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This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field.
Topics and features:
Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction
Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results
Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments
Includes a large number of exercises of varying levels of difficulty, supplementing each chapter
This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field.
Topics and features:
Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction
Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results
Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments
Includes a large number of exercises of varying levels of difficulty, supplementing each chapter
Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut. He obtained his PhD from the University of Chicago, and has held postdoctoral positions at the University of Notre Dame and the University of California, Berkeley. He has held visiting positions at the National University of Singapore and Charles University, Prague. His research focuses on the computability theoretic and reverse mathematical aspects of of combinatorics, and on the interactions of reverse mathematics with computable analysis and other areas.
Carl Mummert is a Professor of Computer and Information Technology at Marshall Univeristy. He obtained his Ph.D. from Pennsylvania State University and held postdoctoral positions at Appalachian State University and the University of Michigan. His research has included the reverse mathematics of topology and combinatorics as well as higher order reverse mathematics.
Offers a comprehensive treatment of the reverse mathematics of combinatorics
Includes a large number of exercises of varying levels of difficulty, supplementing each chapter
Provides central results and methods from the past two decades, appearing in book form for the first time
| Erscheinungsjahr: | 2022 |
|---|---|
| Genre: | Informatik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 508 |
| Reihe: | Theory and Applications of Computability |
| Inhalt: |
xix
488 S. 1 s/w Illustr. 488 p. 1 illus. |
| ISBN-13: | 9783031113666 |
| ISBN-10: | 3031113667 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Mummert, Carl
Dzhafarov, Damir D. |
| Auflage: | 1st ed. 2022 |
| Hersteller: |
Springer International Publishing
Theory and Applications of Computability |
| Maße: | 241 x 160 x 33 mm |
| Von/Mit: | Carl Mummert (u. a.) |
| Erscheinungsdatum: | 26.07.2022 |
| Gewicht: | 0,922 kg |
Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut. He obtained his PhD from the University of Chicago, and has held postdoctoral positions at the University of Notre Dame and the University of California, Berkeley. He has held visiting positions at the National University of Singapore and Charles University, Prague. His research focuses on the computability theoretic and reverse mathematical aspects of of combinatorics, and on the interactions of reverse mathematics with computable analysis and other areas.
Carl Mummert is a Professor of Computer and Information Technology at Marshall Univeristy. He obtained his Ph.D. from Pennsylvania State University and held postdoctoral positions at Appalachian State University and the University of Michigan. His research has included the reverse mathematics of topology and combinatorics as well as higher order reverse mathematics.
Offers a comprehensive treatment of the reverse mathematics of combinatorics
Includes a large number of exercises of varying levels of difficulty, supplementing each chapter
Provides central results and methods from the past two decades, appearing in book form for the first time
| Erscheinungsjahr: | 2022 |
|---|---|
| Genre: | Informatik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 508 |
| Reihe: | Theory and Applications of Computability |
| Inhalt: |
xix
488 S. 1 s/w Illustr. 488 p. 1 illus. |
| ISBN-13: | 9783031113666 |
| ISBN-10: | 3031113667 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Mummert, Carl
Dzhafarov, Damir D. |
| Auflage: | 1st ed. 2022 |
| Hersteller: |
Springer International Publishing
Theory and Applications of Computability |
| Maße: | 241 x 160 x 33 mm |
| Von/Mit: | Carl Mummert (u. a.) |
| Erscheinungsdatum: | 26.07.2022 |
| Gewicht: | 0,922 kg |
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