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This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831.
Intends to serve as a textbook in Real Analysis at the Advanced Calculus level. This book includes topics like Field of real numbers, Foundation of calculus, Compactness, Connectedness, Riemann integration, Fourier series, Calculus of several variables and Multiple integrals are presented systematically with diagrams and illustrations.
With exercises and projects, Exploring Mathematics supports an active approach to the transition to upper-level theoretical math courses.
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.
265 challenging problems in all phases of group theory, gathered for the most part from papers published since 1950, although some classics are included.
"The oldest and strongest emotion of mankind is fear, and the oldest and strongest kind of fear is fear of the unknown." --H. P. LOVECRAFT, "Supernatural Horror in Literature" Howard Phillips Lovecraft forever changed the face of horror, fantasy, and science fiction with a remarkable series of stories as influential as the works of Poe, Tolkien, and Edgar Rice Burroughs. His chilling mythology established a gateway between the known universe and an ancient dimension of otherworldly terror, whose unspeakable denizens and monstrous landscapes--dread Cthulhu, Yog-Sothoth, the Plateau of Leng, the Mountains of Madness--have earned him a permanent place in the history of the macabre. In Tales of ...
From the author of THE PARENT AGENCY comes a thrilling, funny and touching new adventure.
Sulky races at the Mercer County Fair, church suppers, sorghum making, shooting marbles in the school yard, housing tobacco, loafing at the courthouse -- here are 129 beautifully reproduced images of who we were as Kentuckians not so long ago -- during the Depression and the early years of World War II. This collection is part of the remarkable series of photos shot for the Farm Security Administration -- more than 125,000 photographs taken over a period of nine years by some of the best American photographers of the time, including Ben Shahn, Marion Post Wolcott, Russell Lee, John Vachon, and Arthur Rothstein. To reintroduce us to that important slice of our history, Beverly Brannan and Dav...
Since terrorism became a global national security issue in the new millennium, all governments have wrestled with its effects. Yet strong measures against terrorism have often made the root causes of the problem worse, while weak responses have invited further attack. In response, this book explains how governments can construct and execute the most effective strategies to combat terrorism—and how they can manage the consequences of those acts of terrorism they cannot prevent. It provides an overview of the complex problem of terrorism and offers a guide to shaping solutions to fit the unique structures and processes of governments. These issues and their solutions are demonstrated in six case studies. The book's value lies in its holistic treatment of what governments can do to protect their societies, with the ultimate goal of reducing terrorism from the global security threat it is today to a national-level criminal problem. Written by a team of experts, the book offers a concise but complete course on the most important national security challenge of our time.