Science

Elliptic Tales: Curves, Counting, and Number Theory

Elliptic Tales: Curves, Counting, and Number Theory

  • Downloads：4437
  • Type：Epub+TxT+PDF+Mobi
  • Create Date：2021-07-22 09:55:51
  • Update Date：2025-09-06
  • Status：finish
  • Author：Avner Ash
  • ISBN：0691163502
  • Environment：PC/Android/iPhone/iPad/Kindle
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Summary

Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture。 In this book， Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem。

The key to the conjecture lies in elliptic curves， which may appear simple， but arise from some very deep--and often very mystifying--mathematical ideas。 Using only basic algebra and calculus while presenting numerous eye-opening examples， Ash and Gross make these ideas accessible to general readers， and， in the process， venture to the very frontiers of modern mathematics。

-- "Mathematics Magazine"

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Reviews

Colin ，

I made it all the way through this for the first time， having given myself permission to "just read" and not worry too much about grokking everything。 I learnt a few things， which was the goal。On the spectrum between pop maths and textbook， it's much more at the textbook end - but it's close to what I think a textbook ought to be like。 The pace is not too fast， the writing is not overly formal， and it's not afraid to digress on interesting tangents。 I would like to have seen a bit more by way of I made it all the way through this for the first time， having given myself permission to "just read" and not worry too much about grokking everything。 I learnt a few things， which was the goal。On the spectrum between pop maths and textbook， it's much more at the textbook end - but it's close to what I think a textbook ought to be like。 The pace is not too fast， the writing is not overly formal， and it's not afraid to digress on interesting tangents。 I would like to have seen a bit more by way of anecdote， but I enjoyed this。 。。。more

Emil Kerimov ，

Loved it。

Bob Woodley ，

I wanted to learn about elliptic curves and complex projective geometry so I started this book。 It did indeed provide visual intuitions in these areas。 I was not interested in the Birch and Swinnerton-Dyer Conjecture at that time so I stopped half-way through， having extracted what I needed。It is an easy an introduction are you're likely to get to these topics。 Not for beginners， but not too advanced either， and minimal notation。 I wanted to learn about elliptic curves and complex projective geometry so I started this book。 It did indeed provide visual intuitions in these areas。 I was not interested in the Birch and Swinnerton-Dyer Conjecture at that time so I stopped half-way through， having extracted what I needed。It is an easy an introduction are you're likely to get to these topics。 Not for beginners， but not too advanced either， and minimal notation。 。。。more

Daniel ，

As far as maths books go it's good。 But maths really doesn't work in this format。。。 As far as maths books go it's good。 But maths really doesn't work in this format。。。 。。。more

Brandon ，

If you know what linear algebra does with Ax=c， then you can begin to imagine the implications of studying y^2=x^3+Ax+B。 Enter elliptic curves over finite fields

Chris ，

An accessible approach to one of the conjectures of number theory。I found this book quite relaxing， even as it explains complex projective varieties over rings。

Achilleas ，

A challenging but rewarding book。 Elliptic curves is a fascinating subject with surprisingly rich connections to many areas of maths。 Highly recommended for those readers who would like to have an insight in this field。

Andrew Davis ，

Finished with mixed feelings。 An interesting subject of elliptic curves and projective geometry。 Struggled at times and had to refer to other online sources to grasp some of the concepts discussed， especially around the group law。 Some of the other concepts， especially Riemann-Zeta functions need to be followed further in the other books， as not enough space allocated for this topic。

Darrenglass ，

Ash and Gross have taken on a task that I would have guessed was impossible -- a book for general audiences about the Birch and Swinnerton-Dyer Conjecture。 That won't mean much to those of you who aren't mathematicians， but suffice it to say that the BSD Conjecture is one of the most famous open problems in mathematics （the Clay Math Institute has offered a million dollars for a solution） and it is extremely technical to state even to math grad students。。。making it all the more impressive that A Ash and Gross have taken on a task that I would have guessed was impossible -- a book for general audiences about the Birch and Swinnerton-Dyer Conjecture。 That won't mean much to those of you who aren't mathematicians， but suffice it to say that the BSD Conjecture is one of the most famous open problems in mathematics （the Clay Math Institute has offered a million dollars for a solution） and it is extremely technical to state even to math grad students。。。making it all the more impressive that Ash and Gross have attempted a book-length description of it intended for people with little more than a high school math background。 And they have largely succeeded， I think。 Certainly any undergraduate math student could pick this book up and get all the big ideas -- and many of the details as well。 I think they have done a wonderful job of knowing which details to drill down into and which to wave their hands at， and the exposition throughout the book is of a very high level。That said， while this is a very well written exposition of mathematics， it IS a math book， filled with theorems and equations and pictures。 My memory of their previous book （Fearless Symmetry） is that it weaved more of the history and cultural context into its mathematical explorations， and as such I was somewhat disappointed that this book didn't do more of that。 But that probably stems from the fact that I knew all the math before I picked up Ash and Gross's book （I work in a closely related area） so I was hoping for more content that was new to me。 But that is specific to my case and for anyone who is interested in learning some of the exciting mathematics at the forefront of current knowledge， I think Ash and Gross's book is a must read！ 。。。more

Reference

google book https://www.google.com/search?tbm=bks&q=Elliptic Tales: Curves, Counting, and Number Theory

hathitrust digital library https://babel.hathitrust.org/cgi/ls?q1=Elliptic Tales: Curves, Counting, and Number Theory&field1=ocr&a=srchls&ft=ft&lmt=ft

The British Library https://bll01.primo.exlibrisgroup.com/discovery/search?query=any,contains,Elliptic Tales: Curves, Counting, and Number Theory&tab=LibraryCatalog&search_scope=Not_BL_Suppress&vid=44BL_INST:BLL01&lang=en&offset=0