Inquiry-Based Enumerative Combinatorics: One, Two, Skip a Few… Ninety-Nine, One Hundred (Undergraduate Texts in Mathematics)
Equips readers with the fundamentals of enumerativecombinatorics with an emphasis on generating functiontechniquesPromotes an engaging learning experience by utilizingInquiry-Based Learning (IBL)Offers an accessible entry-point to enumerative combinatoricsthat builds from minimal prerequisites to a selection of advancedtopics——————————This textbook offers the opportunity to create a uniquelyengaging combinatorics classroom by embracing Inquiry-BasedLearning (IBL) techniques. Readers are provided with a carefullychosen progression of theorems to prove and problems to activelysolve. Students will feel a sense of accomplishment as theircollective inquiry traces a path from the basics to importantgenerating function techniques.Beginning with an exploration of permutations and combinationsthat culminates in the Binomial Theorem, the text goes on to guidethe study of ordinary and exponential generating functions. Thesetools underpin the in-depth study of Eulerian, Catalan, andNarayana numbers that follows, and a selection of advanced topicsthat includes applications to probability and number theory.Throughout, the theory unfolds via over 150 carefully selectedproblems for students to solve, many of which connect tostate-of-the-art research.Inquiry-Based Enumerative Combinatorics is ideal forlower-division undergraduate students majoring in math or computerscience, as there are no formal mathematics prerequisites. Becauseit includes many connections to recent research, students of anylevel who are interested in combinatorics will also find this avaluable resource.