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Elliptic Tales: Curves, Counting, and Number Theory (Englisch) Taschenbuch – 19. Oktober 2014
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"The authors of "Elliptic Tales" do a superb job in demonstrating the approach that mathematicians take when they confront unsolved problems involving elliptic curves."--Sungkon Chang, "Times Higher Education"
"The authors present their discussion in an informal, sometimes playful manner and with detail that will appeal to an audience with a basic understanding of calculus. This book will captivate math enthusiasts as well as readers curious about an intriguing and still unanswered question."--Margaret Dominy, Library Journal
"Minimal prerequisites and its clear writing make this book (which even has a few exercises) a great choice for a seminar for mathematics majors, who at some point should have such an excursion to one of the frontiers of mathematics."--Mathematics Magazine
"The authors of Elliptic Tales do a superb job in demonstrating the approach that mathematicians take when they confront unsolved problems involving elliptic curves."--Sungkon Chang, Times Higher Education
"One cannot help being impressed, in reading the book and pursuing a few of the references, by the magnitude of the enterprise it chronicles."--James Case, SIAM News
"Ash and Gross thoroughly explain the statement and significance of the linchpin Birch and Swinnerton-Dyer conjection. . . . [A]sh and Gross deliver ample and current intellectual and technical substance."--Choice
"I would envision this book as an excellent text for an undergraduate 'capstone' course in mathematics; the book lends itself to independent reading, but topics may be explored in much greater depth and rigor in the classroom. Additionally, the book indeed brings together ideas from calculus, complex variables and algebra, showing how a single mathematical research question may require an integrated understanding of the various branches of mathematics. Thus, it encourages students to reinforce their understanding of these various fields, while simultaneously introducing them to an open question in mathematics and a vibrant field of study."--Lisa A. Berger, Mathematical Reviews Clippings
"The book is very pleasantly written, and in my opinion, the authors have done an admirable job in giving an idea to non-experts what the Birch-Swinnerton Dyer conjecture is about."--Jan-Hendrik Evertse, Zentralblatt MATH
"The book's most important contributions . . . are the sense of discovery, invention, and insight into the habits of mind used by mathematicians on this journey. I would recommend this book to anyone who wants to be challenged mathematically or who wants to experience mathematics as creative and exciting."--Jacqueline Coomes, Mathematics Teacher
"[T]his book is a wonderful introduction to what is arguably one of the most important mathematical problems of our time and for that reason alone it deserves to be widely read. Another reason to recommend this book is the opportunity to share in the readily apparent joy the authors have for their subject and the beauty they see in it, not least because . . . joy and beauty are the most important reasons for doing mathematics, irrespective of its dollar value."--Rob Ashmore, Mathematics Today
"Assuming only what every mathematically inclined freshman should know, this book leads the reader to an understanding of one of the most important conjectures in current number theory--whose proof is one of the Clay Mathematics Institute's million-dollar prize problems. The book is carefully and clearly written, and can be recommended without hesitation."--Peter Swinnerton-Dyer, University of Cambridge
"The Birch and Swinnerton-Dyer Conjecture is one of the great insights in number theory from the twentieth century, and Ash and Gross write with care and a clear love of the subject.Elliptic Tales will have wide appeal."--Peter Sarnak, Princeton University-- Dieser Text bezieht sich auf eine andere Ausgabe: Gebundene Ausgabe. Alle Produktbeschreibungen
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The authors are careful to develop concepts as needed, but no more than that. For example, groups and finite fields get a nice elementary treatment. I found reading this book to be a real joy.
I also recommend it to anyone with a degree in math who is curious about why elliptic curves are so important in the field of algebraic geometry.
I deducted one star for overselling who can comfortably read this book, but I still highly recommend it for readers who want to know something about elliptic curves--they are, after all, how Fermat's Last Theorem fell! To be clear, you won't be anywhere near understading the proof Wiles developed for FLT, but the concept of rational points on elliptic curves is where it all begins.
I read the first 4 chapters of this book, and can tell the authors have tried to accommodate me. They pay special attention to including ALL of the information needed to follow the arguments right there in the text.
This certainly isn't a typical math book. It is not meant for accomplished, practicing mathematicians; it's a book for intelligent people who want inside that elite club and need all the information explained without too much jargon. I LIKE!!
Like many semi-popular math books on a topic, they sometimes explain in detail pretty simple things as if the reader needs that, but then make the assumption that the reader is already clear on things that are much more advanced. They do explain it but a reader could get lost and have to go back. A better index would help with that.
Well worth reading.