Number And Algebra

Author : Sergei Ovchinnikov
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 43,5 Mb
Release : 2015-02-26
Category : Mathematics
ISBN : 9781470420185

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Number Systems by Sergei Ovchinnikov Pdf

This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.

Author : Sivaramakrishnan R,R Sivaramakrishnan
Publisher : CRC Press
Page : 660 pages
File Size : 43,5 Mb
Release : 2006-09-22
Category : Mathematics
ISBN : 9781420015065

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Certain Number-Theoretic Episodes In Algebra by Sivaramakrishnan R,R Sivaramakrishnan Pdf

Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutati

Author : Henry Burchard Fine
Publisher : Unknown
Page : 154 pages
File Size : 43,9 Mb
Release : 1890
Category : Algebra
ISBN : HARVARD:32044056200835

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The Number-system of Algebra by Henry Burchard Fine Pdf

Author : Jiri Herman,Radan Kucera,Jaromir Simsa
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461212706

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Equations and Inequalities by Jiri Herman,Radan Kucera,Jaromir Simsa Pdf

A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.

Author : Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin
Publisher : John Wiley & Sons
Page : 544 pages
File Size : 52,5 Mb
Release : 2011-07-15
Category : Mathematics
ISBN : 0470640537

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Algebra and Number Theory by Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin Pdf

Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.

Author : Edwin Weiss
Publisher : Courier Corporation
Page : 308 pages
File Size : 44,9 Mb
Release : 2012-01-27
Category : Mathematics
ISBN : 9780486154367

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Algebraic Number Theory by Edwin Weiss Pdf

Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.

Author : Richard S. Millman,Peter J. Shiue,Eric Brendan Kahn
Publisher : Springer
Page : 223 pages
File Size : 44,9 Mb
Release : 2015-02-09
Category : Mathematics
ISBN : 9783319144276

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Problems and Proofs in Numbers and Algebra by Richard S. Millman,Peter J. Shiue,Eric Brendan Kahn Pdf

Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school” course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.

Author : Henry B Fine
Publisher : Unknown
Page : 106 pages
File Size : 45,9 Mb
Release : 2019-12-02
Category : Electronic
ISBN : 1670763404

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The Number-System of Algebra by Henry B Fine Pdf

THENUMBER-SYSTEM OF ALGEBRATREATED THEORETICALLY AND HISTORICALLY

Author : Benjamin Fine,Anthony Gaglione,Anja Moldenhauer,Gerhard Rosenberger,Dennis Spellman
Publisher : Walter de Gruyter GmbH & Co KG
Page : 342 pages
File Size : 42,6 Mb
Release : 2017-09-11
Category : Mathematics
ISBN : 9783110516265

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Algebra and Number Theory by Benjamin Fine,Anthony Gaglione,Anja Moldenhauer,Gerhard Rosenberger,Dennis Spellman Pdf

This two-volume set collects and presents some fundamentals of mathematics in an entertaining and performing manner. The present volume examines many of the most important basic results in algebra and number theory, along with their proofs, and also their history. Contents The natural, integral and rational numbers Division and factorization in the integers Modular arithmetic Exceptional numbers Pythagorean triples and sums of squares Polynomials and unique factorization Field extensions and splitting fields Permutations and symmetric polynomials Real numbers The complex numbers, the Fundamental Theorem of Algebra and polynomial equations Quadratic number fields and Pell’s equation Transcendental numbers and the numbers e and π Compass and straightedge constructions and the classical problems Euclidean vector spaces

Author : Frazer Jarvis
Publisher : Springer
Page : 292 pages
File Size : 40,7 Mb
Release : 2014-06-23
Category : Mathematics
ISBN : 9783319075457

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Algebraic Number Theory by Frazer Jarvis Pdf

This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 45,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662029459

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A Course in Computational Algebraic Number Theory by Henri Cohen Pdf

A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

Author : Tracey Pilone,Dan Pilone
Publisher : "O'Reilly Media, Inc."
Page : 559 pages
File Size : 55,8 Mb
Release : 2009
Category : Computers
ISBN : 9780596514860

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Head First Algebra by Tracey Pilone,Dan Pilone Pdf

Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, the book uses a visually rich format designed for the way your brain works, not a text-heavy approach that puts you to sleep.--Publisher's note.

Author : William J. Gilbert,Scott A. Vanstone
Publisher : Pearson
Page : 0 pages
File Size : 48,5 Mb
Release : 2005
Category : Algebraic logic
ISBN : 0131848682

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An Introduction to Mathematical Thinking by William J. Gilbert,Scott A. Vanstone Pdf

Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while the Problems require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science.

Author : Henry B. Fine
Publisher : Unknown
Page : 128 pages
File Size : 50,5 Mb
Release : 2019
Category : Electronic
ISBN : 0243621558

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Number-System of Algebra by Henry B. Fine Pdf

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 41,8 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233

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A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer Pdf

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.