Graduate Program in Mathematics

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Study Guides for Comprehensive Exams

Comprehensive exams for study purposes are posted here as soon after they have been given as is feasible. Comp exam dates, and sign-up form are available at www.math.illinois.edu/GraduateProgram/comp_signup.html.

Note:
1.  The comp exams for Math 500, 540 and 542 are offered each January, May and August. [Effective 2013.]

2. All other comp exams are offered only in the comp period immediately following the course. e.g. if Math 570 is taught in the Fall, then its comp exam will be offered in January, but not in May or August. [Effective 2013.]

3. The Math 500 exams from August 2012 and earlier are NOT a reliable guide to future exams, because the syllabus was revised substantially in Fall 2012.

January 2014
Math 500. Abstract Algebra I
Math 518. Differentiable Manifolds
Math 540. Real Analysis
Math 542. Complex Analysis
Math 553. PDEs
Math 570. Logic

May 2014
 

August 2014
 

January 2013
Math 500. Abstract Algebra I
Math 540. Real Analysis
Math 542. Complex Analysis

May 2013
Math 500. Abstract Algebra I
Math 540. Real Analysis
Math 542. Complex Analysis

August 2013
Math 500. Abstract Algebra I
Math 540. Real Analysis
Math 542. Complex Analysis

January 2012
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 518. Differentiable Manifolds
Math 525. Topology
Math 530. Algebraic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 570. Logic
Math 580. Combinatorics

 

May 2012
Math 501. Abstract Algebra II
Math 525. Topology
Math 542. Complex Analysis

 

August 2012
Math 500. Abstract Algebra I
Math 518. Differentiable Manifolds
Math 542. Complex Analysis
Math 561. Probability
Math 570. Logic
Math 580. Combinatorics

January 2011
Math 500. Abstract Algebra I
Math 525. Topology
Math 540. Real Analysis
Math 542. Complex Analysis

 

May 2011
Math 501. Abstract Algebra II
Math 540. Real Analysis
Math 542. Complex Analysis
Math 561. Probability

 

August 2011
Math 500. Abstract Algebra I
Math 518. Differentiable Manifolds
Math 525. Topology
Math 540. Real Analysis
Math 542. Complex Analysis
Math 570. Logic

January 2010
Math 500. Abstract Algebra I
Math 518. Differential Manifolds
Math 525. Topology
Math 540. Real Analysis
Math 542. Complex Analysis
Math 550. Ordinary Differential Equations

 

May 2010
Math 501. Abstract Algebra II
Math 540. Real Analysis
Math 542. Complex Analysis
Math 553. PDEs
Math 561. Probability

 

August 2010
Math 500. Abstract Algebra I
Math 525. Topology
Math 540. Real Analysis
Math 542. Complex Analysis

January 2009
Math 500. Abstract Algebra I
Math 520. Differential Manifolds
Math 525. Topology
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 550. Ordinary Differential Equations
Math 580. Combinatorics

 

May 2009
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 520. Differential Manifolds
Math 530. Algebraic Number Theory
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 550. Ordinary Differential Equations
Math 553. PDEs
Math 561. Probability

 

August 2009
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 518. Differential Manifolds I
Math 525. Topology
Math 530. Algebraic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis

January 2008
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 525. Topology
Math 530. Algebraic Number Theory
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 553. PDEs
Math 561. Probability
Math 570. Logic
Math 580. Combinatorics

 

May 2008
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 525. Topology
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 553. PDEs
Math 561. Probability
Math 570. Logic

August 2008
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 525. Topology
Math 540. Real Analysis
Math 542. Complex Analysis

January 2007
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 520. Differentiable Manifolds
Math 525. Topology
Math 530. Algebraic Number Theory
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 550. Ordinary Diff Equations
Math 553. PDEs
Math 561. Probability
Math 570. Logic
Math 580. Combinatorics

 

May 2007
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 520. Differentiable Manifolds
Math 525. Topology
Math 530. Algebraic Number Theory
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 550. Ordinary Diff Equations
Math 553. PDEs
Math 561. Probability
Math 570. Logic
Math 580. Combinatorics

 

August 2007
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 525. Topology
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 553. PDEs
Math 570. Logic
Math 580. Combinatorics
 

January 2006
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 520. Differentiable Manifolds
Math 525. Topology
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 550. Ordinary Diff Equations
Math 553. PDEs
Math 561. Probability
Math 570. Logic
Math 580. Combinatorics

 

May 2006
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 520. Differentiable Manifolds
Math 525. Topology
Math 530. Algebraic Number Theory
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 550. Ordinary Diff Equations
Math 553. PDEs
Math 561. Probability
Math 570. Logic
Math 580. Combinatorics

 

August 2006
Math 500. Abstract Algebra I
Math 501. Abstract Algebra II
Math 520. Differentiable Manifolds
Math 525. Topology
Math 530. Algebraic Number Theory
Math 531. Analytic Number Theory
Math 540. Real Analysis
Math 542. Complex Analysis
Math 550. Ordinary Diff Equations
Math 553. PDEs
Math 561. Probability
Math 570. Logic
Math 580. Combinatorics