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Author : C. D. Olds
Release : 2001-02-22
Genre : Mathematics
Kind : eBook
Book Rating : 437/5 ( reviews)
Book Synopsis The Geometry of Numbers by : C. D. Olds
Download or read book The Geometry of Numbers written by C. D. Olds. This book was released on 2001-02-22. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the geometry of numbers.
Author : J.W.S. Cassels
Release : 1996-12-16
Genre : Mathematics
Kind : eBook
Book Rating : 884/5 ( reviews)
Book Synopsis An Introduction to the Geometry of Numbers by : J.W.S. Cassels
Download or read book An Introduction to the Geometry of Numbers written by J.W.S. Cassels. This book was released on 1996-12-16. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Álvaro Lozano-Robledo
Release : 2019-03-21
Genre : Arithmetical algebraic geometry
Kind : eBook
Book Rating : 16X/5 ( reviews)
Book Synopsis Number Theory and Geometry: An Introduction to Arithmetic Geometry by : Álvaro Lozano-Robledo
Download or read book Number Theory and Geometry: An Introduction to Arithmetic Geometry written by Álvaro Lozano-Robledo. This book was released on 2019-03-21. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Carl Ludwig Siegel
Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 87X/5 ( reviews)
Book Synopsis Lectures on the Geometry of Numbers by : Carl Ludwig Siegel
Download or read book Lectures on the Geometry of Numbers written by Carl Ludwig Siegel. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Diane L. Herrmann
Release : 2012-10-18
Genre : Mathematics
Kind : eBook
Book Rating : 649/5 ( reviews)
Book Synopsis Number, Shape, & Symmetry by : Diane L. Herrmann
Download or read book Number, Shape, & Symmetry written by Diane L. Herrmann. This book was released on 2012-10-18. Available in PDF, EPUB and Kindle. Book excerpt: 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.
