MARC Record from harvard_bibliographic_metadata

LEADER: 03264nam a22004695a 4500
001 013859935-1
005 20140103191402.0
008 131125s2004 xxu| s ||0| 0|eng d
020 $a9780817681548
020 $a9780817681548
020 $a9780817642884
024 7 $a10.1007/978-0-8176-8154-8$2doi
035 $a(Springer)9780817681548
040 $aSpringer
050 4 $aQA164-167.2
072 7 $aPBV$2bicssc
072 7 $aMAT036000$2bisacsh
082 04 $a511.6$223
100 1 $aAndreescu, Titu,$eauthor.
245 12 $aA Path to Combinatorics for Undergraduates :$bCounting Strategies /$cby Titu Andreescu, Zuming Feng.
264 1 $aBoston, MA :$bBirkhäuser Boston :$bImprint: Birkhäuser,$c2004.
300 $aXIX, 228 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
505 0 $aPreface -- Introduction -- Acknowledgments -- Abbreviations and Notations -- Addition on Multiplication?- Combinations -- Properties of Binomial Coefficients -- Bijections -- Inclusions and Exclusions -- Recursions -- Calculating in Two Ways – Fubini's Principle -- Generating Functions -- Review Exercises -- Glossary -- Further Reading.
520 $aThis unique approach to combinatorics is centered around challenging examples, fully-worked solutions, and hundreds of problems---many from Olympiads and other competitions, and many original to the authors. Each chapter highlights a particular aspect of the subject and casts combinatorial concepts in the guise of questions, illustrations, and exercises that are designed to encourage creativity, improve problem-solving techniques, and widen the reader's mathematical horizons. Topics encompass permutations and combinations, binomial coefficients and their applications, recursion, bijections, inclusions and exclusions, and generating functions. The work is replete with a broad range of useful methods and results, such as Sperner's Theorem, Catalan paths, integer partitions and Young's diagrams, and Lucas' and Kummer's Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph-theoretic reasoning and on links between algebra and geometry. The authors' previous text, 102 Combinatorial Problems, makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will stimulate seasoned mathematicians as well. A Path to Combinatorics for Undergraduates is a lively introduction not only to combinatorics, but also to mathematical ingenuity, rigor, and the joy of solving puzzles.
650 20 $aGeometry.
650 20 $aCombinatorial analysis.
650 10 $aMathematics.
650 0 $aDistribution (Probability theory)
650 0 $aCombinatorial analysis.
650 0 $aMathematics.
650 0 $aGeometry.
650 0 $aDiscrete groups.
650 24 $aConvex and Discrete Geometry.
650 24 $aProbability Theory and Stochastic Processes.
700 1 $aFeng, Zuming,$eauthor.
776 08 $iPrinted edition:$z9780817642884
988 $a20131203
906 $0VEN