Cargando…
Sets for mathematics /
Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically commo...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2003.
|
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape. |
|---|---|
| Descripción Física: | 1 online resource (xiii, 261 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 253-255) and index. |
| ISBN: | 0511077947 9780511077944 9780511755460 0511755465 9780521804448 0521804442 1282387324 9781282387324 0521010608 9780521010603 1107131049 9781107131040 0511643500 9780511643507 9786612387326 6612387327 0511205546 9780511205545 0511561369 9780511561368 0511076371 9780511076374 |