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#### Introductory Non-Euclidean Geometry

Dover Publications 2013; US$ 8.95This fine and versatile introduction to non-Euclidean geometry is appropriate for both high-school and college classes. Its first two-thirds requires just a familiarity with plane and solid geometry and trigonometry, and calculus is employed only in the final part. It begins with the theorems common to Euclidean and non-Euclidean geometry, and then... more...

#### Existence Theorems for Ordinary Differential Equations

Dover Publications 2013; US$ 8.99Theorems stating the existence of an object?such as the solution to a problem or equation?are known as existence theorems. This text examines fundamental and general existence theorems, along with the Picard iterants, and applies them to properties of solutions and linear differential equations. The authors assume a basic knowledge of real function... more...

#### Projective Geometry

Dover Publications 2013; US$ 9.95This text explores the methods of the projective geometry of the plane. Some knowledge of the elements of metrical and analytical geometry is assumed; a rigorous first chapter serves to prepare readers. Following an introduction to the methods of the symbolic notation, the text advances to a consideration of the theory of one-to-one correspondence.... more...

#### Non-Euclidean Geometry

Dover Publications 2012; US$ 13.95This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry. Starting with fundamental assumptions, the author examines the theorems... more...

#### Analytical Geometry of Three Dimensions

Dover Publications 2012; US$ 11.95Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics. Mathematician, physicist, and astronomer, William H. McCrea conducted... more...

#### Proof in Geometry

Dover Publications 2012; US$ 7.99This single-volume compilation of two books explores the construction of geometric proofs. In addition to offering useful criteria for determining correctness, it presents examples of faulty proofs that illustrate common errors. High-school geometry is the sole prerequisite. Proof in Geometry, the first in this two-part compilation, discusses the... more...

#### Algebraic Geometry

Dover Publications 2012; US$ 11.99This text for advanced undergraduate students is both an introduction to algebraic geometry and a bridge between its two parts--the analytical-topological and the algebraic. Because of its extensive use of formal power series (power series without convergency), the treatment will appeal to readers conversant with analysis but less familiar with the... more...

#### The Geometry of Geodesics

Dover Publications 2012; US$ 19.99A comprehensive approach to qualitative problems in intrinsic differential geometry, this text for upper-level undergraduates and graduate students emphasizes cases in which geodesics possess only local uniqueness properties--and consequently, the relations to the foundations of geometry are decidedly less relevant, and Finsler spaces become the principal... more...

#### General Investigations of Curved Surfaces

Dover Publications 2013; US$ 12.95Gauss's theory of surfaces is among the purely mathematical achievements inspired by ideas that arose in connection with surveys of the surface of the earth. Long regarded as a masterpiece in content and form, this work features one of the author's most original contributions to mathematics--the discovery that Gauss termed the "Theorema Egregium."... more...

#### Lectures in Projective Geometry

Dover Publications 2012; US$ 11.99An ideal text for undergraduate courses in projective geometry, this volume begins on familiar ground. It starts by employing the leading methods of projective geometry as an extension of high school-level studies of geometry and algebra, and proceeds to more advanced topics with an axiomatic approach. An introductory chapter leads to discussions... more...