To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

Skin Cancer: A Practical Approach presents a comprehensive and up to date overview on skin cancer. With an emphasis on practical aspects that will set the basis for guidelines of treatment, the volume presents different diagnostic tools to help physicians obtain the proper diagnosis. Written by a worldwide base of experts selected on their recognized expertise on the different themes discussed, Skin Cancer: A Practical Approach is a valuable resource for investigators in the field of skin cancer, including pathologists, medical and surgical oncologists, dermatologists, general surgeons, and veterinary oncologists

The third edition of Donald H. Boalch's Makers of the Harpsichord and Clavichord, 1440-1840 is a complete revision of the second edition published in 1974. The volume is now divided into two parts. Part I contains biographical details of all known makers, including some 500 not listed previously, and updated entries for more than 400 makers appearing in the second edition. Enlarged (and in some cases extended) descriptions of more than 2,000 surviving instruments by the makers are consigned to Part II, and the whole is complemented by a number of tables, a geographical and chronological conspectus of makers, and a new Index of Technical Terms in seven languages by Dr Andreas H. Roth.

This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.

This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry. This allows us to recognize the richness of the structure of PDEs. It presents, for the first time, a geometric theory of non-commutative (quantum) PDEs and gives a general application of this theory to quantum field theory and quantum supergravity.