Download or read book Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree written by Felix Klein and published by Courier Corporation. This book was released on 2003-01-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-known work covers the solution of quintics in terms of the rotations of a regular icosahedron around the axes of its symmetry. Its two-part presentation begins with discussions of the theory of the icosahedron itself; regular solids and theory of groups; introductions of (x + iy); a statement and examination of the fundamental problem, with a view of its algebraic character; and general theorems and a survey of the subject. The second part explores the theory of equations of the fifth degree and their historical development; introduces geometrical material; and covers canonical equations of the fifth degree, the problem of A's and Jacobian equations of the sixth degree, and the general equation of the fifth degree. Second revised edition with additional corrections.
Download or read book Lectures on the Ikosahedron and the Solution of Equations of the Fifth Degree written by Felix Klein and published by . This book was released on 1888 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on the Icosahedron and the Solution of the Fifth Degree written by Felix Klein and published by Cosimo, Inc.. This book was released on 2007-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this classic of mathematical literature, first published in 1884, Felix Klein elegantly demonstrates how the rotation of icosahedron can be used to solve complex quintic equations. Divided into two parts-"Theory of the Icosahedron" and "The Theory of Equations of the Fifth Degree"-The Icosahedron covers: . the regular solids and the theory of groups . introduction of (x + iy) . statement and discussion of the fundamental problem, according to the theory of functions . the algebraical character of the fundamental problem . general theorems and survey of the subject . the historical development of the theory of equations of the fifth degree . introduction of geometrical material . the canonical equations of the fifth degree . the problem of the A's and the Jacobian equations of the sixth degree . the general equation of the fifth degree Complete with detailed equations and instructive material, The Icosahedron will be valued by experts in higher mathematics and students of algebra alike. German mathematician FELIX KLEIN (1849-1925) specialized in function theory, group theory, and non-Euclidean geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis; Elementary Mathematics from an Advanced Standpoint: Geometry; and Famous Problems of Elementary Geometry.
Download or read book Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree written by Felix 1849-1925 Klein and published by Hassell Street Press. This book was released on 2021-09-09 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book Lectures on Mathematics written by Felix Klein and published by . This book was released on 1893 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree written by Felix Klein and published by . This book was released on 2019 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vorlesungen Uber Die Theorie For Elliptischen Modulfunctionen written by Dr Robert Fricke and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fricke's groundbreaking study of the theory of elliptic modular functions is a must-read for anyone interested in the foundations of modern mathematics. With clear explanations and insightful examples, Fricke offers a comprehensive overview of this complex and fascinating subject. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book Geometry of the Quintic written by Jerry Michael Shurman and published by John Wiley & Sons. This book was released on 1997-01-31 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book helps students at the advanced undergraduate and beginning graduate levels to develop connections between the algebra, geometry, and analysis that they know, and to better appreciate the totality of what they have learned. The text demonstrates the use of general concepts by applying theorems from various areas in the context of one problem - solving the quintic. The problem is approached from two directions: the first is Felix Klein's nineteenth-century approach, using the icosahedron. The second approach presents recent works of Peter Doyle and Curt McMullen, which update Klein's use of transcendental functions to a solution through pure iteration.
Download or read book The Evanston Colloquium written by Felix Klein and published by . This book was released on 1893 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: I. Clebsch.--II-III. Sophus Lie.--IV. On the real shape of algebraic curves and surfaces.--V. Theory of functions and geometry.--VI. On the mathematical character of space-intuition, and the relation of pure mathematics to the applied sciences.--VII. The transcendency of the numbers [Greek letter epsilon] and [Greek letter pi].--VII. Ideal numbers.--IX. The solution of higher algebraic equations.--X. On some recent advances in hyperelliptic and Abelian functions.--XI. The most recent researches in non-Euclidean geometry.--XII. The study of mathematics at Göttingen.--Appendix.
Download or read book The Second Kind of Impossible written by Paul Steinhardt and published by Simon & Schuster. This book was released on 2020-01-07 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: *Shortlisted for the 2019 Royal Society Insight Investment Science Book Prize* One of the most fascinating scientific detective stories of the last fifty years, an exciting quest for a new form of matter. “A riveting tale of derring-do” (Nature), this book reads like James Gleick’s Chaos combined with an Indiana Jones adventure. When leading Princeton physicist Paul Steinhardt began working in the 1980s, scientists thought they knew all the conceivable forms of matter. The Second Kind of Impossible is the story of Steinhardt’s thirty-five-year-long quest to challenge conventional wisdom. It begins with a curious geometric pattern that inspires two theoretical physicists to propose a radically new type of matter—one that raises the possibility of new materials with never before seen properties, but that violates laws set in stone for centuries. Steinhardt dubs this new form of matter “quasicrystal.” The rest of the scientific community calls it simply impossible. The Second Kind of Impossible captures Steinhardt’s scientific odyssey as it unfolds over decades, first to prove viability, and then to pursue his wildest conjecture—that nature made quasicrystals long before humans discovered them. Along the way, his team encounters clandestine collectors, corrupt scientists, secret diaries, international smugglers, and KGB agents. Their quest culminates in a daring expedition to a distant corner of the Earth, in pursuit of tiny fragments of a meteorite forged at the birth of the solar system. Steinhardt’s discoveries chart a new direction in science. They not only change our ideas about patterns and matter, but also reveal new truths about the processes that shaped our solar system. The underlying science is important, simple, and beautiful—and Steinhardt’s firsthand account is “packed with discovery, disappointment, exhilaration, and persistence...This book is a front-row seat to history as it is made” (Nature).
Download or read book The Mathematics of Harmony written by Alexey Stakhov and published by World Scientific. This book was released on 2009 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."
Download or read book Lectures On Algebraic Topology written by Haynes R Miller and published by World Scientific. This book was released on 2021-09-20 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
Download or read book Representation Theory written by Amritanshu Prasad and published by Cambridge University Press. This book was released on 2015-02-05 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the fundamental results of modern combinatorial representation theory. The exercises are interspersed with text to reinforce readers' understanding of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.
Download or read book The Shaping of Deduction in Greek Mathematics written by Reviel Netz and published by Cambridge University Press. This book was released on 2003-09-18 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice.
Download or read book Lectures on the Ikosahedron and the Solution of Equations of the Fifth Degree written by Felix Klein and published by . This book was released on 1888 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry and Quantum Field Theory written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 1995 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.
Download or read book The Shape of Inner Space written by Shing-Tung Yau and published by Il Saggiatore. This book was released on 2010-09-07 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.
