Geared toward both beginning and advanced undergraduate and graduate students, this self-contained treatment offers an elementary approach to finite projective planes. Following a review of the basics of projective geometry, the text examines finite planes, field planes, and coordinates in an arbitrary plane. Additional topics include central collineations and the little Desargues' property, the fundamental theorem, and examples of finite non-Desarguesian planes.Virtually no knowledge or sophistication on the part of the student is assumed, and every algebraic system that arises is defined and discussed as necessary. Many exercises appear throughout the book, offering significant tools for understanding the subject as well as developing the mathematical methods needed for its study. References and a helpful appendix on the Bruck-Ryser theorem conclude the text.

An Introduction to Finite Projective Planes (Dover Books on Mathematics)

Science & Math

Albert, Abraham Adrian

Sandler, Reuben

Mathematics

Dover Publications

The first seven chapters of this concise text provide an exposition of the basic topics of solid analytic geometry and comprise the material for a one-semester course on the subject for undergraduate mathematics majors. The remaining two chapters offer additional material for longer courses or supplementary study. Chapters 1 and 2 contain a treatment of the equations of lines and planes. Subsequent chapters offer an exposition of classical elementary surface and curve theory, a treatment of spheres, and an examination of the classical descriptions of quadric surfaces in standard position. An exploration of the theory of matrices follows, with applications to the three-dimensional case of quadric surfaces. The text concludes with a survey of spherical coordinates and elements of projective geometry.

Solid Analytic Geometry (Dover Books on Mathematics)

Abraham Adrian Albert was one of the 20th century's leading mathematicians. This 1937 monograph written by him was hailed by the Bulletin of the American Mathematical Society as "a welcome addition to the literature." Besides furnishing an excellent introduction to abstract algebra and a detailed commentary on then-recent developments, the treatment's important features include chapters on matrices and matrix algebras, cyclic fields, and valuations. Suitable for students ready to advance beyond introductory courses, this book will also prove of interest to historians of mathematics. Opening chapters focus on groups and rings, rings with a unity element, matrices, similarity of square matrices, and symmetric and skew matrices. Readers are given as much of the theory of finite groups as is necessary for the treatment of Galois theory. Subsequent chapters explore algebraic extensions and the ideas grouped around the theory of valuations. Numerous problems of varying complexity appear throughout the text, which concludes with a helpful glossary offering brief definitions of frequently used terms.

Modern Higher Algebra (Dover Books on Mathematics)

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Books by Albert, Abraham Adrian

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

An Introduction to Finite Projective Planes (Dover Books on Mathematics)

Solid Analytic Geometry (Dover Books on Mathematics)

Modern Higher Algebra (Dover Books on Mathematics)