Open Positions in the 
Department of
Mathematical Sciences

Tenure-track position at the
Assistant Professor level in the area
of algebra, starting in August 2018.

Algebra   (Position description)

Apply Here

Tenure-track position at the
Assistant Professor level in the area
of topological data analysis, starting
in August 2018.


Topological Data Analysis  (Position description)

Apply Here
 


Recent Funding

Studie Entwicklungsstand Quantencomputer
Study development of quantum computer

PI: Rainer Steinwandt

Funding Agency: Saarland University (GER)
German Federal Office for Information Security


Linking Within-Host and Between-Host
Infectious Disease Dynamics

PI: Necibe Tuncer

Funding Agency: National Science Foundation


Emerging Side-Channel Resistant and
Resource-Friendly Elliptic Curve
Algorithms and Architectures 

PI: Reza Azarderakhsh/Co-PI: Koray Karabina

Funding Agency: US Army


Recent Publications

Dr. Tim Ford, has written a new 
textbook entitles, Separable Algebra.
Due to be published on October 20, 2017,
this book presents a comprehensive
introduction to the theory of separable
algebras over commutative rings.
Azumaya algebras, the henselization of
local rings, and Galois theory are
rigorously introduced and treated.
Essential connections are drawn
between the theory of separable
algebras and Morita theory, the theory
of faithfully flat descent, cohomology,
derivations, differentials, reflexive lattices,
maximal orders, and class groups. 

http://bookstore.ams.org/gsm-183/


 

Subject-wise empirical likelihood

inference in partial linear models
for longitudinal data

Lianfen Qian, Suojin Wang

Computational Statistics & Data Analysis


On the Tucker Circles

Sandor Nagydobai Kiss, Paul Yiu

Forum Geometricorum


Connecting Orbits for Compact Infinite 

Dimensional Maps: Computer Assisted 
Proofs of Existence

R. de la Llave, J.D. Mireles James

SIAM Journal on Applied Dynamical Systems


 

See our Calendar

 

 

 

 

 

 

 

 

 

 

 

 

 

Ph.D. Qualifying Exams 

A Ph.D. student must pass two of the three qualifying exams, before becoming a Ph.D. candidate. 

Upcoming Qualifying Exam Schedule for Fall 2017 :

Analysis: Tuesday, August 22, 2017 SE215, 2pm-5pm

Probability/Statistics : Thursday, August 24, SE 215 2pm-5pm

Algebra: Monday, August 28, 2017, SE215, 2pm-5pm

 

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 three parts. Total 3 hours.

Part 1  (Elementary part). This part consists of 10 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 (Advanced part). This part consists of 3-5 advanced problems from Probability Theory and Math Stat classes. Students are expected to successfully complete at least 60% of these problems.

Part 3 (Proofs). This part contains 3-5 statements from the predetermined list of  about 20 basic well known facts in Probability and Statistics with fairly simple proofs (less than a page). Important: the students are given the list of questions ahead of time and the grading is strict with no partial credits. Students are expected to successfully complete at least 80% of these problems.

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

 

Sample Algebra Exams

Sample Analysis Exams

Samples for Probability & Statistics Exam

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.

A Probability Path by Resnick
Probability theory by Shiryaev
Measure Theory and Probability Theory by Athreya and Lahiri
Mathematical Statistics by Bickel and Doksum
Statistical Inference by Casella


For information contact:
Prof. Yuan Wang, Graduate Director
Department of Mathematical Sciences
Florida Atlantic University
777 Glades RD
Boca Raton, FL 33431
email: mathgraduate@fau.edu