## AFIT Department of Mathematics & Statistics

## Websites of Interest

- arXivarXiv is a highly-automated electronic archive and distribution server for research articles. Covered areas include physics, mathematics, computer science, nonlinear sciences, quantitative biology and statistics. Maintained and operated by the Cornell University Library , arXiv is an openly accessible, moderated repository for scholarly articles in specific scientific disciplines. Material submitted to arXiv is expected to be of interest, relevance, and value to those disciplines. arXiv reserves the right to reject or reclassify any submission.

## Professional Organizations

- American Mathematical Society (AMS)The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
- Mathematical Association of America (MAA)The Mathematical Association of America is the largest professional society that focuses on mathematics accessible at the undergraduate level. MAA is the leading professional association in collegiate mathematics, the preeminent publisher of expository mathematics, the primary source of professional development programs for faculty, and the number one provider of resources for teaching and learning.
- Society for Industrial and Applied Mathematics (SIAM)SIAM exists to ensure the strongest interactions between mathematics and other scientific and technological communities through membership activities, publication of journals and books, and conferences.
- American Statistical Association (ASA)The worlds largest community of statistians, ASA promotes excellence in the development, application, and dissemination of statistical science through meetings, publications, membership services, education, accreditation, and advocacy.
- International Association Statistical Computing (IASC)A division of the International Statitistician Institute (ISI), the IASC focuses on computational statistics, statistical software, exploratory data analysis, data mining, pattern recognition, statistical graphics and data visualisation, statistical data bases, and related fields.

## Start Your Research

Ready to start your research? Try some of the databases below, or use our AFIT Summon for an even broader search.

Still stuck? Sign up for a customized Research Appointment to maximize your research time!

- EbscoHOSTThis multi-disciplinary database provides full text for thousands of journals, including full text for many peer-reviewd titles and PDF backfiles to 1886. Some useful subjects in this database include business, marketing management and economics.
- MathSciNetThis electronic publication offers access to a carefully maintained and easily searchable database of reviews, abstracts and bibliographic information for much of the mathematical sciences literature. Over 100,000 new items are added each year, most of them classified according to the Mathematics Subject Classification. MathSciNet® contains over 2.8 million items and over 1.6 million direct links to original articles. Bibliographic data from retrodigitized articles dates back to the early 1800s. Reference lists are collected and matched internally from approximately 500 journals, and citation data for journals, authors, articles and reviews is provided.
- Science Citation IndexThe Science Citation Index (part of Web of Science) provides access to current and retrospective bibliographic information, author abstracts, and cited references found in approximately 5,900 of the world's leading scholarly science and technical journals covering more than 150 disciplines. AFIT access to partial-full text only.

## Google Scholar

Did you know that we also link our full-text databases through Google Scholar? If you search from any campus computer or authenticate through VPN, Google Scholar will direct you to sources from the D'Azzo Research Library.

## Reading Corner

*NEW Arrivals!*

One-Dimensional Finite Elements

Call Number: TA347.F5 O247 2013

ISBN: 9783642317965

Publication Date: 2012-10-06

This textbook presents finite element methods using exclusively one-dimensional elements. The aim is to present the complex methodology in an easily understandable but mathematically correct fashion. The approach of one-dimensional elements enables the reader to focus on the understanding of the principles of basic and advanced mechanical problems. The reader easily understands the assumptions and limitations of mechanical modeling as well as the underlying physics without struggling with complex mathematics. But although the description is easy it remains scientifically correct. The approach using only one-dimensional elements covers not only standard problems but allows also for advanced topics like plasticity or the mechanics of composite materials. Many examples illustrate the concepts and problems at the end of every chapter help to familiarize with the topics.

Topics in Quaternion Linear Algebra

Call Number: QA196 .R63 2014

ISBN: 9780691161853

Publication Date: 2014-08-24

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Core Statistics

Call Number: QA276.2 .W66 2015

ISBN: 9781107415041

Publication Date: 2015-04-30

Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. The book considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language.

Reversibility in Dynamics and Group Theory

Call Number: QA174.2 .O33 2015

ISBN: 9781107442887

Publication Date: 2015-05-31

Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention.

Mathematics of Two-Dimensional Turbulence

Call Number: QA911 .K85 2012

ISBN: 9781107022829

Publication Date: 2012-09-20

This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) – proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.

Vortex Methods

Call Number: QA925 .C68 2008

ISBN: 9780521061704

Publication Date: 2008-04-24

This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows. Vortex methods have matured, offering an interesting alternative to finite difference and spectral methods for high-resolution numerical solutions of the Navier 2013;Stokes equations. Research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character that was the motivation for their introduction. Scientists working in the areas of numerical analysis and fluid mechanics will benefit from this book, which may serve both communities as both a reference monograph and a textbook for computational fluid dynamics courses.

## AFIT Research Librarian |

## Research Appointment

Need help? Set up an appointment with the ENC library liaison for literature searching assistance.

## OR Software

- AMPLAMPL is a comprehensive and powerful algebraic modeling language for linear and nonlinear optimization problems, in discrete or continuous variables.
- CPLEXCPLEX's mathematical optimization technology enables better decision-making for efficient resource utilization.
- MATLABMATLAB is a programming environment for algorithm development, data analysis, visualization, and numerical computation. Using MATLAB, you can solve technical computing problems faster than with traditional programming languages, such as C, C++, and Fortran.
- MathematicaMathematica is renowned as the world's ultimate application for computations.

## Math Blog

- The Center of Math BlogThe Center of Math was established to strengthen the math community by providing free and affordable resources for all. Focused solely on math, the Center is more than a company - it's a community.

Try solving the Problem of the Week!