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The Fundamental Theorem Of Algebra

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The Fundamental Theorem Of Algebra

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Author : Benjamin Fine
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Fundamental Theorem Of Algebra written by Benjamin Fine 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 2012-12-06 with Mathematics categories.

The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.

The Fundamental Theorem Of Algebra

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Author : Benjamin Fine
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-06-20

Linear Algebra As An Introduction To Abstract Mathematics

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Author : Bruno Nachtergaele
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-11-30

Linear Algebra As An Introduction To Abstract Mathematics written by Bruno Nachtergaele and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-30 with Mathematics categories.

This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.

Constructive Aspects Of The Fundamental Theorem Of Algebra

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Author : Bruno Dejon
language : en
Publisher: John Wiley & Sons
Release Date : 1969

Constructive Aspects Of The Fundamental Theorem Of Algebra written by Bruno Dejon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.

Algebraic Number Theory And Fermat S Last Theorem

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Author : Ian Stewart
language : en
Publisher: CRC Press
Release Date : 2001-12-12

Algebraic Number Theory And Fermat S Last Theorem written by Ian Stewart and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-12 with Mathematics categories.

First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it

Fundamental Structures Of Algebra And Discrete Mathematics

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Author : Stephan Foldes
language : en
Publisher: John Wiley & Sons
Release Date : 2011-02-14

Fundamental Structures Of Algebra And Discrete Mathematics written by Stephan Foldes and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-14 with Mathematics categories.

Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.

Algebra And Number Theory

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Author : Benjamin Fine
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-09-11

Algebra And Number Theory written by Benjamin Fine and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.

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

Fundamental Algebraic Geometry

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Author : Barbara Fantechi
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Fundamental Algebraic Geometry written by Barbara Fantechi 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.

Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.

Elementary Real And Complex Analysis

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Author : Georgi E. Shilov
language : en
Publisher: Courier Corporation
Release Date : 1996-01-01

Elementary Real And Complex Analysis written by Georgi E. Shilov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.

Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, much more. Each chapter contains a problem set with hints and answers. 1973 edition.

Algorithmic Algebra

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Author : Bhubaneswar Mishra
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algorithmic Algebra written by Bhubaneswar Mishra 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 2012-12-06 with Computers categories.

Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.

The Fundamental Theorem Of Algebra

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