 600, seminars, and directed study). These may include graduate
courses taken for the M.S. degree. [Students with prior graduate work
at another university must take at least 18 credits (6 courses) of these
courses at the University of Idaho.] Note that the Graduate Catalog
requires a minimum of 78 credits beyond the BS; however, that number
can include Math 500, 599, 600, seminars, and directed study, as well
as 400 level math courses and some supporting courses from outside mathematics.
Preliminary Examinations: Three preliminary exams
must be passed. These cover
- Algebra (two of 551, 552, 553)
- Analysis (535, and one of 531, 536)
and one exam from one of the following three areas
- Topology (521 and 522)
- Combinatorics (two of 575, 576, 578)
- Differential Equations (539,540)
Preliminary exams are at a significantly higher level than MS exams.
When there is a choice of courses covered on a preliminary exam, the
student may choose which two courses the exam will cover. Note that
course work in the listed courses is not generally adequate preparation
for preliminary exams. Each exam is written and is 4.5 hours in length.
The following list of texts indicates the coverage on the different
exams. Students should be prepared for questions covering any topic
in the given texts.
Reading List for Preliminary Exams
(Students are advised to consult the professors making the exams to
confirm that the list is current.)
Groups (553):
1. Rotman, The Theory of Groups
2. Hungerford, Algebra
3. Dummit and Foote, Abstract Algebra
Rings (551):
1. Dummit and Foote, Abstract Algebra
2. Hungerford, Algebra
Fields (552):
1. Garling, A Course in Galois Theory
2. Hungerford, Algebra
3. Dummit and Foote, Abstract Algebra
Real Analysis (535):
1. Wheeden and Zygmund, Measure and Integral
2. Royden, Real Analysis
Probability (536):
1. Durrett, Probability: Theory and Examples
2. Billingsley, Probability and Measure
3. Chung, A Course in Probability Theory
Complex Analysis (531):
1. Conway, Functions of One Complex Variable
Topology (521 and 522):
1. Christenson and Voxman, Aspects of Topology (2nd ed.)
2. Munkres, Topology (2nd ed.)
Graph Theory I (575):
1. Bondy and Murty, Graph Theory with Applications
2. Chartrand and Lesniak, Graphs and Digraphs
3. West, Introduction to Graph Theory
Graph Theory II (576):
Same reading list as for 575
Combinatorial Optimization (578):
1. Hall, Combinatorial Theory
2. Bondy and Murty, Graph Theory with Applications
3. See instructor; this course can vary a lot and not all material is
in texts
- DIFFERENTIAL EQUATIONS EXAM:
Ordinary Differential Equations (539):
1. Perko, Differential Equations and Dynamical Systems
2. Hofbauer and Sigmund, Evolutionary Games and Population Dynamics
3. Hirsch and S. Smale, Differential Equations, Dynamical Systems,
and Linear Algebra
Partial Differential Equations (540):
1. Evans, Partial Differential Equations
2. McOwen, Partial Differential Equations
All three preliminary examinations must be passed no later than the
end the fourth year of graduate study (this includes years at other
universities). Moreover, the first attempt must be taken no later than
the end of the third year of graduate study. The three exams need not
all be passed at once. Prelims will be given according to the following
schedule:
·Beginning the second full week of classes of the fall semester.
·Beginning the third week prior to finals week of the spring
semester.
Foreign Language Proficiency: The department requires a reading
knowledge in one of the four languages: French, German, Russian, and
Chinese. This requirement is satisfied by translating a journal article
in the student’s area of interest.
Dissertation: The dissertation should contain original
research and constitute a significant contribution to knowledge in the
student’s field of study. Acceptability of the dissertation is
to be determined by the student’s major professor and graduate
committee.
