000 03756nam a22005055i 4500
001 978-1-4614-4265-3
003 DE-He213
005 20140220083249.0
007 cr nn 008mamaa
008 120604s2012 xxu| s |||| 0|eng d
020 _a9781461442653
_9978-1-4614-4265-3
024 7 _a10.1007/978-1-4614-4265-3
_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 _aGerstein, Larry J.
_eauthor.
245 1 0 _aIntroduction to Mathematical Structures and Proofs
_h[electronic resource] /
_cby Larry J. Gerstein.
250 _a2nd ed. 2012.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2012.
300 _aXIII, 401 p. 133 illus.
_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 -- 1. Logic -- 2. Sets -- 3. Functions -- 4. Finite and Infinite Sets -- 5. Combinatorics -- 6. Number Theory -- 7. Complex Numbers -- Hints and Partial Solutions to Selected Odd-Numbered Exercises -- Index.
520 _aAs a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study.  This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—required to prove a nontrivial result.  In short, this book seeks to enhance the mathematical maturity of the reader.   The new material in this second edition includes a section on graph theory, several new sections on number theory (including primitive roots, with an application to card-shuffling), and a brief introduction to the complex numbers (including a section on the arithmetic of the Gaussian integers).   From a review of the first edition: "...Gerstein wants—very gently—to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. ...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge…. Gerstein’s book states quite plainly that the text is designed for use in a transitions course.  Nothing benefits a textbook author more than having his goals clearly in mind, and Gerstein’s book achieves its goals.  I would be happy to use it in a transitions course.” —Steven Krantz, American Mathematical Monthly
650 0 _aMathematics.
650 0 _aCombinatorics.
650 0 _aLogic, Symbolic and mathematical.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aNumber Theory.
650 2 4 _aCombinatorics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461442646
830 0 _aUndergraduate Texts in Mathematics,
_x0172-6056
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-4265-3
912 _aZDB-2-SMA
999 _c101492
_d101492