LEADER 03289nam 22004815 450 001 9910338253003321 005 20200702130935.0 010 $a3-030-18308-4 024 7 $a10.1007/978-3-030-18308-0 035 $a(CKB)4100000008527454 035 $a(DE-He213)978-3-030-18308-0 035 $a(MiAaPQ)EBC5926106 035 $a(PPN)269145532 035 $a(EXLCZ)994100000008527454 100 $a20190628d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInquiry-Based Enumerative Combinatorics $eOne, Two, Skip a Few... Ninety-Nine, One Hundred /$fby T. Kyle Petersen 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XI, 238 p. 104 illus., 9 illus. in color.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 311 $a3-030-18307-6 327 $a0. Introduction to this book -- 1. First Principles -- 2. Permutations -- 3. Combinations -- 4. The Binomial Theorem -- 5. Recurrences -- 6. Generating Functions -- 7. Exponential Generating Functions and Bell Numbers -- 8. Eulerian Numbers -- 9. Catalan and Narayana Numbers -- 10. Refined Enumeration -- 11. Applications to Probability -- 12. Some Partition Theory -- 13. A Bit of Number Theory -- A. Supplementary Exercises. 330 $aThis textbook offers the opportunity to create a uniquely engaging combinatorics classroom by embracing Inquiry-Based Learning (IBL) techniques. Readers are provided with a carefully chosen progression of theorems to prove and problems to actively solve. Students will feel a sense of accomplishment as their collective inquiry traces a path from the basics to important generating function techniques. Beginning with an exploration of permutations and combinations that culminates in the Binomial Theorem, the text goes on to guide the study of ordinary and exponential generating functions. These tools underpin the in-depth study of Eulerian, Catalan, and Narayana numbers that follows, and a selection of advanced topics that includes applications to probability and number theory. Throughout, the theory unfolds via over 150 carefully selected problems for students to solve, many of which connect to state-of-the-art research. Inquiry-Based Enumerative Combinatorics is ideal for lower-division undergraduate students majoring in math or computer science, as there are no formal mathematics prerequisites. Because it includes many connections to recent research, students of any level who are interested in combinatorics will also find this a valuable resource. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aCombinatorics 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 615 0$aCombinatorics. 615 14$aCombinatorics. 676 $a511.6 676 $a511.6 700 $aPetersen$b T. Kyle$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755510 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910338253003321 996 $aInquiry-Based Enumerative Combinatorics$91732506 997 $aUNINA