Perspectives in Computation

The subject of computation deals with solutions to mathematical problems by procedures, i.e., solutions that could be generated by a machine; that require no original thought. For which problems are there such procedures, and when they do exist how efficient can they be? In recent years, the landscape of this subject has changed somewhat by the introduction of "machines" that utilize quantum mechanics in their operation. 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 a combination of general discussions of broader issues, the mathematical formulation of those issues and examples. 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 related fields.