Steps to Achieving PhD Candidacy

Doctoral students who successfully complete their prelim examinations and obtain the written approval of a faculty member to serve as the thesis advisor are formally recommended to the Graduate College as doctoral candidates.

Candidacy Requirements = Prelims + Minor Sequence + Advisor

1. Two written prelims must be selected from the list of approved written prelims outlined below. Each written prelim is based on a designated sequence of two graduate courses and must be passed with qualifying scores. Prelim scores are assigned on the basis of 1 (best), 2, 3, and 5 (fail). The sum of the scores of the two written prelims may not exceed 4. Prelim exams are offered each spring semester during the 2 weeks following finals week.

2. Students declare their minor sequence on the Minor Sequence Request form, consists of a sequence of two 500-level courses described in the Graduate Handbook as leading to a written prelim. The minor sequence may not overlap an area in which a written prelim is taken. Doctoral students may satisfy the minor sequence in one of two ways, either by completing the sequence of two 500-level courses leading to the prelim OR by passing a third written prelim.

The two course grades earned in the minor sequence are converted into a numerical score as follows:

Two A’s = 1
One A and One B = 2
Two B’s = 3      
All other combinations = 5

3. The combined preliminary exams plus minor sequence score must be 6 or less.

4. PhD students in the Probability and Statistics program must pass an oral prelim exam, which should be done soon after successfully completing the two written prelims and the minor sequence. To arrange a date for the oral prelim exam, students must submit the Committee Recommendation form, endorsed by the thesis advisor, to the Graduate Studies office at least 30 days prior to the oral prelim exam. The committee consists of five members; three members must be UIC Graduate Faculty with full membership, and two must be tenured. The committee vote is pass or fail.


Pure and Applied Mathematics


  • MATH 516        Second Course in Abstract Algebra I
  • MATH 517        Second Course in Abstract Algebra II


  • MATH 533        Real Analysis I
  • MATH 535        Complex Analysis I

Geometry and Topology

  • MATH 547        Algebraic Topology I
  • MATH 549        Differentiable Manifolds I


  • MATH 502        Mathematical Logic plus one of the following:
  • MATH 504        Set Theory
  • MATH 506        Model Theory I
  • MATH 511        Descriptive Set Theory

Differential Equations

  • MATH 576        Classical Methods of Partial Differential Equations
  • MATH 585        Ordinary Differential Equations

Methods in Applied Analysis

  • MATH 539        Functional Analysis I
  • MCS 571            Numerical Analysis of Partial Differential Equations

Number Theory

  • MATH 514        Number Theory I
  • MATH 515        Number Theory II

Mathematical Computer Science

Combinatorics: Two of the following courses

  • MCS 521            Combinatorial Optimization
  • MCS 582            The Probabilistic Method
  • MCS 583            Extremal Combinatorics
  • MSC 584            Enumerative Combinatorics
  • MSC 591            Advanced Topics in Combinatorial Theory

Algorithms and Complexity: Two of the following courses

  • MCS 501           Computer Algorithms II
  • MCS 521            Combinatorial Optimization
  • MCS 541            Computational Complexity
  • MCS 548            Mathematical Theory of Artificial Intelligence
  • MCS 549            Mathematical Foundations of Data Science
  • MCS 590            Advanced Topics in Computer Science

Computational Science:  Two of the following courses

  • MCS 507            Mathematical, Statistical and Scientific Software
  • MCS 563            Analytic Symbolic Computation
  • MCS 571            Numerical Analysis for Partial Differential Equations
  • MCS 572            Introduction to Supercomputing

Probability and Statistics

Probability and Statistics (required for all Statistics PhD students)

  • STAT 501          Probability Theory I
  • STAT 511          Advanced Statistical Theory I

Linear Inference, Sampling, and Design

  • STAT 521           Linear Statistical Inference plus one of the following:
  • STAT 522           Multivariate Statistical Analysis
  • STAT 531           Sampling Theory I
  • STAT 535           Optimal Design Theory I