Modular Forms and Fermat’s Last Theorem PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Modular Forms and Fermat’s Last Theorem PDF full book. Access full book title Modular Forms and Fermat’s Last Theorem by Gary Cornell. Download full books in PDF and EPUB format.
Author: Gary Cornell
Publisher: Springer Science & Business Media
ISBN: 1461219744
Category : Mathematics
Languages : en
Pages : 592
Get Book Here
Book Description
This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.
Author: Gary Cornell
Publisher: Springer Science & Business Media
ISBN: 1461219744
Category : Mathematics
Languages : en
Pages : 592
Get Book Here
Book Description
This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 292
Get Book Here
Book Description
Author: Ann McNeal
Publisher: DIANE Publishing
ISBN: 9780788142413
Category : Education
Languages : en
Pages : 324
Get Book Here
Book Description
Contains abstracts of innovative projects designed to improve undergraduate education in science, mathematics, engineering, and technology. Descriptions are organized by discipline and include projects in: astronomy, biology, chemistry, computer science, engineering, geological sciences, mathematics, physics, and social sciences, as well as a selection of interdisciplinary projects. Each abstract includes a description of the project, published and other instructional materials, additional products of the project, and information on the principal investigator and participating institutions.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 214
Get Book Here
Book Description
Author: A. J. Van Der Poorten
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 246
Get Book Here
Book Description
Around 1637, the French jurist Pierre de Fermat scribbled in the margin of his copy of the book Arithmetica what came to be known as Fermat's Last Theorem, the most famous question in mathematical history. Stating that it is impossible to split a cube into two cubes, or a fourth power into two fourth powers, or any higher power into two like powers, but not leaving behind the marvelous proof he claimed to have had, Fermat prompted three and a half centuries of mathematical inquiry which culminated only recently with the proof of the theorem by Andrew Wiles. This book offers the first serious treatment of Fermat's Last Theorem since Wiles's proof. It is based on a series of lectures given by the author to celebrate Wiles's achievement, with each chapter explaining a separate area of number theory as it pertains to Fermat's Last Theorem. Together, they provide a concise history of the theorem as well as a brief discussion of Wiles's proof and its implications. Requiring little more than one year of university mathematics and some interest in formulas, this overview provides many useful tips and cites numerous references for those who desire more mathematical detail. The book's most distinctive feature is its easy-to-read, humorous style, complete with examples, anecdotes, and some of the lesser-known mathematics underlying the newly discovered proof. In the author's own words, the book deals with "serious mathematics without being too serious about it." Alf van der Poorten demystifies mathematical research, offers an intuitive approach to the subject-loosely suggesting various definitions and unexplained facts-and invites the reader to fill in the missing links in some of the mathematical claims. Entertaining, controversial, even outrageous, this book not only tells us why, in all likelihood, Fermat did not have the proof for his last theorem, it also takes us through historical attempts to crack the theorem, the prizes that were offered along the way, and the consequent motivation for the development of other areas of mathematics. Notes on Fermat's Last Theorem is invaluable for students of mathematics, and of real interest to those in the physical sciences, engineering, and computer sciences-indeed for anyone who craves a glimpse at this fascinating piece of mathematical history. An exciting introduction to modern number theory as reflected by the history of Fermat's Last Theorem This book displays the unique talents of author Alf van der Poorten in mathematical exposition for mathematicians. Here, mathematics' most famous question and the ideas underlying its recent solution are presented in a way that appeals to the imagination and leads the reader through related areas of number theory. The first book to focus on Fermat's Last Theorem since Andrew Wiles presented his celebrated proof, Notes on Fermat's Last Theorem surveys 350 years of mathematical history in an amusing and intriguing collection of tidbits, anecdotes, footnotes, exercises, references, illustrations, and more. Proving that mathematics can make for lively reading as well as intriguing thought, this thoroughly accessible treatment Helps students and professionals develop a background in number theory and provides introductions to the various fields of theory that are touched upon * Offers insight into the exciting world of mathematical research * Covers a number of areas appropriate for classroom use * Assumes only one year of university mathematics background even for the more advanced topics * Explains why Fermat surely did not have the proof to his theorem * Examines the efforts of mathematicians over the centuries to solve the problem * Shows how the pursuit of the theorem contributed to the greater development of mathematics
Author: Jochen Brüning
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110452154
Category : Mathematics
Languages : en
Pages : 518
Get Book Here
Book Description
This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Author: Richard Courant
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 560
Get Book Here
Book Description
Author: John Fauvel
Publisher: Springer Science & Business Media
ISBN: 079236399X
Category : Education
Languages : en
Pages : 456
Get Book Here
Book Description
This ground-breaking book investigates how the learning and teaching of mathematics can be improved through integrating the history of mathematics into all aspects of mathematics education: lessons, homework, texts, lectures, projects, assessment, and curricula. It draws upon evidence from the experience of teachers as well as national curricula, textbooks, teacher education practices, and research perspectives across the world. It includes a 300-item annotated bibliography of recent work in the field in eight languages.
Author:
Publisher:
ISBN:
Category : Education
Languages : en
Pages : 374
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages :
Get Book Here
Book Description
