Numbers And Geometry

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Numbers and Geometry

John Stillwell
Numbers and Geometry Book PDF

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206873

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Numbers and Geometry by John Stillwell Pdf

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.

The Geometry of Numbers

C. D. Olds,Anneli Lax,Giuliana P. Davidoff,Giuliana Davidoff
The Geometry of Numbers Book PDF

Author : C. D. Olds,Anneli Lax,Giuliana P. Davidoff,Giuliana Davidoff
Publisher : Cambridge University Press
Page : 198 pages
File Size : 44,7 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0883856433

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The Geometry of Numbers by C. D. Olds,Anneli Lax,Giuliana P. Davidoff,Giuliana Davidoff Pdf

A self-contained introduction to the geometry of numbers.

Number Theory and Geometry: An Introduction to Arithmetic Geometry

Álvaro Lozano-Robledo
Number Theory and Geometry An Introduction to Arithmetic Geometry Book PDF

Author : Álvaro Lozano-Robledo
Publisher : American Mathematical Soc.
Page : 488 pages
File Size : 53,5 Mb
Release : 2019-03-21
Category : Arithmetical algebraic geometry
ISBN : 9781470450168

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Number Theory and Geometry: An Introduction to Arithmetic Geometry by Álvaro Lozano-Robledo Pdf

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.

Complex Numbers and Geometry

Liang-shin Hahn
Complex Numbers and Geometry Book PDF

Author : Liang-shin Hahn
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 43,8 Mb
Release : 2019-12-26
Category : Education
ISBN : 9781470451820

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Complex Numbers and Geometry by Liang-shin Hahn Pdf

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.

Geometry of Complex Numbers

Hans Schwerdtfeger
Geometry of Complex Numbers Book PDF

Author : Hans Schwerdtfeger
Publisher : Courier Corporation
Page : 224 pages
File Size : 40,6 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486135861

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Geometry of Complex Numbers by Hans Schwerdtfeger Pdf

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Complex Numbers in Geometry

I. M. Yaglom
Complex Numbers in Geometry Book PDF

Author : I. M. Yaglom
Publisher : Academic Press
Page : 256 pages
File Size : 45,6 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483266633

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Complex Numbers in Geometry by I. M. Yaglom Pdf

Complex Numbers in Geometry focuses on the principles, interrelations, and applications of geometry and algebra. The book first offers information on the types and geometrical interpretation of complex numbers. Topics include interpretation of ordinary complex numbers in the Lobachevskii plane; double numbers as oriented lines of the Lobachevskii plane; dual numbers as oriented lines of a plane; most general complex numbers; and double, hypercomplex, and dual numbers. The text then takes a look at circular transformations and circular geometry, including ordinary circular transformations, axial circular transformations of the Lobachevskii plane, circular transformations of the Lobachevskii plane, axial circular transformations, and ordinary circular transformations. The manuscript is intended for pupils in high schools and students in the mathematics departments of universities and teachers' colleges. The publication is also useful in the work of mathematical societies and teachers of mathematics in junior high and high schools.

An Introduction to the Geometry of Numbers

J.W.S. Cassels
An Introduction to the Geometry of Numbers Book PDF

Author : J.W.S. Cassels
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 43,6 Mb
Release : 1996-12-16
Category : Mathematics
ISBN : 3540617884

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An Introduction to the Geometry of Numbers by J.W.S. Cassels Pdf

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

Number, Shape, & Symmetry

Diane L. Herrmann,Paul J. Sally, Jr.
Number Shape Symmetry Book PDF

Author : Diane L. Herrmann,Paul J. Sally, Jr.
Publisher : CRC Press
Page : 446 pages
File Size : 45,9 Mb
Release : 2012-10-18
Category : Mathematics
ISBN : 9781466554641

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Number, Shape, & Symmetry by Diane L. Herrmann,Paul J. Sally, Jr. Pdf

Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.

