Hyperbolic Geometry - (Springer Undergraduate Mathematics) 2nd Edition by James W Anderson (Paperback)
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<p/><br></br><p><b> Book Synopsis </b></p></br></br><p>Thoroughly updated, featuring new material on important topics such as hyperbolic geometry in higher dimensions and generalizations of hyperbolicity </p> <p>Includes full solutions for all exercises</p> <p>Successful first edition sold over 800 copies in North America </p><p/><br></br><p><b> From the Back Cover </b></p></br></br><p>The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations.</p> <p></p> <p>Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications.</p> <p></p> <p>This updated second edition also features: </p> <p></p> <p>an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; </p><p></p> <p>the hyperboloid model of the hyperbolic plane; </p><p></p> <p>brief discussion of generalizations to higher dimensions; </p><p></p> <p>many new exercises. </p><p></p> <p></p> <p>The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape.</p> <p></p> <p> </p> <p> </p> <p> </p>
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