000			03500nam a22004935i 4500
001			978-1-4419-7127-2
003			DE-He213
005			20140220083722.0
007			cr nn 008mamaa
008			110214s2011 xxu| s |||| 0|eng d
020			_a9781441971272 _9978-1-4419-7127-2
024	7		_a10.1007/978-1-4419-7127-2 _2doi
050		4	_aQA8.9-10.3
072		7	_aPBC _2bicssc
072		7	_aPBCD _2bicssc
072		7	_aMAT018000 _2bisacsh
082	0	4	_a511.3 _223
100	1		_aBloch, Ethan D. _eauthor.
245	1	0	_aProofs and Fundamentals _h[electronic resource] : _bA First Course in Abstract Mathematics / _cby Ethan D. Bloch.
264		1	_aNew York, NY : _bSpringer New York, _c2011.
300			_aXXVI, 358 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUndergraduate Texts in Mathematics, _x0172-6056
505	0		_aPreface to the Second Edition -- Preface to the First Edition -- To the Student -- To the Instructor -- Part I. Proofs -- 1. Informal Logic -- 2. Strategies for Proofs -- Part II. Fundamentals -- 3. Sets -- 4. Functions -- 5. Relations -- 6. Finite and Infinite Sets -- Part III. Extras -- 7. Selected Topics -- 8. Explorations -- Appendix: Properties of Numbers -- Bibliography -- Index.
520			_aThis textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis. This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. Reviews of the first edition: This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course. —Zentralblatt Math 'Proofs and Fundamentals' has many strengths. One notable strength is its excellent organization... There are large exercise sets throughout the book... the exercises are well integrated with the text and vary appropriately from easy to hard... Perhaps the book’s greatest strength is the author’s zeal and skill for helping students write mathematics better. —MAA Online
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aCombinatorics.
650		0	_aLogic, Symbolic and mathematical.
650	1	4	_aMathematics.
650	2	4	_aMathematical Logic and Foundations.
650	2	4	_aAlgebra.
650	2	4	_aCombinatorics.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781441971265
830		0	_aUndergraduate Texts in Mathematics, _x0172-6056
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4419-7127-2
912			_aZDB-2-SMA
999			_c105695 _d105695