The Theory Of Prime Number Classification
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The Theory Of Prime Number Classification
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Author : Zwide Mbulawa
language : en
Publisher: Xlibris Corporation
Release Date : 2010-11-30
The Theory Of Prime Number Classification written by Zwide Mbulawa and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-30 with Mathematics categories.
The Theory of Prime Number Classification This is an expository work of mathematical research into the prime numbers based on pattern methodology and classification techniques. As a comprehensive research into the classification systems for prime numbers, it address the following: „X Why prime numbers are regular yet random. „X What are the building blocks of prime numbers „X What is the framework for prime number generation This is done by developing the following classification systems: „X The Prime Root Classification. All prime numbers are constituted by roots, which are defined as the building blocks of the prime number. „X The Positional Classification. A two dimensional prime number space is defined that allows certain types of distribution analysis of primes to be made, deriving count functions and establishing the mean property of primes „X The Delta Classification of Primes. This classification creates prime families in terms of gaps. Prime gaps are found to have positive, negative and a steady gap acceleration. „X The Gap Theory Classification. All prime gaps and prime number behavior are based on Gap 2, Gap 4 and Gap 6. This then develops a classification system. Using the above classification systems, and defining a special function, a theory of prime number generation is then suggested, where this leads to the development of an algebraic sieve for finding prime numbers. The algebraic sieve contains all the relevant information about prime numbers, including how gaps widen, and prime number patterns. Consequently, it is then used to address the problem of finding a proof for the twin prime conjecture. As an expository work, the book also shares personal experiences and thoughts with regard to the research, and the development of expository mathematics. A program for prime number classification is available at www.zwideprimes.com
The Development Of Prime Number Theory
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Author : Wladyslaw Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Development Of Prime Number Theory written by Wladyslaw Narkiewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.
The Great Prime Number Race
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Author : Roger Plymen
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-08-13
The Great Prime Number Race written by Roger Plymen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-13 with Education categories.
Have you ever wondered about the explicit formulas in analytic number theory? This short book provides a streamlined and rigorous approach to the explicit formulas of Riemann and von Mangoldt. The race between the prime counting function and the logarithmic integral forms a motivating thread through the narrative, which emphasizes the interplay between the oscillatory terms in the Riemann formula and the Skewes number, the least number for which the prime number theorem undercounts the number of primes. Throughout the book, there are scholarly references to the pioneering work of Euler. The book includes a proof of the prime number theorem and outlines a proof of Littlewood's oscillation theorem before finishing with the current best numerical upper bounds on the Skewes number. This book is a unique text that provides all the mathematical background for understanding the Skewes number. Many exercises are included, with hints for solutions. This book is suitable for anyone with a first course in complex analysis. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.
The Theory Of Algebraic Numbers
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Author : Harry Pollard
language : en
Publisher: Courier Corporation
Release Date : 1998-01-01
The Theory Of Algebraic Numbers written by Harry Pollard and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; Fermat conjecture. 1975 edition.
Notes And Problems In Number Theory Volume I
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Author : Taha Sochi
language : en
Publisher: Taha Sochi
Release Date : 2023-10-22
Notes And Problems In Number Theory Volume I written by Taha Sochi and has been published by Taha Sochi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-22 with Mathematics categories.
This book is the first volume of a collection of notes and solved problems about number theory. Like my previous books, maximum clarity was one of the main objectives and criteria in determining the style of writing, presenting and structuring the book as well as selecting its contents. Modest mathematical background knowledge is required for understanding most of the contents of the book. In fact, the book in most parts requires no more than a college or secondary school level of general mathematics. So, the intended readers of the book are primarily college (or A-level) students as well as junior undergraduate students (e.g. in mathematics or science or engineering). The book can be used as a text or as a reference for an introductory course on this subject and may also be used for general reading in mathematics. The book may also be adopted as a source of pedagogical materials which can supplement, for instance, tutorial sessions (e.g. in undergraduate courses on mathematics or science).
Encyclopaedia Of Mathematics Set
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-02-28
Encyclopaedia Of Mathematics Set written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-28 with Mathematics categories.
The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Encyclopaedia Of Mathematics
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Author : M. Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by M. Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Classified List Of Publications Of The Carnegie Institution Of Washington
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Author : Carnegie Institution of Washington
language : en
Publisher:
Release Date : 1919
Classified List Of Publications Of The Carnegie Institution Of Washington written by Carnegie Institution of Washington and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1919 with categories.
Introduction To Quadratic Forms Over Fields
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Author : Tsit-Yuen Lam
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Introduction To Quadratic Forms Over Fields written by Tsit-Yuen Lam and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.