Perspectives in Computation

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.

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Perspectives in Computation

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.

34.99 In Stock
Perspectives in Computation

Perspectives in Computation

by Robert Geroch
Perspectives in Computation

Perspectives in Computation

by Robert Geroch

eBook

$34.99 

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Overview

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.


Product Details

ISBN-13: 9780226288567
Publisher: University of Chicago Press
Publication date: 09/15/2009
Series: Chicago Lectures in Physics
Sold by: Barnes & Noble
Format: eBook
Pages: 128
File size: 772 KB

About the Author

Robert Geroch is professor in the Department of Physics at the University of Chicago and author of General Relativity from A to B and Mathematical Physics, both published by the University of Chicago Press.

Table of Contents

1          Introduction

2          Characters and Strings

3          Problems

4          Computability

5          Turing Machines

6          Noncomputable Problems

7          Noncomputable Numbers

8          Formal Mathematics

9          Difficulty Functions

10        Difficult Problems; Best Algorithms

11        A Language for Efficiency

12        Are There Better Languages?

13        Probabilistic Computing

14        Quantum Mechanics

15        Grover Construction

16        Grover Construction: Six Issues

            16.1     Initial State

            16.2     Final Observation on Hin

            16.3     Building the Operator W

            16.4     Building the Operator V

            16.5     Errors

            16.6     What Is the Problem?

17        Quantum-Assisted Computing

18        Quantum-Assisted Computability

19        Quantum-Assisted Difficulty Functions

20        Quantum-Assisted Efficiency I

21        Quantum-Assisted Efficiency II

22        Conclusion

            References

            Index

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