Download or read book Abel s Proof written by Peter Pesic and published by MIT Press. This book was released on 2004-02-27 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intellectual and human story of a mathematical proof that transformed our ideas about mathematics. In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra—which even Newton resisted—and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.
Download or read book Abel s Theorem in Problems and Solutions written by V.B. Alekseev and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.
Download or read book Abel s Proof written by Peter Pesic and published by MIT Press. This book was released on 2016-06-17 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intellectual and human story of a mathematical proof that transformed our ideas about mathematics. In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra—which even Newton resisted—and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.
Download or read book The Legacy of Niels Henrik Abel written by Olav Arnfinn Laudal and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique series of fascinating research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields. Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century.
Download or read book Abel s Theorem and the Allied Theory written by Henry Frederick Baker and published by . This book was released on 1897 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Resource Sensitivity Binding and Anaphora written by Geert-Jan M. Kruijff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geert-Jan Kruijff & Richard T. Oehrle A categorial grammar is both a grammar and a type inference system. As a result of this duality, the categorial framework offers a natural setting in which to study questions of grammatical composition, both empirically and abstractly. There are affinities in this perspective, of course, to basic questions in formal language theory. But the fact that categorial grammars are type in ference systems makes possible intrinsic connections among syntactic types, syntactic type inference, semantic types, and semantic type inference, a con nection less apparent in the standard constructions of formal language theory. Fixing a system of grammatical type inference T, we may explore what gram matical phenomena are compatible with T-and equally, what grammatical phenomena are not. Equally, fixing a class of grammatical phenomena g, we may seek to ascertain what systems of type inference characterize g. This dual perspective is a strong current in the categorial literature, going back to the classical papers of Ajdukiewicz, Bar-Hillel, Curry, and Lambek.
Download or read book Galois Theory written by David A. Cox and published by John Wiley & Sons. This book was released on 2012-03-27 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition ". . .will certainly fascinate anyone interested in abstractalgebra: a remarkable book!" —Monatshefte fur Mathematik Galois theory is one of the most established topics inmathematics, with historical roots that led to the development ofmany central concepts in modern algebra, including groups andfields. Covering classic applications of the theory, such assolvability by radicals, geometric constructions, and finitefields, Galois Theory, Second Edition delves into noveltopics like Abel’s theory of Abelian equations, casusirreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of severaltopics not covered in standard texts on Galois theory,including: The contributions of Lagrange, Galois, and Kronecker How to compute Galois groups Galois's results about irreducible polynomials of primeor prime-squared degree Abel's theorem about geometric constructions on thelemniscates Galois groups of quartic polynomials in allcharacteristics Throughout the book, intriguing Mathematical Notes andHistorical Notes sections clarify the discussed ideas andthe historical context; numerous exercises and examples use Mapleand Mathematica to showcase the computations related to Galoistheory; and extensive references have been added to provide readerswith additional resources for further study. Galois Theory, Second Edition is an excellent book forcourses on abstract algebra at the upper-undergraduate and graduatelevels. The book also serves as an interesting reference for anyonewith a general interest in Galois theory and its contributions tothe field of mathematics.
Download or read book Function Spaces and Partial Differential Equations written by Ali Taheri and published by Oxford Lecture Mathematics and. This book was released on 2015 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.
Download or read book World Drama Volume 1 written by Barrett H. Clark and published by Courier Corporation. This book was released on 2013-02-28 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1 of this two-volume set contains 26 plays including Aeschylus "Prometheus Bound"; Sophocles "Antigone"; Seneca "Medea"; Marlowe, "Dr. Faustus"; Heywood, "A Woman Killed with Kindness"; Johnson, "Every Man in His Humour"; Beaumont and Fletcher "The Maid's Tragedy"; Sheridan "The School for Scandal"; plus plays from the Orient, medieval plays and more.
Download or read book Fourier Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2011-02-11 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Download or read book Reports of Cases at Law and in Equity Argued and Determined in the Supreme Court of the State of Iowa Taken from the Original Opinions and Records and Embracing All the Cases Decided During the Period Covered by the First Volumes of Iowa Reports by Clarke with Copious Notes written by Iowa. Supreme Court and published by . This book was released on 1892 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reports of Cases at Law and in Equity Argued and Determined in the Supreme Court of the State of Iowa written by Iowa. Supreme Court and published by . This book was released on 1892 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abels V Iceland Products Inc written by and published by . This book was released on 1959 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Military Air Transportation written by United States. Congress. House. Committee on Government Operations and published by . This book was released on 1959 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book All Past Time and Almanack for written by and published by . This book was released on 1883 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abel s Theorem and the Allied Theory written by Henry Frederick Baker and published by . This book was released on 1989 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Abel s Photographic Weekly written by and published by . This book was released on 1914 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt:
