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Paperback. Zustand: New. 1st ed. 2015. This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution.  Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation.Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the "wedding," via analytic geometry, of algebra and geometry; the "taming" of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor's creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted.  Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided.Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.

Paperback. Zustand: New. 2001 ed. In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond Euclid, using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus, where one stud­ ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus, but in many mathematical situations. So trigonometry is a part of pre-calculus, and is related to other pre-calculus topics, such as exponential and logarithmic functions, and complex numbers.

Paperback. Zustand: New. 2014 ed. Many probability books are written by mathematicians and have the built-in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance and engineering. A one-semester course is laid out in an efficient and readable manner covering the core material. The first three chapters provide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation) and applied probability. Two subsequent chapters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treats conditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance. Like Adventures in Stochastic Processes, Resnick's related and very successful textbook, A Probability Path is rich in appropriate examples, illustrations and problems and is suitable for classroom use or self-study. The present uncorrected, softcover reprint is designed to make this classic textbook available to a wider audience. This book is different from the classical textbooks on probability theory in that it treats the measure theoretic background not as a prerequisite but as an integral part of probability theory. The result is that the reader gets a thorough and well-structured framework needed to understand the deeper concepts of current day advanced probability as itis used in statistics, engineering, biology and finance. The pace of the book is quick and disciplined. Yet there are ample examples sprinkled over the entire book and each chapter finishes with a wealthy section of inspiring problems. -Publications of the International Statistical Institute This textbook offers material for a one-semester course in probability, addressed to students whose primary focus is not necessarily mathematics. Each chapter is completed by an exercises section. Carefully selected examples enlighten the reader in many situations. The book is an excellent introduction to probability and its applications. -Revue Roumaine de Mathématiques Pures et Appliquées.

Paperback. Zustand: New. Softcover reprint of the original 1st ed. 1981.

Paperback. Zustand: New. 2007 ed. Prior to the nineteenth century, algebra meant the study of the solution of polynomial equations. By the twentieth century it came to encompass the study of abstract, axiomatic systems such as groups, rings, and fields. This presentation provides an account of the history of the basic concepts, results, and theories of abstract algebra.The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared unsolvable by classical means. A major theme of the approach in this book is to show how abstract algebra has arisen in attempts to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.Mathematics instructors, algebraists, and historians of science will find the work a valuable reference. The book may also serve as a supplemental text for courses in abstract algebra or the history of mathematics.

Paperback. Zustand: New. This fairly self-contained work embraces a broad range of topics in analysis at the graduate level, requiring only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic exposition is the historical accounts of ideas and methods pertaining to the relevant topics. Most interesting and useful are the connections developed between analysis and other mathematical disciplines, in this case, numerical analysis and probability theory.The text is divided into two parts: The first examines the systems of real and complex numbers and deals with the notion of sequences in this context. After the presentation of natural numbers as a subset of the reals, elements of combinatorics and a discussion of the mathematical notion of the infinite are introduced. The second part is dedicated to discrete processes starting with a study of the processes of infinite summation both in the case of numerical series and of power series. Softcover reprint of the original 1st ed. 2004.

Paperback. Zustand: New. The problem of developing a systematic approach to the design of feed­ back strategies capable of shaping the response of complicated dynamical control systems illustrates the integration of a wide variety of mathemat­ ical disciplines typical of the modern theory of systems and control. As a concrete example, one may consider the control of fluid flow across an airfoil, for which recent experiments indicate the possibility of delaying the onset of turbulence by controlling viscosity through thermal actuators located on the airfoil. In general, there are two approaches to the con­ trol of such a complica. ted process, the development of extremely detailed models of the process followed by the derivation of a more "dedicated" feed­ back law or the development of a more simple model class followed by the derivation of control laws which are more robust to unmodelled dynamics and exogeneous disturbances. In either approach, the two twin themes of approximation and computation play a significant role in the derivation and implementation of resulting control laws. And there is no doubt that the cross-fertilization between these twin themes and control theory will increase unabated throughout the next decade, not just as an important component of design and implementation of control laws but also as a source of new problems in computational mathematics. In this volume, we present a collection of papers which were deliv­ ered at the first Bozeman Conference on Computation and Control, held at Montana State University on August 1-11, 1988.

