000			02888nam a22003618i 4500
001			CR9780511740305
003			UkCbUP
005			20200124160233.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100408s2011||||enk o ||1 0|eng|d
020			_a9780511740305 (ebook)
020			_z9781107002029 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA300 _b.V28 2011
082	0	0	_a515 _222
100	1		_aVakil, Nader, _eauthor.
245	1	0	_aReal analysis through modern infinitesimals / _cNader Vakil.
264		1	_aCambridge : _bCambridge University Press, _c2011.
300			_a1 online resource (xix, 565 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aEncyclopedia of mathematics and its applications ; _vvolume 140
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aPreface; Introduction; Part I. Elements of Real Analysis: 1. Internal set theory; 2. The real number system; 3. Sequences and series; 4. The topology of R; 5. Limits and continuity; 6. Differentiation; 7. Integration; 8. Sequences and series of functions; 9. Infinite series; Part II. Elements of Abstract Analysis: 10. Point set topology; 11. Metric spaces; 12. Complete metric spaces; 13. Some applications of completeness; 14. Linear operators; 15. Differential calculus on Rn; 16. Function space topologies; A. Vector spaces; B. The b-adic representation of numbers; C. Finite, denumerable, and uncountable sets; D. The syntax of mathematical languages; References; Index.
520			_aReal Analysis Through Modern Infinitesimals provides a course on mathematical analysis based on Internal Set Theory (IST) introduced by Edward Nelson in 1977. After motivating IST through an ultrapower construction, the book provides a careful development of this theory representing each external class as a proper class. This foundational discussion, which is presented in the first two chapters, includes an account of the basic internal and external properties of the real number system as an entity within IST. In its remaining fourteen chapters, the book explores the consequences of the perspective offered by IST as a wide range of real analysis topics are surveyed. The topics thus developed begin with those usually discussed in an advanced undergraduate analysis course and gradually move to topics that are suitable for more advanced readers. This book may be used for reference, self-study, and as a source for advanced undergraduate or graduate courses.
650		0	_aMathematical analysis.
650		0	_aSet theory.
776	0	8	_iPrint version: _z9781107002029
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 140.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511740305
999			_c517832 _d517830