Ph.D. Degree Requirements

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 B.S.; 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 (555 and 557)
  • Analysis (535, and one of 531, 536)
and one exam from one of the following three areas:
  • Topology (521 and 528)
  • Combinatorics (two of 575, 576, 579)
  • Differential Equations (539, 540)
Course descriptions can be found in the online course catalog.

Preliminary exams are at a significantly higher level than M.S. 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.

ALGEBRA EXAM:
Groups and Fields I (555):
  1. Rotman, The Theory of Groups
  2. Hungerford, Algebra
  3. Dummit and Foote, Abstract Algebra
  4. Garling, A Course in Galois Theory
Rings (557):
  1. Dummit and Foote, Abstract Algebra
  2. Hungerford, Algebra

ANALYSIS EXAM:
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 EXAM:
Topology (521 and 528):
  1. Christenson and Voxman, Aspects of Topology (2nd ed.)
  2. Munkres, Topology (2nd ed.)
  3. Boothby,  An Introduction to Differentiable Manifolds and Riemannian
    Geometry

COMBINATORICS EXAM:
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

Combinatorics (579):
  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.

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.