Qualifying Exams Fall Term 2008
Algebra: August 20 from 10 AM to 1 PM -- Location: TBA
Analysis: August 21 from 10 AM to 1 PM -- Location: TBA
All new graduate students who started Fall 2004 or later, and receive a teaching assistantship, must pass at least one of the Algebra and Analysis qualifying exams during their first 18 months at FAU. Both exams (one in Algebra and one in Analysis) must be passed in 24 months.
Samples
Intro Analysis Exam Topics
Books: (1) Real Mathematical Analysis, by Charles Pugh, Chapters 1 through 4.
(2) Real Analysis, 3rd ed., by H.L. Royden, Chapters 3, 4, 5.
(3) Principles of Mathematical Analysis, 3rd ed., by Rudin, Chapters 2 through 8 and 11.
(4) Measure and Integral, by Wheeden amd Zygmund, Chapters 3, 4, 5.
Topics include: the real numbers, metric space topology, uniform convergence, Arzela-Ascoli Theorem, differentiation and Riemann integration of single-variable functions, power series, Stone-Weierstrauss Theorem, measure theory, Lebesgue integral, convergence theorems for the Lebesgue integral, absolute continuity, the Fundamental Theorem of Calculus.
Intro Algebra Exam Topics
Books: (1) Topics in Algebra 2nd ed., by Herstein, Chapters 2 through 5 and 7.
(2) Algebra, 3rd ed., by Lang, Chapters 1 through 6.
(3) Abstract Algebra, 3rd ed., by Dummit and Foote, Chapters 1-5, 7-9, and 13-14, excluding 9.6 and 14.9.
Topics include: group theory (including Sylow theorems and structure of finite abelian groups), ring theory (including Euclidean rings and the result that if R is a UFD then so is R[x]), vector spaces and modules (including the theorem that finitely generated modules over a Euclidean ring are direct sums of cyclics), Galois theory (including constructions with straightedge and compass), and finite fields (existence, uniqueness, and construction).
