Download or read book Beyond the Quartic Equation written by R. Bruce King and published by Springer Science & Business Media. This book was released on 2009-01-16 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians. The book includes an initial introductory chapter on group theory and symmetry, Galois theory and Tschirnhausen transformations, and some elementary properties of elliptic function in order to make some of the key ideas more accessible to less sophisticated readers. The book also includes a discussion of the much simpler algorithms for roots of the general quadratic, cubic, and quartic equations before discussing the algorithm for the roots of the general quintic equation. A brief discussion of algorithms for roots of general equations of degrees higher than five is also included. "If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations." --New Scientist

Download or read book Solution of Cubic and Quartic Equations written by S. Neumark and published by Elsevier. This book was released on 2014-05-16 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solution of Cubic and Quartic Equations presents the classical methods in solving cubic and quartic equations to the highest possible degree of efficiency. This book suggests a rapid and efficient method of computing the roots of an arbitrary cubic equation with real coefficients, by using specially computed 5-figure tables. The method of factorizing an arbitrary quartic equation by an appropriate use of a resolvent cubic is also discussed. Section 4 of this text gives several numerical examples that show the rapidity of the procedures suggested. This publication is valuable to mathematicians and students intending to acquire knowledge of the cubic and quartic equations.

Download or read book Beyond the Quadratic Formula written by Ron Irving and published by American Mathematical Soc.. This book was released on 2020-01-29 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial's coefficients can be used to obtain detailed information on its roots. The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.

Download or read book A Journey Through The Realm of Numbers written by Menny Aka and published by Springer Nature. This book was released on 2020-10-03 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done. Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions. This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.

Download or read book Kummer s Quartic Surface written by Ronald William Henry Turnbull Hudson and published by Cambridge University Press. This book was released on 1990-10-11 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many questions involving the theory of surfaces, such as the classification of quartic surfaces, the description of moduli spaces for abelian surfaces, and the automorphism group of a Kummer surface, are touched upon in this volume.

Download or read book Galois Theory Fourth Edition written by Ian Stewart and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discriminant Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2017 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.

Download or read book Galois Theory of Algebraic Equations written by Jean-Pierre Tignol and published by World Scientific. This book was released on 2001 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois' Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as ?group? and ?field?. A brief discussion on the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way that the most technical details can be skipped by readers who are interested primarily in a broad survey of the theory.This book will appeal to both undergraduate and graduate students in mathematics and the history of science, and also to teachers and mathematicians who wish to obtain a historical perspective of the field. The text has been designed to be self-contained, but some familiarity with basic mathematical structures and with some elementary notions of linear algebra is desirable for a good understanding of the technical discussions in the later chapters.

Download or read book Solving Transcendental Equations written by John P. Boyd and published by SIAM. This book was released on 2014-10-23 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute?not always needed, but indispensable when it is. The author?s goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations. Solving Transcendental Equations is unique in that it is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval, and the very reliable spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding, and it includes three chapters on analytical methods?explicit solutions, regular pertubation expansions, and singular perturbation series (including hyperasymptotics)?unlike other books that give only numerical algorithms for solving algebraic and transcendental equations. This book is written for specialists in numerical analysis and will also appeal to mathematicians in general. It can be used for introductory and advanced numerical analysis classes, and as a reference for engineers and others working with difficult equations.

Download or read book Diophantine Equations and Power Integral Bases written by Istvan Gaal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.