Paperback. Zustand: New. To most graph theorists there are two outstanding landmarks in the history of their subject. One is Euler's solution of the Konigsberg Bridges Problem, dated 1736, and the other is the appearance of Denes Konig's textbook in 1936. "From Konigsberg to Konig's book" sings the poetess, "So runs the graphic tale ." [10]. There were earlier books that took note of graph theory. Veb- len's Analysis Situs, published in 1931, is about general combinato- rial topology. But its first two chapters, on "Linear graphs" and "Two-Dimensional Complexes", are almost exclusively concerned with the territory still explored by graph theorists. Rouse Ball's Mathematical Recreations and Essays told, usually without proofs, of the major graph-theoretical advances ofthe nineteenth century, of the Five Colour Theorem, of Petersen's Theorem on I-factors, and of Cayley's enumerations of trees. It was Rouse Ball's book that kindled my own graph-theoretical enthusiasm. The graph-theoretical papers of Hassler Whitney, published in 1931-1933, would have made an excellent textbook in English had they been collected and published as such.But the honour of presenting Graph Theory to the mathe- matical world as a subject in its own right, with its own textbook, belongs to Denes Konig. Low was the prestige of Graph Theory in the Dirty Thirties. It is still remembered, with resentment now shading into amuse- ment, how one mathematician scorned it as "The slums of Topol- ogy". Softcover reprint of the original 1st ed. 1990.

Hardback. Zustand: New. 2008 ed. This self-contained work illustrates the application of integral methods to diverse problems in mathematics, physics, biology, and engineering. The chapters contain state-of-the-art information on current research in a variety of important practical disciplines. The problems examined arise in real-life processes and phenomena and use a wide range of solution techniques. This is a useful and practical guide.

Hardback. Zustand: New. 2003 ed. For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today the traditional place of mathematics in education is in grave danger. Unfortunately, professional representatives of mathematics share in the reponsibiIity. The teaching of mathematics has sometimes degen­ erated into empty drill in problem solving, which may develop formal ability but does not lead to real understanding or to greater intellectual indepen­ dence. Mathematical research has shown a tendency toward overspecialization and over-emphasis on abstraction. Applications and connections with other fields have been neglected . . . But . . . understanding of mathematics cannot be transmitted by painless entertainment any more than education in music can be brought by the most brilliant journalism to those who never have lis­ tened intensively. Actual contact with the content of living mathematics is necessary. Nevertheless technicalities and detours should be avoided, and the presentation of mathematics should be just as free from emphasis on routine as from forbidding dogmatism which refuses to disclose motive or goal and which is an unfair obstacle to honest effort. (From the preface to the first edition of What is Mathematics? by Richard Courant and Herbert Robbins, 1941.

Paperback. Zustand: New. Softcover reprint of the original 1st ed. 1994.

Paperback. Zustand: New. 1st ed. 2004. Corr. 2nd printing 2003. This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

Paperback. Zustand: New. 1st ed. 2004. Corr. 2nd printing 2003. This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

Paperback. Zustand: New. 1st ed. 1989. 2nd printing 2008. Softcover reprint of the original 1st ed. 1989.

Paperback. Zustand: New. 2009 ed. This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis.

Paperback. Zustand: New. 1st ed. 2015. This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution.  Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation.Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the "wedding," via analytic geometry, of algebra and geometry; the "taming" of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor's creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted.  Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided.Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.

