Auxiliary Polynomials In Number Theory
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Auxiliary Polynomials In Number Theory
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Author : David Masser
language : en
Publisher: Cambridge University Press
Release Date : 2016-07-21
Auxiliary Polynomials In Number Theory written by David Masser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-21 with Mathematics categories.
A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.
Auxiliary Polynomials In Number Theory
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Author : David William Masser
language : en
Publisher:
Release Date : 2016
Auxiliary Polynomials In Number Theory written by David William Masser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Number theory categories.
A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.
Number Theory And Polynomials
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Author : James Fraser McKee
language : en
Publisher: Cambridge University Press
Release Date : 2008-05-08
Number Theory And Polynomials written by James Fraser McKee and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-08 with Mathematics categories.
Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Additive Number Theory Of Polynomials Over A Finite Field
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Author : Gove W. Effinger
language : en
Publisher:
Release Date : 1991
Additive Number Theory Of Polynomials Over A Finite Field written by Gove W. Effinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This book helps gather the sum of additive number theory.
A Brief Guide To Algebraic Number Theory
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Author : H. P. F. Swinnerton-Dyer
language : en
Publisher: Cambridge University Press
Release Date : 2001-02-22
A Brief Guide To Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-22 with Mathematics categories.
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Asymptotic Properties Of Polynomials With Auxiliary Conditions Of Interpolation
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Author : Joseph Leonard Walsh
language : en
Publisher:
Release Date : 1961
Asymptotic Properties Of Polynomials With Auxiliary Conditions Of Interpolation written by Joseph Leonard Walsh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Mathematics categories.
Let a closed bounded point set E be given in the z-plane. Necessary and sufficient conditions are found for validity of the following: given assigned conditions of interpolation in a finite number of points: pn(zk) = Ank; there exists a sequence of polynomials pn(z) satisfying these conditions and lim sup max pn(z), z on E 1/n = (E), where (E) is the transfinite diameter of E. (Author).
Fundamental Number Theory With Applications
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Author : Richard A. Mollin
language : en
Publisher: CRC Press
Release Date : 2008-02-21
Fundamental Number Theory With Applications written by Richard A. Mollin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-21 with Mathematics categories.
An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.
Elementary Number Theory
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Author : Gove Effinger
language : en
Publisher: CRC Press
Release Date : 2021-09-09
Elementary Number Theory written by Gove Effinger and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with Mathematics categories.
Elementary Number Theory, Gove Effinger, Gary L. Mullen This text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students (and instructors) to study, understand, and come to love this truly beautiful subject. Each chapter, after an introduction, develops a new topic clearly broken out in sections which include theoretical material together with numerous examples, each worked out in considerable detail. At the end of each chapter, after a summary of the topic, there are a number of solved problems, also worked out in detail, followed by a set of supplementary problems. These latter problems give students a chance to test their own understanding of the material; solutions to some but not all of them complete the chapter. The first eight chapters discuss some standard material in elementary number theory. The remaining chapters discuss topics which might be considered a bit more advanced. The text closes with a chapter on Open Problems in Number Theory. Students (and of course instructors) are strongly encouraged to study this chapter carefully and fully realize that not all mathematical issues and problems have been resolved! There is still much to be learned and many questions to be answered in mathematics in general and in number theory in particular.
Around The Unit Circle
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Author : James McKee
language : en
Publisher: Springer Nature
Release Date : 2021-12-08
Around The Unit Circle written by James McKee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-08 with Mathematics categories.
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.
An Experimental Introduction To Number Theory
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Author : Benjamin Hutz
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-04-17
An Experimental Introduction To Number Theory written by Benjamin Hutz 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 2018-04-17 with Number theory categories.
This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.