# PhD Candidacy

## Steps to Achieving PhD Candidacy Heading link

Doctoral students with an MS Degree or a High Pass on the MS exam 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*.

**PhD Candidacy Related Forms:**

Preliminary Exam Registration

Minor Sequence Request

PhD Advisor Request

Oral Exam Paperwork for Statistics

**PhD 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 and students should register by mid-April.

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. Request the written approval of a faculty member to serve as the thesis advisor

5. 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.

**APPROVED WRITTEN PRELIMS**

**Pure and Applied Mathematics**

**Algebra**

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

**Analysis**

- MATH 533 Real Analysis I
- MATH 535 Complex Analysis I

**Geometry and Topology**

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

**Logic**

- 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