000 04767nam a22005055i 4500
001 978-1-4419-9479-0
003 DE-He213
005 20140220083729.0
007 cr nn 008mamaa
008 110622s2011 xxu| s |||| 0|eng d
020 _a9781441994790
_9978-1-4419-9479-0
024 7 _a10.1007/978-1-4419-9479-0
_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 _aDaepp, Ulrich.
_eauthor.
245 1 0 _aReading, Writing, and Proving
_h[electronic resource] :
_bA Closer Look at Mathematics /
_cby Ulrich Daepp, Pamela Gorkin.
264 1 _aNew York, NY :
_bSpringer New York,
_c2011.
300 _aXIV, 378 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 _a-Preface. -1. The How, When, and Why of Mathematics -- 2. Logically Speaking -- 3.Introducing the Contrapositive and Converse -- 4. Set Notation and Quantifiers -- 5. Proof Techniques -- 6. Sets -- 7. Operations on Sets -- 8. More on Operations on Sets -- 9. The Power Set and the Cartesian Product -- 10. Relations -- 11. Partitions -- 12. Order in the Reals -- 13. Consequences of the Completeness of (\Bbb R) -- 14. Functions, Domain, and Range.- 15. Functions, One-to-One, and Onto -- 16. Inverses -- 17. Images and Inverse Images -- 18. Mathematical Induction -- 19. Sequences -- 20. Convergence of Sequences of Real Numbers -- 21. Equivalent Sets -- 22. Finite Sets and an Infinite Set -- 23. Countable and Uncountable Sets -- 24. The Cantor-Schröder-Bernstein Theorem -- 25. Metric Spaces -- 26. Getting to Know Open and Closed Sets -- 27. Modular Arithmetic -- 28. Fermat’s Little Theorem -- 29. Projects -- Appendix -- References -- Index.
520 _aReading, Writing, and Proving is designed to guide mathematics students during their transition from algorithm-based courses such as calculus, to theorem and proof-based courses. This text not only introduces the various proof techniques and other foundational principles of higher mathematics in great detail, but also assists and inspires students to develop the necessary abilities to read, write, and prove using mathematical definitions, examples, and theorems that are required for success in navigating advanced mathematics courses. In addition to an introduction to mathematical logic, set theory, and the various methods of proof, this textbook prepares students for future courses by providing a strong foundation in the fields of number theory, abstract algebra, and analysis. Also included are a wide variety of examples and exercises as well as a rich selection of unique projects that provide students with an opportunity to investigate a topic independently or as part of a collaborative effort. New features of the Second Edition include the addition of formal statements of definitions at the end of each chapter; a new chapter featuring the Cantor–Schröder–Bernstein theorem with a spotlight on the continuum hypothesis; over 200 new problems; two new student projects; and more. An electronic solutions manual to selected problems is available online.  From the reviews of the First Edition: “The book…emphasizes Pòlya’s four-part framework for problem solving (from his book How to Solve It)…[it] contains more than enough material for a one-semester course, and is designed to give the instructor wide leeway in choosing topics to emphasize…This book has a rich selection of problems for the student to ponder, in addition to "exercises" that come with hints or complete solutions…I was charmed by this book and found it quite enticing.” – Marcia G. Fung for MAA Reviews “… A book worthy of serious consideration for courses whose goal is to prepare students for upper-division mathematics courses. Summing Up: Highly recommended.” – J. R. Burke, Gonzaga University for CHOICE Reviews
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aLogic, Symbolic and mathematical.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aAnalysis.
650 2 4 _aNumber Theory.
700 1 _aGorkin, Pamela.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441994783
830 0 _aUndergraduate Texts in Mathematics,
_x0172-6056
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-9479-0
912 _aZDB-2-SMA
999 _c106060
_d106060