000			03937nam a2200385 i 4500
001			OTLid0000007
003			MnU
005			20241120064006.0
006			m o d s
007			cr
008			180907s2013 mnu o 0 0 eng d
020			_a9780989472104
040			_aMnU _beng _cMnU
050		4	_aQA1
050		4	_aQA37.3
100	1		_aHammack, Richard _eauthor
245	0	0	_aBook of Proof _cRichard Hammack
250			_aThird Edition
264		2	_aMinneapolis, MN _bOpen Textbook Library
264		1	_aRichmond, VA _bRichard Hammack _c[2013]
264		4	_c©2013.
300			_a1 online resource
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	0		_aOpen textbook library.
505	0		_aI Fundamentals -- 1. Sets -- 2. Logic -- 3. Counting -- II How to Prove Conditional Statements -- 4. Direct Proof -- 5. Contrapositive Proof -- 6. Proof by Contradiction -- III More on Proof -- 7. Proving Non-Conditional Statements -- 8. Proofs Involving Sets -- 9. Disproof -- 10. Mathematical Induction -- IV Relations, Functions and Cardinality -- 11. Relations -- 12. Functions -- 13. Proofs in Calculus -- 14. Cardinality of Sets
520	0		_aThis is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers. But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the fundamental theorem of calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics. This text has been used in classes at: Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei, Christian Brothers High School, University of Texas Pan American, Schola Europaea, James Madison University, Heriot-Watt University, Prince of Songkla University, Queen Mary University of London, University of Nevada - Reno, University of Georgia - Athens, Saint Peter's University, California State University,Bogaziçi University, Pennsylvania State University, University of Notre Dame
542	1		_fAttribution-NoDerivs
546			_aIn English.
588	0		_aDescription based on print resource
650		0	_aMathematics _vTextbooks
710	2		_aOpen Textbook Library _edistributor
856	4	0	_uhttps://open.umn.edu/opentextbooks/textbooks/7 _zAccess online version
999			_c38317 _d38317