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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.
Each part starts with a brief description of the political and religious climate of the period and the way such factors affected the compositions and the organ-building of the time.
This volume is a superb introduction to the richness and originality of Abraham and Torok's approach to psychoanalysis and their psychoanalytic approach to literature. Abraham and Torok advocate a form of psychoanalysis that insists on the particularity of any individual's life story, the specificity of texts, and the singularity of historical situations. In what is both a critique and an extension of Freud, they develop interpretive strategies with powerful implications for clinicians, literary theorists, feminists, philosophers, and all others interested in the uses and limits of psychoanalysis. Central to their approach is a general theory of psychic concealment, a poetics of hiding. Whether in a clinical setting or a literary text, they search out the unspeakable secret as a symptom of devastating trauma revealed only in linguistic or behavioral encodings. Their view of trauma provides the linchpin for new psychic and linguistic structures such as the "transgenerational phantom," an undisclosed family secret handed down to an unwitting descendant, and the intra-psychic secret or "crypt," which entombs an unspeakable but consummated desire. Throughout, Abraham and Torok seek to restore communication with those intimate recesses of the mind which are, for one reason or another, denied expression. Classics of French theory and practice, the essays in volume one include four previously uncollected works by Maria Torok. Nicholas Rand supplies a substantial introductory essay and commentary throughout. Abraham and Torok's theories of fractured meaning and their search for coherence in the face of discontinuity and disruption have the potential to reshape not only psychoanalysis but all disciplines concerned with issues of textual, oral, or visual interpretation.