Algebra and tiling : homomorphisms in the service of geometry / Sherman K. Stein and Sándor Szabó.

Format:

Book

Author/Creator:

Stein, Sherman K., author.

Szabó, Sándor, 1954- author.

Contributor:

Mathematical Association of America, issuing body.

Series:

Carus mathematical monographs ; Number 25.

Carus Mathematical Monographs ; Number 25

Language:

English

Subjects (All):

Tiling (Mathematics).

Algebra.

Homomorphisms (Mathematics).

Physical Description:

1 online resource (xii, 209 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Algebra & Tiling

Place of Publication:

Washington : Mathematical Association of America, 1994.

Language Note:

English

Summary:

Read what reviewers had to say about this excellent monograph: Algebra and Tiling is perfect for bringing alive an abstract algebra course. Intuitive but difficult problems of geometry are translated into algebraic problems more amenable to solution... Full of surprises, the book is a pleasure to read. Essential for collections that serve undergraduates. Choice The authors have arranged the text so that exercises are stated frequently throughout the chapters, rather than at the end, and they have presented as problems some questions that have not yet been answered. Historical background relating to tiling problems helps focus the reader on the mathematical discussions. The student or mathematician whose area of interest is algebra should enjoy this text. The Mathematics Teacher There are many questions about tilings which lend themselves nicely to the tools of modern algebra. This book is about several such questions. Each chapter is an independent instance of turning a tiling problem into a problem in algebra... This book is almost self-contained; a lot of time is spent describing carefully the relevant algebra. Zentralblatt fu̘r Mathematik Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper division algebra courses, but teachers, researchers, and professional mathematicians will find the book equally appealing. Beginners will find the exercises and the appendices especially useful. The unsolved problems will challenge both beginners and experts. The book could serve as the basis of an undergraduate or graduate seminar or a source of applications to enrich an algebra or geometry course.

Contents:

Minkowski's conjecture

Cubical clusters

Tiling by the semicross and cross

Packing and covering by the semicross and cross

Tiling by triangles of equal areas

Tiling by similar triangles

Rédei's theorem

Epilog

Lattices

The character group and exact sequences

Formal sums

Cyclotomic polynomials.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Includes bibliographical references and indexes.

Description based on print version record.

ISBN:

1-61444-024-7