Hardback. Zustand: New. 1984 ed. This book presents a self-contained introduction to H.M. Stark's remarkable conjectures about the leading term of the Taylor expansion of Artin's L-functions at s=0. These conjectures can be viewed as a vast generalization of Dirichlet's class number formula and Kronecker's limit formula. They provide an unexpected contribution to Hilbert's 12th problem on the generalization of class fields by the values of transcendental functions.This volume also treats these topics: a proof of the main conjecture for rational characters, and Chinburg's invariant; P. Delgne's proof of a function field analogue; p-adic versions of the conjectures due to B. Gross and J.-P. Serre.This volume belongs on the shelf of every mathematics library.

Mixed Media Product. Zustand: New. 2007. Satellite navigation receivers are used to receive and decode satellite navigation signals, including those provided by the GPS constellation of satellites. There is an increasing need for a unified platform that will enable enhanced receiver development and design, as well as cost-effective testing procedures for various applications. This book explores the use of such new technologies in the area of satellite navigation receivers. In order to obtain a reconfigurable receiver with a wide range of applications, the authors discuss receiver architecture based on software-defined radio techniques. The presentation unfolds in a systematic user-friendly style and goes from the basics to cutting-edge research.Key features and topics include:* presentation of basic signal structures used in GPS and Galileo---the European satellite navigation system * design and implementation of a GPS signal generator using the simulated signals * analysis of three different methods of signal acquisition: the serial search, the parallel-frequency space search, and the newer method of parallel-code phase search * implementation of analyzed methods in MATLAB and a discussion of the choice of algorithms involved * MATLAB-based exercises * a hands-on method of testing the material covered in the book: hardware equipment---which may be purchased online---enables readers to generate real-world data, and downloadable MATLAB software---available at www gps.aau.dk/ borre/sw--- allows readers to change various parameters and immediately see their effect * bibliography of recent results and comprehensive index The book is aimed at applied mathematicians, electrical engineers, geodesists, and graduate students. It may be used as a textbook in various GPS technology and signal processing courses, or as a self-study reference for anyone working with satellite navigation receivers.

Paperback. Zustand: New. 2001 ed. In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond Euclid, using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus, where one stud­ ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus, but in many mathematical situations. So trigonometry is a part of pre-calculus, and is related to other pre-calculus topics, such as exponential and logarithmic functions, and complex numbers.

Hardback. Zustand: New. 2010 ed. This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants - including Olympiad and Putnam competitors - as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

Hardback. Zustand: New. 2nd ed. 2013.

Hardback. Zustand: New. 2011.

Paperback. Zustand: New. 1st ed. 2004. Corr. 2nd printing 2003. This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

Hardback. Zustand: New. 2nd ed. 2013.

Hardback. Zustand: New. This volume presents a selection of contributions by Russian scholars - historians and philosophers to science - to the Einstein Studies industry, broadly construed. This work explores the historical and foundational issues in general relativity and relativistic cosmology, Einstein's contributions to early quantum mechanics and the rise of Dirac's quantum electrodynamics. It also includes a detailed description of the physics colloquium Einstein established and coordinated in 1912-1913 and comments on his brief interest in the construction of the plane wing in 1916. The contributors draw extensively on documentation previously unavailable to most scholars. Materials from various Russian archives shed new light on the famous exchange (regarding the first evolutionary cosmological models) between Einstein and Alexander Friedmann in the early 1920s and on the role of Boris Podolsky and Vladimir Fock in the emergence of quantum electrodynamics. The little-known correspondence between Einstein and a famous German pilot Paul Erhardt suggests that during World War I, the former was involved with aero- and hydrodynamics research and ways of improving airplane design.Other articles introduce new approaches to important foundational questions in general relativity and cosmology.

