Bøger af Jonathan Borwein

Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts. Neverending Fractions brings these results together, offering fresh perspectives on a mature subject. Beginning with a standard introduction to continued fractions, the book covers a diverse range of topics, from elementary and metric properties, to quadratic irrationals, to more exotic topics such as folded continued fractions and Somos sequences. Along the way, the authors reveal some amazing applications of the theory to seemingly unrelated problems in number theory. Previously scattered throughout the literature, these applications are brought together in this volume for the first time. A wide variety of exercises guide readers through the material, which will be especially helpful to readers using the book for self-study, and the authors also provide many pointers to the literature.

The digital era has dramatically changed the ways that researchers search, produce, publish, and disseminate their scientific work. These processes are still rapidly evolving due to improvements in information science, new achievements in computer science technologies, and initiatives such as DML and open access journals, digitization projects, scientific reference catalogs, and digital repositories. These changes have prompted many mathematicians to play an active part in the developments of the digital era, and have led mathematicians to promote and discuss new ideas with colleagues from other fields, such as technology developers and publishers. This book is a collection of contributions by key leaders in the field, offering the paradigms and mechanisms for producing, searching, and exploiting scientific and technical scholarship in mathematics in the digital era.

How do we recognize that the number . How do we decide that such a number is actually a special value of a familiar function without the tools Gauss had at his disposal, which were, presumably, phenomenal insight and a prodigious memory?

Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This new edition adds material on semismooth optimization, as well as several new proofs.

Borwein is an authority in the area of mathematical optimization, and his book makes an important contribution to variational analysisProvides a good introduction to the topic

Includes a chapter called 'Recent Experiences' that is dedicated to examples of experimental mathematics.