Download or read book On Cyclides and Sphero quartics written by John Casey and published by . This book was released on 1871 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Shape Of Algebra In The Mirrors Of Mathematics The A Visual Computer aided Exploration Of Elementary Algebra And Beyond With Cd rom written by Gabriel Katz and published by World Scientific Publishing Company. This book was released on 2011-10-10 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Shape of Algebra in the Mirrors of Mathematics is a unique text aiming to explain some elements of modern mathematics and to show its flavor and unity. It is neither a standard textbook nor a tour of algebra for a casual reader. Rather, it is an attempt to share authors' mathematical experiences and philosophy with readers who have more than a passing interest in mathematics, but only a traditional exposure to High School Algebra and some elements of Calculus. The book gives the readers a sense of visual nature of significant part of mathematics.The reader becomes an owner of and a researcher in VisuMatica, a virtual math laboratory. It is an original and comprehensive PC software package (a brainchild of the second author) that will enable the reader to experience mathematics both as a human intellectual endeavor and as an experimental science. Although it is possible to read and appreciate the book without ever visiting the VisuMatica lab, those who engage with the interactive demos found in the lab will greatly advance their understanding of the text. The book seeks to encourage an interactive, investigative style of learning that can promote the habits of mind characteristic of modern mathematical thinking.An outline of the topics that are discussed may read like a list of graduate courses: Abstract Algebra, Topology, Singularity Theory, Complex Analysis, and Number Theory. However, they are presented from an intuitive perspective that uses primarily visual models and concepts. Although the main subject is polynomials and polynomial equations, the true story line is the interplay between basic ideas from algebra, geometry, analysis and topology.The Shape of Algebra might serve as a text for an “appreciation” course in modern mathematics designed for non-mathematics majors or for students who are considering majoring in mathematics or related disciplines. The authors' goal is to present the reader with a fresh viewpoint on the sense and flavor of mathematics. The subject is often presented in a fashion that students find stale and uncompelling. The book's emphasis, in contrast, is on how a modern practitioner thinks about and works within the discipline.The book aims to attract students of all ages, particularly including professional mathematicians interested in pedagogy. In part, The Shape of Algebra is directed at secondary and college teachers and students who want to expand their horizons in the field and to find both a fresh presentation of familiar concepts and, perhaps, some unexpected results. Many of the topics and demos are self-contained and can be used individually to enhance traditional courses. Several of the ideas and materials developed in the book have been tested in high school and college classrooms. The book will enable readers to approach its content on three levels: the first level requires only some fluency with routine algebraic manipulations; the second also presumes familiarity with the notions of derivatives, and the third uses some basic concepts of multivariable calculus and linear algebra. All three levels are clearly marked in the text, and allow for a smooth reading enhanced by virtual experiments.

Download or read book The History of Mathematics written by Roger L. Cooke and published by John Wiley & Sons. This book was released on 2012-11-08 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Second Edition "An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential." —CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented as individual lessons New and revised exercises ranging between technical, factual, and integrative Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.

Download or read book The Equations World written by Boris Pritsker and published by Courier Dover Publications. This book was released on 2019-08-14 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations are the lifeblood of mathematics, science, and technology, and this book examines equations of all kinds. With his masterful ability to convey the excitement and elegance of mathematics, author Boris Pritsker explores equations from the simplest to the most complex—their history, their charm, and their usefulness in solving problems. The Equations World bridges the fields of algebra, geometry, number theory, and trigonometry, solving more than 280 problems by employing a wide spectrum of techniques. The author demystifies the subject with efficient hints, tricks, and methods that reveal the fun and satisfaction of problem solving. He also demonstrates how equations can serve as important tools for expressing a problem's data, showing the ways in which they assist in fitting parts together to solve the whole puzzle. In addition, brief historical tours reveal the foundations of mathematical thought by tracing the ideas and approaches developed by mathematicians over the centuries. Both recreational mathematicians and ambitious students will find this book an ample source of enlightenment and enjoyment.

Download or read book Mathematics From the Birth of Numbers written by Jan Gullberg and published by W. W. Norton & Company. This book was released on 1997-01-07 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustrated exploration of mathematics and its history, beginning with a study of numbers and their symbols, and continuing with a broad survey that includes consideration of algebra, geometry, hyperbolic functions, fractals, and many other mathematical functions.

Download or read book NASA Thesaurus written by and published by . This book was released on 1994 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Equations of State for Fluids and Fluid Mixtures written by J.V. Sengers and published by Elsevier. This book was released on 2000-10-30 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been prepared under the auspices of Commission I.2 on Thermodynamics of the International Union of Pure and Applied Chemistry (IUPAC). The authors of the 18 chapters are all recognized experts in the field. The book gives an up-to-date presentation of equations of state for fluids and fluid mixtures. All principal approaches for developing equations of state are covered. The theoretical basis and practical use of each type of equation is discussed and the strength and weaknesses of each is addressed. Topics addressed include the virial equation of state, cubic equations and generalized van der Waals equations, perturbation theory, integral equations, corresponding stated and mixing rules. Special attention is also devoted to associating fluids, polydisperse fluids, polymer systems, self-assembled systems, ionic fluids and fluids near critical points.