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Top charts. New arrivals. Numbers and Geometry John Stillwell December 6, The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus or a pre-calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. The key is algebra, which brings arithmetic and geometry together, and allows them to flourish and branch out in new directions.
Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He believes that most of mathematics is about numbers, curves and functions, and the links between these concepts can be suggested by a thorough study of simple examples, such as the circle and the square. This book covers the main ideas of Euclid--geometry, arithmetic and the theory of real numbers, but with years of extra insights attached.
Moreover, this book will be popular with graduate students and researchers in mathematics because it is such an attractive and unusual treatment of fundamental topics. Also, it will serve admirably in courses aimed at giving students from other areas a view of some of the basic ideas in mathematics. There is a set of well-written exercises at the end of each section, so new ideas can be instantly tested and reinforced. Reviews Review Policy. Published on. Original pages.
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Please follow the detailed Help center instructions to transfer the files to supported eReaders. More related to number theory. See more. Peter Hilton. Focusing Your Attention The purpose of this book is Cat least twofold. First, we want to show you what mathematics is, what it is about, and how it is done-by those who do it successfully. We are, in fact, trying to give effect to what we call, in Section 9. We want to attract you-and, through you, future readers-to mathematics.
There is general agreement in the so-called civilized world that mathematics is important, but only a very small minority of those who make contact with mathematics in their early education would describe it as delightful.
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We want to correct the false impression of mathematics as a combination of skill and drudgery, and to re inforce for our readers a picture of mathematics as an exciting, stimulating and engrossing activity; as a world of accessible ideas rather than a world of incomprehensible techniques; as an area of continued interest and investigation and not a set of procedures set in stone. Moduli of Abelian Varieties. Book Applications range from algebraic geometry and number theory to mathematical physics.
The present collection of 17 refereed articles originates from the third "Texel Conference" held in Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field. The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics.
An Introduction to the Geometry of Numbers. From the reviews: "The work is carefully written. It is well motivated, and interesting to read, even if it is not always easy Among the topi are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references. This book is a revised and greatly expanded version of our book Elements of Number Theory published in As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students.
We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary.
Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry.
By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time. Number Theory for Beginners.
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