An Introduction to the Geometry of Numbers

J.W.S. Cassels
An Introduction to the Geometry of Numbers Book PDF

Author : J.W.S. Cassels
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642620355

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An Introduction to the Geometry of Numbers by J.W.S. Cassels Pdf

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

Geometry of Numbers

C. G. Lekkerkerker
Geometry of Numbers Book PDF

Author : C. G. Lekkerkerker
Publisher : Elsevier
Page : 520 pages
File Size : 42,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483259277

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Geometry of Numbers by C. G. Lekkerkerker Pdf

Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VIII: Geometry of Numbers focuses on bodies and lattices in the n-dimensional euclidean space. The text first discusses convex bodies and lattice points and the covering constant and inhomogeneous determinant of a set. Topics include the inhomogeneous determinant of a set, covering constant of a set, theorem of Minkowski-Hlawka, packing of convex bodies, successive minima and determinant of a set, successive minima of a convex body, extremal bodies, and polar reciprocal convex bodies. The publication ponders on star bodies, as well as points of critical lattices on the boundary, reducible, and irreducible star bodies and reduction of automorphic star bodies. The manuscript reviews homogeneous and inhomogeneous s forms and some methods. Discussions focus on asymmetric inequalities, inhomogeneous forms in more variables, indefinite binary quadratic forms, diophantine approximation, sums of powers of linear forms, spheres and quadratic forms, and a method of Blichfeldt and Mordell. The text is a dependable reference for researchers and mathematicians interested in bodies and lattices in the n-dimensional euclidean space.

17 Lectures on Fermat Numbers

Michal Krizek,Florian Luca,Lawrence Somer
17 Lectures on Fermat Numbers Book PDF

Author : Michal Krizek,Florian Luca,Lawrence Somer
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 52,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9780387218502

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17 Lectures on Fermat Numbers by Michal Krizek,Florian Luca,Lawrence Somer Pdf

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.

Lectures on the Geometry of Numbers

Carl Ludwig Siegel
Lectures on the Geometry of Numbers Book PDF

Author : Carl Ludwig Siegel
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 46,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662082874

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Lectures on the Geometry of Numbers by Carl Ludwig Siegel Pdf

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.

Algebraic Geometry over the Complex Numbers

Donu Arapura
Algebraic Geometry over the Complex Numbers Book PDF

Author : Donu Arapura
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 52,6 Mb
Release : 2012-02-15
Category : Mathematics
ISBN : 9781461418092

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Algebraic Geometry over the Complex Numbers by Donu Arapura Pdf

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.

Noncommutative Geometry and Number Theory

Caterina Consani,Matilde Marcolli
Noncommutative Geometry and Number Theory Book PDF

Author : Caterina Consani,Matilde Marcolli
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 40,7 Mb
Release : 2007-12-18
Category : Mathematics
ISBN : 9783834803528

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Noncommutative Geometry and Number Theory by Caterina Consani,Matilde Marcolli Pdf

In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Lectures on Celestial Mechanics

Carl L. Siegel,Jürgen Moser,Jürgen K. Moser
Lectures on Celestial Mechanics Book PDF

Author : Carl L. Siegel,Jürgen Moser,Jürgen K. Moser
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 44,8 Mb
Release : 1995-02-15
Category : Mathematics
ISBN : 3540586563

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Lectures on Celestial Mechanics by Carl L. Siegel,Jürgen Moser,Jürgen K. Moser Pdf

The present book represents to a large extent the translation of the German "Vorlesungen über Himmelsmechanik" by C. L. Siegel. The demand for a new edition and for an English translation gave rise to the present volume which, however, goes beyond a mere translation. To take account of recent work in this field a number of sections have been added, especially in the third chapter which deals with the stability theory. Still, it has not been attempted to give a complete presentation of the subject, and the basic prganization of Siegel's original book has not been altered. The emphasis lies in the development of results and analytic methods which are based on the ideas of H. Poincare, G. D. Birkhoff, A. Liapunov and, as far as Chapter I is concerned, on the work of K. F. Sundman and C. L. Siegel. In recent years the measure-theoretical aspects of mechanics have been revitalized and have led to new results which will not be discussed here. In this connection we refer, in particular, to the interesting book by V. I. Arnold and A. Avez on "Problemes Ergodiques de la Mecanique Classique", which stresses the interaction of ergodic theory and mechanics. We list the points in which the present book differs from the German text. In the first chapter two sections on the tri pie collision in the three body problem have been added by C. L. Siegel.