Beyond The Quartic Equation

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Beyond the Quartic Equation

R. Bruce King
Beyond the Quartic Equation Book PDF

Author : R. Bruce King
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 54,9 Mb
Release : 2009-01-16
Category : Mathematics
ISBN : 9780817648497

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Beyond the Quartic Equation by R. Bruce King Pdf

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

Beyond the Quadratic Formula

Ron Irving
Beyond the Quadratic Formula Book PDF

Author : Ron Irving
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 40,5 Mb
Release : 2020-01-29
Category : Education
ISBN : 9781470451769

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Beyond the Quadratic Formula by Ron Irving Pdf

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.

Beyond the Quadratic Formula

Ronald S. Irving
Beyond the Quadratic Formula Book PDF

Author : Ronald S. Irving
Publisher : MAA
Page : 246 pages
File Size : 54,6 Mb
Release : 2013-10-10
Category : Mathematics
ISBN : 9780883857830

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Beyond the Quadratic Formula by Ronald S. Irving Pdf

A study guide to polynomials that goes beyond the familiar quadratic formula to cover cubic and quartic equations.

The Equation That Couldn't Be Solved

Mario Livio
The Equation That Couldn t Be Solved Book PDF

Author : Mario Livio
Publisher : Simon and Schuster
Page : 367 pages
File Size : 54,8 Mb
Release : 2005-09-19
Category : Mathematics
ISBN : 9780743274623

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The Equation That Couldn't Be Solved by Mario Livio Pdf

What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

Fields and Galois Theory

John M. Howie
Fields and Galois Theory Book PDF

Author : John M. Howie
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 42,8 Mb
Release : 2007-10-11
Category : Mathematics
ISBN : 9781852339869

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Fields and Galois Theory by John M. Howie Pdf

A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study Previous books by Howie in the SUMS series have attracted excellent reviews

Advanced Problems in Mathematics

Stephen Siklos
Advanced Problems in Mathematics Book PDF

Author : Stephen Siklos
Publisher : Unknown
Page : 188 pages
File Size : 45,5 Mb
Release : 2019-10-16
Category : Mathematics
ISBN : 1783747765

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Advanced Problems in Mathematics by Stephen Siklos Pdf

This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Learning Modern Algebra

Albert Cuoco,Joseph Rotman
Learning Modern Algebra Book PDF

Author : Albert Cuoco,Joseph Rotman
Publisher : MAA
Page : 481 pages
File Size : 54,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9781939512017

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Learning Modern Algebra by Albert Cuoco,Joseph Rotman Pdf

A guide to modern algebra for mathematics teachers. It makes explicit connections between abstract algebra and high-school mathematics.

Solving Transcendental Equations

John P. Boyd
Solving Transcendental Equations Book PDF

Author : John P. Boyd
Publisher : SIAM
Page : 446 pages
File Size : 53,7 Mb
Release : 2014-09-23
Category : Mathematics
ISBN : 9781611973525

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Solving Transcendental Equations by John P. Boyd Pdf

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 indispensible 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.

Introduction to Applied Linear Algebra

Stephen Boyd,Lieven Vandenberghe
Introduction to Applied Linear Algebra Book PDF

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 47,8 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Elements of Abstract Algebra

Allan Clark
Elements of Abstract Algebra Book PDF

Author : Allan Clark
Publisher : Courier Corporation
Page : 224 pages
File Size : 54,5 Mb
Release : 2012-07-06
Category : Mathematics
ISBN : 9780486140353

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Elements of Abstract Algebra by Allan Clark Pdf

Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.

Numerical Methods for Roots of Polynomials - Part II

J.M. McNamee,V.Y. Pan
Numerical Methods for Roots of Polynomials Part II Book PDF

Author : J.M. McNamee,V.Y. Pan
Publisher : Elsevier Inc. Chapters
Page : 728 pages
File Size : 49,7 Mb
Release : 2013-07-19
Category : Mathematics
ISBN : 9780128077023

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Numerical Methods for Roots of Polynomials - Part II by J.M. McNamee,V.Y. Pan Pdf

We deal here with low-degree polynomials, mostly closed-form solutions. We describe early and modern solutions of the quadratic, and potential errors in these. Again we give the early history of the cubic, and details of Cardan’s solution and Vieta’s trigonometric approach. We consider the discriminant, which decides what type of roots the cubic has. Then we describe several ways (both old and new) of solving the quartic, most of which involve first solving a “resolvent” cubic. The quintic cannot in general be solved by radicals, but can be solved in terms of elliptic or related functions. We describe an algorithm due to Kiepert, which transforms the quintic into a form having no or term; then into a form where the coefficients depend on a single parameter; and later another similar form. This last form can be solved in terms of Weierstrass elliptic and theta functions, and finally the various transformations reversed.

Abel's Proof

Peter Pesic
Abel s Proof Book PDF

Author : Peter Pesic
Publisher : MIT Press
Page : 242 pages
File Size : 45,9 Mb
Release : 2004-02-27
Category : Technology & Engineering
ISBN : 0262661829

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Abel's Proof by Peter Pesic Pdf

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.

Achievement In Mathematics

D. Bhaskara Rao
Achievement In Mathematics Book PDF

Author : D. Bhaskara Rao
Publisher : Discovery Publishing House
Page : 140 pages
File Size : 43,7 Mb
Release : 1995
Category : Electronic
ISBN : 8171412785

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Achievement In Mathematics by D. Bhaskara Rao Pdf

Contents: - Introduction, Related Literature, Research Desigh, Data Analysis, Summary, Conclusions and Discussion.

Making up Numbers: A History of Invention in Mathematics

Ekkehard Kopp
Making up Numbers A History of Invention in Mathematics Book PDF

Author : Ekkehard Kopp
Publisher : Open Book Publishers
Page : 280 pages
File Size : 48,5 Mb
Release : 2020-10-23
Category : Mathematics
ISBN : 9781800640979

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Making up Numbers: A History of Invention in Mathematics by Ekkehard Kopp Pdf

Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

Food Webs

S. Pimm
Food Webs Book PDF

Author : S. Pimm
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400959255

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Food Webs by S. Pimm Pdf

Often the meanings of words are changed subtly for interesting reasons. The implication of the word 'community' has changed from including all the organisms in an area to only those species at a particular trophic level (and often a taxonomically restricted group), for example, 'bird-community'. If this observation is correct, its probable cause is the dramatic growth in our knowledge of the ecological patterns along trophic levels (I call these horizontal patterns) and the processes that generate them. This book deals with vertical patterns - those across trophic levels -and tries to compensate for their relative neglect. In cataloging a dozen vertical patterns I hope to convince the reader that species interactions across trophic levels are as patterned as those along trophic levels and demand explanations equally forcefully. But this is not the only objective. A limited number of processes shape the patterns of species interaction; to demonstrate their existence is an essential step in understanding why ecosystems are the way they are. To achieve these aims I must resort to both mathematical techniques to develop theories and statistical techniques to decide between rival hypotheses. The level of mathematics is likely to offend nearly everyone. Some will find any mathematics too much, while others will consider the material to be old, familiar ground and probably explained with a poor regard for rigour and generality.