An introduction to Morse theory. An introduction to probability theory.
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- Computability Theory.
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.
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- Computability Theory.
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. This is only a page book, but it covers a wealth of material This short text does an excellent job of covering those topics that should be included in an undergraduate introduction to computability theory There are both appropriate exercises and enticing doorways to open topics and current research.
The exposition is precise, but still conversational. I believe my students will enjoy reading this text.
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Sign up. Ordering on the AMS Bookstore is limited to individuals for personal use only. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field.
Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way. Herbert B.
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