the prime number theorem london mathematical society student texts

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The Prime Number Theorem

Author : G. J. O. Jameson
ISBN : 0521891108
Genre : Mathematics
File Size : 80. 71 MB
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The prime numbers appear to be distributed in a very irregular way amongst the integers, but the prime number theorem provides a simple formula that tells us (in an approximate but well-defined sense) how many primes we can expect to find that are less than any integer we might choose. This is indisputably one of the the great classical theorems of mathematics. Suitable for advanced undergraduates and beginning graduates, this textbook demonstrates how the tools of analysis can be used in number theory to attack a famous problem.

An Introduction To Number Theory

Author : G. Everest
ISBN : 9781852339173
Genre : Mathematics
File Size : 85. 13 MB
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Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight

Why Prove It Again

Author : John W. Dawson, Jr.
ISBN : 9783319173689
Genre : Mathematics
File Size : 40. 16 MB
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This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials. Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians. Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.

Types For Proofs And Programs

Author : Stefano Berardi
ISBN : 9783642024443
Genre : Computers
File Size : 78. 32 MB
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These proceedings contain a selection of refereed papers presented at or - lated to the Annual Workshop of the TYPES project (EU coordination action 510996), which was held during March 26–29, 2008 in Turin, Italy. The topic of this workshop, and of all previous workshops of the same project, was f- mal reasoning and computer programming based on type theory: languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certi?ed software, mobile code, formali- tion of mathematics, mathematics education. The workshop was attended by more than 100 researchers and included more than 40 presentations. We also had three invited lectures, from A. Asperti (University of Bologna), G. Dowek (LIX, Ecole polytechnique, France) and J. W. Klop (Vrije Universiteit, A- terdam, The Netherlands). From 27 submitted papers, 19 were selected after a reviewing process. Each submitted paper was reviewed by three referees; the ?nal decisions were made by the editors. This workshop is the last of a series of meetings of the TYPES working group funded by the European Union (IST project 29001, ESPRIT Working Group 21900, ESPRIT BRA 6435).

A Brief Guide To Algebraic Number Theory

Author : H. P. F. Swinnerton-Dyer
ISBN : 0521004233
Genre : Mathematics
File Size : 47. 65 MB
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Broad graduate-level account of Algebraic Number Theory, including exercises, by a world-renowned author.

An Introduction To Sieve Methods And Their Applications

Author : Alina Carmen Cojocaru
ISBN : 0521848164
Genre : Mathematics
File Size : 69. 13 MB
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Rather than focus on the technical details which can obscure the beauty of sieve theory, the authors focus on examples and applications, developing the theory in parallel.

Number Theory In The Spirit Of Liouville

Author : Kenneth S. Williams
ISBN : 9781107002531
Genre : Mathematics
File Size : 51. 90 MB
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A gentle introduction to Liouville's powerful method in elementary number theory. Suitable for advanced undergraduate and beginning graduate students.

Gazette Australian Mathematical Society

Author : Australian Mathematical Society
ISBN : UOM:39015057373808
Genre : Mathematics
File Size : 48. 56 MB
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Lmsst 24 Lectures On Elliptic Curves

Author : John William Scott Cassels
ISBN : 0521425301
Genre : Mathematics
File Size : 68. 26 MB
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The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.

Mathematical Reviews

Author :
ISBN : UOM:39015068492373
Genre : Mathematics
File Size : 80. 49 MB
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