Zero-symmetric graphs: Trivalent graphical regular representations of groups

Science & Math

Coxeter, H.S.M.

Mathematics

Academic Press

When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely generated group that the reader might propose. But we soon realized that more or less arbitrary restrictions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i.e.' .subgroups of es), the reader cannot do better than consult the tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-142) deal with groups of low order, finite and infinite groups of congruent transformations, symmetric and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions. The best substitute for a more extensive catalogue is the description (in Chapter 2) of a method whereby the reader can easily work out his own abstract definition for almost any given finite group. This method is sufficiently mechanical for the use of an electronic computer.

Generators and Relations for Discrete Groups (ERGEBNISSE DER MATHEMATIK UND IHRER GRENZGEBIETE 2 FOLGE)

Springer, Verlag

Projective Geometry

In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.

Springer

The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation.

The Fifty-Nine Icosahedra (Lecture Notes in Statistics)

DuVal, P.

Flather, H. T.

Petrie, J. F.

Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.

The Real Projective Plane

Computers & Technology

BRAND NEW dust jacket hardcover, clean text, solid binding, no remainders, NOT ex-library, slight shelfwear; spine cover shows slight scuffing WE SHIP FAST. 201307123 This is a wonderful book. It isn't for mathematical beginners, but it isn't opaque either. It requires a student to think, experiment and to learn by puzzling things out in one's mind rather than simple memorization and regurgitation. Nor does it follow the all too common modern method of over simplifying things to allow people to pretend they have learned math while only dabbling in a few basic topics. This book is amply illustrated with many exercises (answers are provided at the back for all the exercises). The book also has some humor and wit with the quotes it distributes throughout the book to help liven things up. There is also a list of helpful references and an index. When reading the book, don't be afraid of going to a dictionary or the web or some other math books for clarification of some terms or more basic concepts. It is essential to have everything clear in your mind before moving on or you will stumble. As in all math, it is like a building with the next stage being built on the present one which is built on the previous one. You can't skip steps very successfully very often. This is a great volume to have in your library, but even better to work through. We recommend Priority Mail where/when available -- $3.99 Standard / Media Mail can take up to 15 business days.

Introduction to Geometry

John Wiley

This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises.

wiley

The properties of regular solids exercise a fascination which often appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book Professor Coxeter explores these properties in easy stages, introducing the reader to complex polyhedra (a beautiful generalization of regular solids derived from complex numbers) and unexpected relationships with concepts from various branches of mathematics: magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, crystallographic and non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. In the latter half of the book, these preliminary ideas are put together to describe a natural generalization of the Five Platonic Solids. This updated second edition contains a new chapter on Almost Regular Polytopes, with beautiful 'abstract art' drawings. New exercises and discussions have been added throughout the book, including an introduction to Hopf fibration and real representations for two complex polyhedra.

Regular Complex Polytopes

Cambridge University Press

A text which surveys real projective geometry, the elliptic metric, and supplies applicable definitions and theorems

Non-Euclidean Geometry

Univ of Toronto Pr

Twelve Geometric Essays

Southern Illinois Univ Pr

See the best price to sell, buy, or rent books by Coxeter, H.S.M.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Coxeter, H.S.M.

See the best price to sell, buy, or rent books by Coxeter, H.S.M.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Zero-symmetric graphs: Trivalent graphical regular representations of groups

Generators and Relations for Discrete Groups (ERGEBNISSE DER MATHEMATIK UND IHRER GRENZGEBIETE 2 FOLGE)

Projective Geometry

The Fifty-Nine Icosahedra (Lecture Notes in Statistics)

The Real Projective Plane

Introduction to Geometry

Introduction to Geometry

Regular Complex Polytopes

Non-Euclidean Geometry

Twelve Geometric Essays