Turing's Vision

The Birth of Computer Science

Chris Bernhardt

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English

Massachusetts Inst of Tec
21 April 2017

Mathematics & Sciences; Computing: general; Computer science

Series: Turing's Vision

"Turing's fascinating and remarkable theory, which now forms the basis of computer science, explained for the general reader.

In 1936, when he was just twenty-four years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision, Chris Bernhardt explains the theory, Turing's most important contribution, for the general reader. Bernhardt argues that the strength of Turing's theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, ""The sheer simplicity of the theory's foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory."" Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer.

In the paper, ""On Computable Numbers, with an Application to the Entscheidungsproblem,"" Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers.

An accessible and fascinating exploration of how Alan Turing's mathematical theory gave rise to modern computer science and applications-from the desktops to cell phones

In 1936, when he was just 24 years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision, Chris Bernhardt explains the theory for the general reader, beginning with its foundations and systematically building to its surprising conclusions.

He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer.

Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines 3 well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers."

By: Chris Bernhardt
Imprint: Massachusetts Inst of Tec
Country of Publication: United States
Edition: 1
Dimensions: Height: 203mm, Width: 137mm, Spine: 14mm
Weight: 318g
ISBN: 9780262533515
ISBN 10: 0262533510
Series: Turing's Vision
Pages: 208
Publication Date: 21 April 2017
Recommended Age: From 18 years
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Chris Bernhardt is Professor of Mathematics at Fairfield University.