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Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.

Mathematicians at every level use diagrams to prove theorems. Mathematical Reasoning with Diagrams investigates the possibilities of mechanizing this sort of diagrammatic reasoning in a formal computer proof system, even offering a semi-automatic formal proof system—called Diamond—which allows users to prove arithmetical theorems using diagrams.

John Allen Paulos cleverly scrutinizes the mathematical structures of jokes, puns, paradoxes, spoonerisms, riddles, and other forms of humor, drawing examples from such sources as Rabelais, Shakespeare, James Beattie, René Thom, Lewis Carroll, Arthur Koestler, W. C. Fields, and Woody Allen.

"Jokes, paradoxes, riddles, and the art of non-sequitur are revealed with great perception and insight in this illuminating account of the relationship between humor and mathematics."—Joseph Williams, New York Times

"'Leave your mind alone,' said a Thurber cartoon, and a really complete and convincing analysis of what humour is might spoil all jokes forever. This book avoids that danger. What it does. . .is describe broadly several kinds of mathematical theory and apply them to throw sidelights on how many kinds of jokes work."—New Scientist

"Many scholars nowadays write seriously about the ludicrous. Some merely manage to be dull. A few—like Paulos—are brilliant in an odd endeavor."—Los Angeles Times Book Review

"Not the least unexpected thing about Mathematics and the Unexpected is that a real mathematician should write not just a literate work, but a literary one."—Ian Stewart, New Scientist

"In this brief, elegant treatise, assessable to anyone who likes to think, Ivar Ekelund explains some philosophical implications of recent mathematics. He examines randomness, the geometry involved in making predictions, and why general trends are easy to project (it will snow in January) but particulars are practically impossible (it will snow from 2 p.m. to 5 p.m. on the 21st)."—Village Voice

Modal logic is the study of modalities—expressions that qualify assertions about the truth of statements—like some ordinary language phrases and mathematically motivated expressions. The study of modalities dates from antiquity, but has been most actively pursued in the last three decades. This volume collects together a number of Golblatt's papers on modal logic, beginning with his work on the duality between algebraic and set-theoretic models, and including two new articles, one on infinitary rules of inference, and the other about recent results on the relationship between modal logic and first-order logic.

Mathematics, Science, and Postclassical Theory is a unique collection of essays dealing with the intersections between science and mathematics and the radical reconceptions of knowledge, language, proof, truth, and reality currently emerging from poststructuralist literary theory, constructivist history and sociology of science, and related work in contemporary philosophy. Featuring a distinguished group of international contributors, this volume engages themes and issues central to current theoretical debates in virtually all disciplines: agency, causality, determinacy, representation, and the social dynamics of knowledge.
In a substantive introductory essay, the editors explain the notion of "postclassical theory" and discuss the significance of ideas such as emergence and undecidability in current work in and on science and mathematics. Other essays include a witty examination of the relations among mathematical thinking, writing, and the technologies of virtual reality; an essay that reconstructs the conceptual practices that led to a crucial mathematical discovery—or construction—in the 19th century; a discussion of the implications of Bohr’s complementarity principle for classical ideas of reality; an examination of scientific laboratories as "hybrid" communities of humans and nonhumans; an analysis of metaphors of control, purpose, and necessity in contemporary biology; an exploration of truth and lies, and the play of words and numbers in Shakespeare, Frege, Wittgenstein, and Beckett; and a final chapter on recent engagements, or nonengagements, between rationalist/realist philosophy of science and contemporary science studies.

Contributors. Malcolm Ashmore, Michel Callon, Owen Flanagan, John Law, Susan Oyama, Andrew Pickering, Arkady Plotnitsky, Brian Rotman, Barbara Herrnstein Smith, John Vignaux Smyth, E. Roy Weintraub

This thoroughly revised third edition of Harry H. Harman's authoritative text incorporates the many new advances made in computer science and technology over the last ten years. The author gives full coverage to both theoretical and applied aspects of factor analysis from its foundations through the most advanced techniques. This highly readable text will be welcomed by researchers and students working in psychology, statistics, economics, and related disciplines.

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras.

           

The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.