This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein fall into various classes. First and foremost there is a selection from the mathematical and computational literature of four millennia. There is also a variety of historical studies on the cultural significance of the number. Additionally, there is a selection of pieces that are anecdotal, fanciful, or simply amusing.
For this...
This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it all...
"Fortunately we have the Borwein's beautiful book . . . explores in the first five chapters the glorious world so dear to Ramanujan . . . would be a marvelous text book for a graduate course."--Bulletin of the American Mathematical Society
"What am I to say about this quilt of a book? One is reminded of Debussy who, on being asked by his harmony teacher to explain what rules he was following as he improvised at the piano, replied, "Mon plaisir." The authors are cultured mathematicians. They have selected what has amused and...
Critical Acclaim for Pi and the AGM:
"Fortunately we have the Borwein's beautiful book . . . explores in the first five chapters the glo...
With the continued advance of computing power and accessibility, the view that "real mathematicians don't compute" no longer has any traction for a newer generation of mathematicians. The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doing to highlight some of the key algorithms and to teach some of the key experimental approaches.
With the continued advance of computing power and accessibility, the view that "real mathematicians don't compute" no longer has any traction for a ne...
New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of experimental research in the statement of new hypotheses and the discovery of new results that chart the road to future developments. Following the lead of Mathematics by Experiment: Plausible Reasoning in the 21st Century this book gives...
New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and ana...
This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences," that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational Paths to Discovery is a highly recommended companion.
This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences," that p...
Presents an introduction to experimental mathematics. This title covers a variety of topics and examples to give the reader a sense of the state of play in the field of experimental mathematics. It features explanations that are enhanced by relevant histor
Presents an introduction to experimental mathematics. This title covers a variety of topics and examples to give the reader a sense of the state of pl...
Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises....
Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more so...
"Number Theory and Related Fields" collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished...
"Number Theory and Related Fields" collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van...
