000			03521 a2200313 4500
001			200043891
999			_c200043891 _d34712
003			TR-AnTOB
005			20200812112951.0
008			111215s2010 nju 001 0
020			_a9780470551387 (hardback)
040			_aDLC _cDLC _dTR-AnTOB
041			_aeng
050	0	0	_aQA248 _b.S358 2010
090			_aQA248 .S358 2010
100	1		_aSchroder, Bernd S. W., _q(Bernd Siegfried Walter), _d1966- _979783
245	1	0	_aFundamentals of mathematics : _ban introduction to proofs, logic, sets, and numbers / _cBernd S. W. Schröder.
264		1	_aHoboken : _bWiley, _cc2010.
300			_ax, 338 p. : _bill. ; _c25 cm.
504			_aIncludes bibliographical references (p. 329-331) and index.
505			_a1. Logic -- 2. Set theory -- 3. Number systems I.Natural numbers -- 4.Number systems II.Integers -- 5. Number System III: Fields -- 6. Unsolvability of the Quintic by Radicals -- 7. More Axioms A historical Oveview and Commentary
520			_a"The foundation of mathematics is not found in a single discipline since it is a general way of thinking in a very rigorous logical fashion. This book was written especially for readers who are about to make their first contact with this very way of thinking. Chapters 1-5 provide a rigorous, self contained construction of the familiar number systems (natural numbers, integers, real, and complex numbers) from the axioms of set theory. This construction trains readers in many of the proof techniques that are ultimately used almost subconsciously. In addition to important applications, the author discusses the scientific method in general (which is the reason why civilization has advanced to today’s highly technological state), the fundamental building blocks of digital processors (which make computers work), and public key encryption (which makes internet commerce secure). The book also includes examples and exercises on the mathematics typically learned in elementary and high school. Aside from serving education majors, this further connection of abstract content to familiar ideas explains why these ideas work so well. Chapter 6 provides a condensed introduction to abstract algebra, and it fits very naturally with the idea that number systems were expanded over and over to allow for the solution of certain types of equations. Finally, Chapter 7 puts the finishing touches on the excursion into set theory. The axioms presented there do not directly impact the elementary construction of the number systems, but once they are needed in an advanced class, readers will certainly appreciate them. Chapter coverage includes: Logic; Set Theory; Number Systems I: Natural Numbers; Number Systems II: Integers; Number Systems III: Fields; Unsolvability of the Quintic by Radicals; and More Axioms"-- _cProvided by publisher.
520			_a"The foundation of mathematics is not found in a single discipline since it is a general way of thinking in a very rigorous logical fashion. This book was written especially for readers who are about to make their first contact with this very way of thinking. Chapters 1-5 provide a rigorous, self contained construction of the familiar number systems (natural numbers, integers, real, and complex numbers) from the axioms of set theory"-- _cProvided by publisher.
650		0	_aSet theory _959719
650		7	_aKüme teorisi _2etuturkob _959721
650		0	_aLogic, Symbolic and mathematical _91361
650		0	_aMantık, Sembolik ve matematiksel _914118
942			_cBK