Florida Atlantic University
#189 in National Universities
Florida Atlantic University, established in 1961, officially opened its doors in 1964 as the fifth public university in Florida . The doctoral program is for students who have a strong desire to perform independent and original research in the mathematical sciences. To be accepted to the program, the applicant must have a strong record of work in mathematics.
Application Fee: $30
a) Areas for doctoral research
b) Application Deadlines:
Fall - February 15
Spring - July 15
Summer-January 15
c) Requirements to be Admitted to Candidacy
1. The student must complete the following courses: Introductory Analysis 1 and 2 (MAA 5228 and 5229), Introductory Abstract Algebra 1 and 2 (MAS 5311 and 5312), Linear Algebra (MAS 5145) and Multivariable Analysis (MAA 5105).
2. Satisfy one of the following:
Option A. Pass two of the three exams (Algebra, Analysis, Probability and Statistics) within five semesters (not counting the summer terms) of admission to doctoral study. Then form a supervisory committee as outlined in Item 3.
Option B.Complete the following steps within six semesters (not counting the summer terms) of admission to doctoral study.
1. Earn a pass on one exam and a constructive attempt on a different exam within four semesters (not counting the summer terms) of admission to doctoral study.
2. Select a prospective research advisor, and complete two courses at the 6000 level, selected by the prospective research advisor and approved by the departmental graduate committee. These courses will need to be passed with a combined GPA of at least 3.5. They will count toward Degree Requirement 1a below, but not 1b or 1c. The prospective research advisor may propose additional requirements.
3. Receive a positive recommendation by the prospective research advisor and the graduate committee. Then form a supervisory committee as outlined in Item 3 with the prospective research advisor serving as research advisor.
3. Form a supervisory committee of at least four members including the research advisor and at least two other members of the graduate faculty of the Department of Mathematics and Statistics.
d) Degree Requirements
1. Credits and course requirements:
a. Earn a minimum of 72 credits;
b. Complete 6000-level or higher courses with at least four of these prefixes: MAA, MAD, MAP, MAS, MHF, MTG and STA;
c. For at least two of the prefixes in Item 1b, complete at least two 6000-level or higher courses.
2. Successful completion of a preliminary examination covering specific areas of study and set by the student's supervisory committee.
3. Presentation and oral defense of a dissertation.
4. Completion of all University requirements, including at least 18 credits at FAU beyond the master's level.
Core - 18 credits
Multivariable Analysis-3
Introductory Analysis 1-3
Introductory Analysis 2-3
Linear Algebra-3
Introductory Abstract Algebra 1-3
Introductory Abstract Algebra 2-3
Electives - 18 credits
Choose18 credits at the 6000 or 7000 level from the Mathematics and Statistics Department
Remaining Requirements - 35 credits
Choose 35 credits at the 5000, 6000 or 7000 level from the Mathematics and Statistics Department. Students may take
MAT 7978, but not MAS 6318, MHF 6405 or MHF 6410.
Dissertation - 1 credit (minimum)
Dissertation -1
e) Ph.D. Qualifying Exams
A Ph.D. student must pass two of the three qualifying exams, before becoming a Ph.D. candidate.
Topics covered in the Ph.D. Qualifying Exams
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.
Probability & Statistics Exam: Advanced topics in Probability and Statistics: Borel-Cantelli lemma, normal and Poisson distributions, Chi-square and exponential distributions, t and F distributions, Markov and Chebyshev inequalities, convergence in distribution, in probability and almost surely, law of large numbers, central limit theorem, delta method, Slutsky lemma, LSE, MLE, BLUE, sufficient statistics, Cramer-Rao inequality, Fisher information matrix, hypothesis tests via likelihood ratio test and Bayes test.
The Probability & Statistics Exam will be divided into two parts. Total 3 hours.
Part 1 (Elementary part). This part consists of 5 elementary Probability and Stat questions. These will be the same (or very similar) questions that are given for Actuarial Exam. Students are expected to successfully complete at least 80% of these problems.
Part 2 (Challenging part). This part consists of 5 advanced problems from Probability Theory and Math Stat classes, including 2-3 proof problems from the predetermined list of about 20 basic well known facts in Probability and Statistics with fairly simple proofs (less than a page). Students are expected to successfully complete at least 70% of these problems.
f) Ph.D. Preliminary Exam
After admission to candidacy, and before submission of the Ph.D. thesis, students must pass a preliminary exam (Prelim).
Main purpose of the Preliminary Exam: The purpose of the Prelim is to test the student's in-depth understanding of an area in which he or she will develop the dissertation research. The exam is intended to assess the student's mathematical maturity and knowledge at a high level that goes beyond any particular course.The candidate should demonstrate the maturity and expertise required for carrying out dissertation research.
The paradigm: Before the candidate writes his/her thesis, which should be an original and relevant contribution to the area of study, the candidate should be able to present one (or two) relevant peer-reviewed journal articles or an excerpt from a textbook or a monograph well beyond a normal graduate course in the relevant area.
The focus should be on quality instead of quantity. The candidate is expected to demonstrate full expertise and understanding of the topics and theorems presented. The exam should be evaluated on the performance of the candidate and not on the material presented.
g) Admission Requirement
International Students
• Undergraduate GPA of 3.0 • Graduate GPA of 3.0 (if applicable)
• GRE is required; minimum test score of 157 on the Quantitative Reasoning section* (*Temporarily waived thru Fall 2024)
• Three letters of recommendation
• BA degree in Mathematical Science or related field required • Statement of personal objectives in essay form
• A general evaluation of international transcripts is required; FAU will do the evaluation or it must be done by a NACES member • TOEFL score of 500 (PBT) or 61 (IBT); IELTS 6.0; Duolingo 90
h) Contact Information
Sonia Clayton
Graduate Programs Coordinator
561-297-4629
Science Building (43), Rm. 240
mathgraduate@fau.edu