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Inquiry-based enumerative combinator...

Petersen, T. Kyle.

Inquiry-based enumerative combinatoricsone, two, skip a Few.. ninety-nine, one hundred /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Inquiry-based enumerative combinatoricsby T. Kyle Petersen.
其他題名:	one, two, skip a Few.. ninety-nine, one hundred /
作者:	Petersen, T. Kyle.
出版者:	Cham :Springer International Publishing :2019.
面頁冊數:	xi, 238 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Combinatorial analysis.
電子資源:	https://doi.org/10.1007/978-3-030-18308-0
ISBN:	9783030183080$q(electronic bk.)

Inquiry-based enumerative combinatoricsone, two, skip a Few.. ninety-nine, one hundred /
Petersen, T. Kyle.

Inquiry-based enumerative combinatoricsone, two, skip a Few.. ninety-nine, one hundred /[electronic resource] :by T. Kyle Petersen. - Cham :Springer International Publishing :2019. - xi, 238 p. :ill., digital ;24 cm. - Undergraduate texts in mathematics,0172-6056. - Undergraduate texts in mathematics..

0. 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.

This 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.

ISBN: 9783030183080$q(electronic bk.)

Standard No.: 10.1007/978-3-030-18308-0doiSubjects--Topical Terms:

182280
Combinatorial analysis.

LC Class. No.: QA164 / .P48 2019

Dewey Class. No.: 511.6

Inquiry-based enumerative combinatoricsone, two, skip a Few.. ninety-nine, one hundred /
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505 0 $a 0. 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.
520 $a This 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.
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