North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geometrical configurations and nets, as well as pentagon theorem and the Desarguesian configuration, two pentagons inscribed into each other, and the concept of geometrical nets. The publication takes a look at combinatorial applications of finite geometries and combinatorics and finite geometries. Topics include generalizations of the Petersen graph, combinatorial extremal problem, and theorem of closure of the hyperbolic space. The book is a valuable source of data for readers interested in finite geometries.

This book contains material elaborated during courses held at the Eötvös Loránd University of Budapest since 1948, under the title 'projective geometry' wherein the notation of finite projective planes in connection with the classical projective geometry was mentioned. The share of finite geometries increased over time. The book is somewhat experimental--as the lectures were--thus the presentation of these lectures in the form of an introductory textbook of a didactical character. -- Author's preface.

Over the past two decades, research in the theory of Latin Squares has been growing at a fast pace, and new significant developments have taken place. This book offers a unique approach to various areas of discrete mathematics through the use of Latin Squares.

Finite Geometries stands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on recent works. The authors examine how finite geometries’ applicable nature led to solutions of open problems in different fields, such as design theory, cryptography and extremal combinatorics. Other areas covered include proof techniques using polynomials in case of Desarguesian planes, and applications in extremal combinatorics, plus, recent material and developments. Features: Includes exercise sets for possible use in a graduate course Discusses applications to graph theory and extremal combinatorics Covers coding theory and cryptography Translated and revised text from the Hungarian published version

NeutroAlgebra and AntiAlgebra were extended to NeutroGeometry and AntiGeometry in order to catch the Non-Euclidean Geometries. In the real world, the spaces and the elements that populate them and the rules that apply to them are not perfect, uniform, homogeneous, or complete. They are fragmentary and disparate, with unclear and conflicting information, and they do not apply in the same degree to each element. Therefore, these partial, hybrid, and mixed structures are necessary. NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World presents applications of many NeutroStructures in our real world and considers NeutroGeometry and AntiGeometry as new fields of research that resemble everyday life. Covering key topics such as hyperbolic geometry, elliptic geometry, and AntiGeometry, this reference work is ideal for mathematicians, industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.

Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several parallels) has led to the emergence of mathematical theories based on an arbitrary system of axioms, an essential feature of contemporary mathematics. This is a fascinating book for all those who teach or study axiomatic geometry, and who are interested in the history of geometry or who want to see a complete proof of one of the famous problems encountered, but not solved, during their studies: circle squaring, duplication of the cube, trisection of the angle, construction of regular polygons, construction of models of non-Euclidean geometries, etc. It also provides hundreds of figures that support intuition. Through 35 centuries of the history of geometry, discover the birth and follow the evolution of those innovative ideas that allowed humankind to develop so many aspects of contemporary mathematics. Understand the various levels of rigor which successively established themselves through the centuries. Be amazed, as mathematicians of the 19th century were, when observing that both an axiom and its contradiction can be chosen as a valid basis for developing a mathematical theory. Pass through the door of this incredible world of axiomatic mathematical theories!

A 1982 introduction to developments which had taken place in finite group theory related to finite geometries.

Presents an introduction to the theory of finite fields and some of its most important applications.

Contains the proceedings of a conference on Finite Geometries, Groups, and Computation that took place in September 4-9, 2004, at Pingree Park, Colorado (a campus of Colorado State University). This work serves to introduce both students and the mathematical community to the important topics and gives an overview of developments in these fields.