Numbers And Geometry
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Author | : John Stillwell |
Publisher | : Springer Science & Business Media |
Total Pages | : 348 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461206871 |
Download Numbers and Geometry Book in PDF, Epub and Kindle
A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a 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. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He covers the main ideas of Euclid, but with 2000 years of extra insights attached. Presupposing only high school algebra, it can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics due to its attractive and unusual treatment of fundamental topics. A set of well-written exercises at the end of each section allows new ideas to be instantly tested and reinforced.
Author | : C. D. Olds |
Publisher | : Cambridge University Press |
Total Pages | : 198 |
Release | : 2001-02-22 |
Genre | : Mathematics |
ISBN | : 9780883856437 |
Download The Geometry of Numbers Book in PDF, Epub and Kindle
A self-contained introduction to the geometry of numbers.
Author | : Hans Schwerdtfeger |
Publisher | : Courier Corporation |
Total Pages | : 228 |
Release | : 2012-05-23 |
Genre | : Mathematics |
ISBN | : 0486135861 |
Download Geometry of Complex Numbers Book in PDF, Epub and Kindle
Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.
Author | : Liang-shin Hahn |
Publisher | : American Mathematical Soc. |
Total Pages | : 192 |
Release | : 2019-12-26 |
Genre | : Education |
ISBN | : 1470451824 |
Download Complex Numbers and Geometry Book in PDF, Epub and Kindle
The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained—no background in complex numbers is assumed—and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.
Author | : Michal Krizek |
Publisher | : Springer Science & Business Media |
Total Pages | : 280 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 0387218505 |
Download 17 Lectures on Fermat Numbers Book in PDF, Epub and Kindle
The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.
Author | : Álvaro Lozano-Robledo |
Publisher | : American Mathematical Soc. |
Total Pages | : 488 |
Release | : 2019-03-21 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 147045016X |
Download Number Theory and Geometry: An Introduction to Arithmetic Geometry Book in PDF, Epub and Kindle
Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Author | : J.W.S. Cassels |
Publisher | : Springer Science & Business Media |
Total Pages | : 364 |
Release | : 1996-12-16 |
Genre | : Mathematics |
ISBN | : 9783540617884 |
Download An Introduction to the Geometry of Numbers Book in PDF, Epub and Kindle
From the reviews: "A well-written, very thorough account ... Among the topics are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." The American Mathematical Monthly
Author | : Carl Ludwig Siegel |
Publisher | : Springer Science & Business Media |
Total Pages | : 168 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 366208287X |
Download Lectures on the Geometry of Numbers Book in PDF, Epub and Kindle
Carl Ludwig Siegel gave a course of lectures on the Geometry of Numbers at New York University during the academic year 1945-46, when there were hardly any books on the subject other than Minkowski's original one. This volume stems from Siegel's requirements of accuracy in detail, both in the text and in the illustrations, but involving no changes in the structure and style of the lectures as originally delivered. This book is an enticing introduction to Minkowski's great work. It also reveals the workings of a remarkable mind, such as Siegel's with its precision and power and aesthetic charm. It is of interest to the aspiring as well as the established mathematician, with its unique blend of arithmetic, algebra, geometry, and analysis, and its easy readability.
Author | : J.W.S. Cassels |
Publisher | : Springer Science & Business Media |
Total Pages | : 357 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642620353 |
Download An Introduction to the Geometry of Numbers Book in PDF, Epub and Kindle
From the reviews: "A well-written, very thorough account ... Among the topics are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." The American Mathematical Monthly
Author | : Z. A. Melzak |
Publisher | : Courier Corporation |
Total Pages | : 244 |
Release | : 2014-01-15 |
Genre | : Mathematics |
ISBN | : 0486789489 |
Download Invitation to Geometry Book in PDF, Epub and Kindle
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra. This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty.