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001 978-1-4614-3631-7
003 DE-He213
005 20140220082812.0
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008 120919s2013 xxu| s |||| 0|eng d
020 _a9781461436317
_9978-1-4614-3631-7
024 7 _a10.1007/978-1-4614-3631-7
_2doi
050 4 _aQA1-939
072 7 _aPB
_2bicssc
072 7 _aMAT000000
_2bisacsh
082 0 4 _a510
_223
100 1 _aCunningham, Daniel W.
_eauthor.
245 1 2 _aA Logical Introduction to Proof
_h[electronic resource] /
_cby Daniel W. Cunningham.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXV, 356 p. 145 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- The Greek Alphabet -- 1. Propositional Logic -- 2. Predicate Logic -- 3. Proof Strategies and Diagrams -- 4. Mathematical Induction -- 5. Set Theory -- 6. Functions -- 7. Relations -- 8. Core Concepts in Abstract Algebra -- 9. Core Concepts in Real Analysis -- A Summary of Strategies -- References -- List of Symbols. Index.
520 _aA Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or “bridge” course  between calculus and advanced mathematics courses.  The author’s approach  prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may also be beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs.   Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument for analyzing the structure of mathematical assertions and is a tool for composing mathematical proofs. Exercises are given at the end of each section within a chapter. Chapter 1 focuses on propositional logic while Chapter 2 is devoted to the logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs; each presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theorems concerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamental theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts that appear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finally, Chapter 9 presents proof strategies that explicitly show students how to deal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies.  The appendix provides a useful summary of strategies for dealing with proofs.
650 0 _aMathematics.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aMathematics.
650 2 4 _aMathematics, general.
650 2 4 _aMathematical Logic and Foundations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461436300
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-3631-7
912 _aZDB-2-SMA
999 _c94996
_d94996