Rebecca Weber: Dartmouth College, Hanover, NH
What can we compute—even with unlimited resources? Is everything within reach? Or are computations necessarily drastically limited, not just in practice, but theoretically? These questions are at the heart of computability theory.
The goal of this book is to give the reader a firm grounding in the fundamentals of computability theory and an overview of currently active areas of research, such as reverse mathematics and algorithmic randomness. Turing machines and partial recursive functions are explored in detail, and vital tools and concepts including coding, uniformity, and diagonalization are described explicitly. From there the material continues with universal machines, the halting problem, parametrization and the recursion theorem, and thence to computability for sets, enumerability, and Turing reduction and degrees. A few more advanced topics round out the book before the chapter on areas of research. The text is designed to be self-contained, with an entire chapter of preliminary material including relations, recursion, induction, and logical and set notation and operators. That background, along with ample explanation, examples, exercises, and suggestions for further reading, make this book ideal for independent study or courses with few prerequisites.
發表於2024-11-08
Computability Theory 2024 pdf epub mobi 電子書 下載
圖書標籤: MathLogic Math
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評分習題不算很難,但問題是有些應該解釋的細節沒說清楚,作為入門書的話有個教授能問問最好。computability是個很神奇的領域,個人覺得
評分習題不算很難,但問題是有些應該解釋的細節沒說清楚,作為入門書的話有個教授能問問最好。computability是個很神奇的領域,個人覺得
評分習題不算很難,但問題是有些應該解釋的細節沒說清楚,作為入門書的話有個教授能問問最好。computability是個很神奇的領域,個人覺得
Computability Theory 2024 pdf epub mobi 電子書 下載