Download or read book Famous Problems and Other Monographs written by and published by . This book was released on 1962 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Famous problems and other monographs written by Felix Klein and published by . This book was released on 1980 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Famous Problems and Other Monographs written by Felix Klein and published by . This book was released on 1962 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Famous Problems of Geometry and How to Solve Them written by Benjamin Bold and published by Courier Corporation. This book was released on 2012-05-11 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.
Download or read book Abstract Algebra and Famous Impossibilities written by Arthur Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these men and women, the problems would not yield to purely geometrical methods. It was only the development. of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. In this book we develop enough abstract algebra to prove that these constructions are impossible. Our approach introduces all the relevant concepts about fields in a way which is more concrete than usual and which avoids the use of quotient structures (and even of the Euclidean algorithm for finding the greatest common divisor of two polynomials). Having the geometrical questions as a specific goal provides motivation for the introduction of the algebraic concepts and we have found that students respond very favourably. We have used this text to teach second-year students at La Trobe University over a period of many years, each time refining the material in the light of student performance.
Download or read book Abstract Algebra and Famous Impossibilities written by Sidney A. Morris and published by Springer Nature. This book was released on 2022-11-26 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction. Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel’s original approach. Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus.
Download or read book Mathematical Mountaintops written by J. L. Casti and published by Oxford University Press, USA. This book was released on 2001 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this brilliant account of mathematicians in action, Casti invites readers to scale mathematical peaks as he recreates solutions to the five greatest mathematical problems of all time. 30 halftones and line illustrations.
Download or read book University of California Union Catalog of Monographs Cataloged by the Nine Campuses from 1963 Through 1967 Authors titles written by University of California (System). Institute of Library Research and published by . This book was released on 1972 with total page 878 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book CRC Concise Encyclopedia of Mathematics written by Eric W. Weisstein and published by CRC Press. This book was released on 2002-12-12 with total page 3253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Download or read book The Development of Mathematics in China and Japan written by Yoshio Mikami and published by . This book was released on 1913 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Invitation to Real Analysis written by Luis F. Moreno and published by The Mathematical Association of America. This book was released on 2015-05-17 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Invitation to Real Analysis is written both as a stepping stone to higher calculus and analysis courses, and as foundation for deeper reasoning in applied mathematics. This book also provides a broader foundation in real analysis than is typical for future teachers of secondary mathematics. In connection with this, within the chapters, students are pointed to numerous articles from The College Mathematics Journal and The American Mathematical Monthly. These articles are inviting in their level of exposition and their wide-ranging content. Axioms are presented with an emphasis on the distinguishing characteristics that new ones bring, culminating with the axioms that define the reals. Set theory is another theme found in this book, beginning with what students are familiar with from basic calculus. This theme runs underneath the rigorous development of functions, sequences, and series, and then ends with a chapter on transfinite cardinal numbers and with chapters on basic point-set topology. Differentiation and integration are developed with the standard level of rigor, but always with the goal of forming a firm foundation for the student who desires to pursue deeper study. A historical theme interweaves throughout the book, with many quotes and accounts of interest to all readers. Over 600 exercises and dozens of figures help the learning process. Several topics (continued fractions, for example), are included in the appendices as enrichment material. An annotated bibliography is included.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book College Geometry written by Howard Whitley Eves and published by Jones & Bartlett Learning. This book was released on 1995 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: College Geometry is divided into two parts. Part I is a sequel to basic high school geometry and introduces the reader to some of the important modern extensions of elementary geometry- extension that have largely entered into the mainstream of mathematics. Part II treats notions of geometric structure that arose with the non-Euclidean revolution in the first half of the nineteenth century.
Download or read book Euclides Vindicatus written by Girolamo Saccheri and published by American Mathematical Soc.. This book was released on 1986 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the axiom systems of non-Euclidean geometry. This book states and proves theorem after theorem of (hyperbolic) non-Euclidean geometry.
Download or read book University of California Union Catalog of Monographs Cataloged by the Nine Campuses from 1963 Through 1967 Subjects written by University of California (System). Institute of Library Research and published by . This book was released on 1972 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Catalog of Copyright Entries Third Series written by Library of Congress. Copyright Office and published by Copyright Office, Library of Congress. This book was released on 1964 with total page 1116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes Part 1, Number 2: Books and Pamphlets, Including Serials and Contributions to Periodicals July - December)
Download or read book Antiphon the Sophist written by Antiphon (of Athens.) and published by Cambridge University Press. This book was released on 2002-08-29 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition collects all the surviving evidence for the fifth-century BCE Athenian sophist Antiphon and presents it together with a translation and a full commentary, which assesses its reliability and significance. Although Antiphon is not as familiar a figure as sophists such as Protagoras and Gorgias, substantial fragments have survived from his major works, On Truth and On Concord, including extensive remains preserved on papyrus. In addition, information about his doctrines is preserved by ancient writers ranging in time from Aristotle to Simplicius and beyond. The introduction provides a brief sketch of Antiphon, his works, and his place in the fifth-century BCE sophistic movement, including his important contribution to the contemporary debate over the relation of law (nomos) and nature (physis). It also deals with the controversial question of the identity of Antiphon the sophist in relation to Antiphon of Rhamnus and other men of the same name.
