"This beautiful little book is certainly suitable for anyone who has had an introductory course in physics and even for some who have not."—Joshua N. Goldberg, Physics Today
"An imaginative and convincing new presentation of Einstein's theory of general relativity. . . . The treatment is masterful, continual emphasis being placed on careful discussion and motivation, with the aim of showing how physicists think and develop their ideas."—Choice
Robert Geroch University of Chicago Press, 1984 Library of Congress QC20.G47 1985 | Dewey Decimal 530.15
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.
Perspectives in Computation
Robert Geroch University of Chicago Press, 2009 Library of Congress QA267.7.G47 2009 | Dewey Decimal 511.352
Computation is the process of applying a procedure or algorithm to the solution of a mathematical problem. Mathematicians and physicists have been occupied for many decades pondering which problems can be solved by which procedures, and, for those that can be solved, how this can most efficiently be done. In recent years, quantum mechanics has augmented our understanding of the process of computation and of its limitations.
Perspectives in Computation covers three broad topics: the computation process and its limitations, the search for computational efficiency, and the role of quantum mechanics in computation. The emphasis is theoretical; Robert Geroch asks what can be done, and what, in principle, are the limitations on what can be done? Geroch guides readers through these topics by combining general discussions of broader issues with precise mathematical formulations—as well as through examples of how computation works.
Requiring little technical knowledge of mathematics or physics, Perspectives in Computation will serve both advanced undergraduates and graduate students in mathematics and physics, as well as other scientists working in adjacent fields.