**Ph.D. Qualifying Exams**

A Ph.D. student must pass two qualifying exams, one in Algebra and one in Analysis, before becoming a Ph.D. candidiate. Each part may be attempted at most three times.

**Upcoming Qualifying Exam Schedule for Spring **** 2016:** (to be posted soon)

**Algebra:**

**Analysis:**

**
Algebra Exam:** group theory, Sylow theorems, the structure of finitely-generated abelian groups, ring theory, Euclidean rings, UFDs, polynomial rings, vector spaces, modules, linear transformations, eigenvalues, minimal polynomials, matrices of linear transformations, Galois theory, and finite fields.

**Analysis Exam: **the real numbers, metric space topology, uniform convergence, Arzela-Ascoli Theorem, differentiation and Riemann integration of single-variable functions, power series, Stone-Weierstrass Theorem, measure theory, Lebesgue integral, convergence theorems for the Lebesgue integral, absolute continuity, the Fundamental Theorem of Calculus.

**Note: ** the syllabus in any particular section of the Introductory Abstract Algebra and Introductory Analysis courses might differ slightly from the subject material listed above.

**Sample Algebra Exams**

**Sample Analysis Exams**

**References:**

*Topics in Algebra*, 2nd ed., by Herstein, Chapters 2-5, 6.1-6.3, and 7.

*Algebra*, 3rd ed., by Lang, Chapters 1-6.

*Abstract Algebra*, 3rd ed., by Dummit and Foote, Chapters 1-5, 7-9, and 13-14, excluding 9.6 and 14.9.

*Introduction to Analysis*, by Maxwell Rosenlicht, Chapters 2-7.

*Real Mathematical Analysis*, by Charles Pugh, Chapters 1-4.

*Real Analysis*, 3rd ed., by H.L. Royden, Chapters 3, 4, 5.

*Principles of Mathematical Analysis*, 3rd ed., by Rudin, Chapters 2-8 and 11.

*Measure and Integral*, by Wheeden amd Zygmund, Chapters 3-5.

**For information contact:**

Prof. Y. Wang, Graduate Director

Department of Mathematical Sciences

Florida Atlantic University

777 Glades RD

Boca Raton, FL 33431