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 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
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