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Nine revolutionary algorithms that power our computers and smartphonesEvery day, we use our computers to perform remarkable feats. A simple web search picks out a handful of relevant needles from the world's biggest haystack. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers, and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? John MacCormick answers this question in language anyone can understand, using vivid examples to explain the fundamental tricks behind nine computer algorithms that power our PCs, tablets, and smartphones.

An accessible and rigorous textbook for introducing undergraduates to computer science theoryWhat Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference.The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems.Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation.An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computationFeatures a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understandingGives equal emphasis to computability and complexityIncludes special topics that demonstrate the profound nature of key ideas in the theory of computationLecture slides and Python programs are available at whatcanbecomputed.com

Nine revolutionary algorithms that power our computers and smartphonesEvery day, we use our computers to perform remarkable feats. A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease?This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental'tricks'behind nine types of computer algorithms, including artificial intelligence (where we learn about the'nearest neighbor trick'and'twenty questions trick'), Google's famous PageRank algorithm (which uses the'random surfer trick'), data compression, error correction, and much more.These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.