Paperback. Zustand: New. by Gian-Carlo Rota The subjects of mathematics, like the subjects of mankind, have finite lifespans, which the historian will record as he freezes history at one instant of time. There are the old subjects, loaded with distinctions and honors. As their problems are solved away and the applications reaped by engineers and other moneymen, ponderous treatises gather dust in library basements, awaiting the day when a generation as yet unborn will rediscover the lost paradise in awe. Then there are the middle-aged subjects. You can tell which they are by roaming the halls of Ivy League universities or the Institute for Advanced Studies. Their high priests haughtily refuse fabulous offers from eager provin­ cial universities while receiving special permission from the President of France to lecture in English at the College de France. Little do they know that the load of technicalities is already critical, about to crack and submerge their theorems in the dust of oblivion that once enveloped the dinosaurs. Finally, there are the young subjects-combinatorics, for instance. Wild­ eyed individuals gingerly pick from a mountain of intractable problems, chil­ dishly babbling the first words of what will soon be a new language. Child­ hood will end with the first Seminaire Bourbaki. It could be impossible to find a more fitting example than matroid theory of a subject now in its infancy. The telltale signs, for an unfailing diagnosis, are the abundance of deep theorems, going together with a paucity of theories. Softcover reprint of the original 1st ed. 1986.

Paperback. Zustand: New. 2014 ed. Many probability books are written by mathematicians and have the built-in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance and engineering. A one-semester course is laid out in an efficient and readable manner covering the core material. The first three chapters provide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation) and applied probability. Two subsequent chapters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treats conditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance. Like Adventures in Stochastic Processes, Resnick's related and very successful textbook, A Probability Path is rich in appropriate examples, illustrations and problems and is suitable for classroom use or self-study. The present uncorrected, softcover reprint is designed to make this classic textbook available to a wider audience. This book is different from the classical textbooks on probability theory in that it treats the measure theoretic background not as a prerequisite but as an integral part of probability theory. The result is that the reader gets a thorough and well-structured framework needed to understand the deeper concepts of current day advanced probability as itis used in statistics, engineering, biology and finance. The pace of the book is quick and disciplined. Yet there are ample examples sprinkled over the entire book and each chapter finishes with a wealthy section of inspiring problems. -Publications of the International Statistical Institute This textbook offers material for a one-semester course in probability, addressed to students whose primary focus is not necessarily mathematics. Each chapter is completed by an exercises section. Carefully selected examples enlighten the reader in many situations. The book is an excellent introduction to probability and its applications. -Revue Roumaine de Mathématiques Pures et Appliquées.

Paperback. Zustand: New. 2007 ed. Modern aerospace vehicles, such as the space shuttle, other launch vehicles, and long-range ballistic missiles, do not discriminate between atmospheric and space flight. Most texts on flight dynamics, however, make this artificial distinction and therefore do not simultaneously cover aircraft and spacecraft. Bridging this gap in the literature, "Atmospheric and Space Flight Dynamics" is a unified presentation, demonstrating that the two disciplines have actually evolved from the same set of physical principles. Introduced is a broad range of modern topics in an accessible, yet mathematically rigorous presentation. A key feature of the text is the integration of many MATLAB- and Simulink-based numerical examples and real-world simulations throughout for the design of aircraft, missiles, launch vehicles, re-entry vehicles, and spacecraft. The author uses the software as an instructional, hands-on tool, moving away from the "cook book" approach found in other works. Replete with illustrations, end-of-chapter exercises, and selected solutions, the work is primarily useful as a textbook for advanced undergraduate and beginning graduate-level students.The book is also suitable as a reference or self-study guide for researchers and practitioners in aerospace engineering, aviation, mechanical engineering, dynamics, astrodynamics, aeronautics, and astronautics.

Hardback. Zustand: New. 2004 ed. In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer­ sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". . The theo­ pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.

Paperback. Zustand: New. 2007 ed. Prior to the nineteenth century, algebra meant the study of the solution of polynomial equations. By the twentieth century it came to encompass the study of abstract, axiomatic systems such as groups, rings, and fields. This presentation provides an account of the history of the basic concepts, results, and theories of abstract algebra.The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared unsolvable by classical means. A major theme of the approach in this book is to show how abstract algebra has arisen in attempts to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.Mathematics instructors, algebraists, and historians of science will find the work a valuable reference. The book may also serve as a supplemental text for courses in abstract algebra or the history of mathematics.