Discrete Mathematics with Ducks

by sarah-marie belcastro

Overview

Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels.

The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems.

The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction.

Features:

• The book’s Try This! sections encourage students to construct components of discussed concepts, theorems, and proofs
• Provided sets of discovery problems and illustrative examples reinforce learning
• Bonus sections can be used by instructors as part of their regular curriculum, for projects, or for further study

Product Details

ISBN-13:	9781351683685
Publisher:	CRC Press
Publication date:	11/15/2018
Series:	Textbooks in Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	700
File size:	12 MB
Note:	This product may take a few minutes to download.

About the Author

sarah-marie belcastro is a free-range mathematician who works primarily in topological graph theory. She enjoys connecting people to each other, connecting ideas to each other, and connecting people to ideas. Among her many non-pure-mathematics interests are the mathematics of knitting, pharmacokinetics, dance (principally ballet and modern), and changing the world. sarah-marie did her undergraduate work at Haverford College and her Ph.D. at the University of Michigan. She currently directs the summer program MathILy.

Table of Contents

Preface for Instructors and Other Teachers

Preface for Students and Other Learners

Theme: The Basics

1 Counting and Proofs

2 Sets and Logic

3 Graphics and Functions

4 Induction

5 Algorithms with Ciphers

Theme I Supplement

6 Binomial Coefficients and Pascal’s Triangle

7 Balls and Boxes and PIE: Counting Techniques

8 Recurrences

9 Cutting Up Food: Counting and Geometry

III Theme: Graph Theory

10 Trees

11 Euler’s Formula and Applications

12 Graph Traversals

13 Graph Coloring

Theme III Supplement: Problems on the Theme of Graph Theory

IV Other Material

14 Probability and Expectation

15 Fun with Cardinality

16 Number Theory

17 Computational Complexity

A Solutions to Check Yourself Problems

B Solutions to Bonus Check-Yourself Problems

C The Greek Alphabet and Some Uses for Some Letters

D List of Symbols

Bibliography

Index

What People are Saying About This

From the Publisher

This book can certainly be used to teach the standard course in discrete mathematics designed for computer science majors. The lighter touch of duck references does amuse you and does not ever overshadow or disguise the mathematical concepts.
—Charles Ashbacher, MAA Reviews, August 2012

When I used Discrete Mathematics with Ducks in class, I assigned readings, and my students came to class full of questions and ideas. Every day we had a good time in one way or another; these classes were a highlight of my teaching career. I give a lot of credit to this book, thanks to the author's skill at blending rigor, great examples, casual humor, and precise writing.
—David Perkins, author of Calculus and Its Origins

I had a lot of fun teaching from Discrete Mathematics with Ducks! ... I think the discovery/exploratory/problem solving approach is ABSOLUTELY the way this course should be taught, and of all the discrete books I have looked at, this text does the best job of supporting that kind of approach to the subject while still giving enough of the material in writing to fill in the gaps. ... I found that the material provided and the instructor notes cut down on my prep time, and I definitely referred to them. Having the in-class activities included is a huge benefit to this book.
—Dana Rowland, Associate Professor of Mathematics, Merrimack College

... an incredible book ... readable by students, useful for instructors, and constructed with style and flair. This book will make it much easier to teach an exciting, student-centered discrete mathematics course that will also serve as an excellent introduction to advanced critical thinking, problem solving, and proofs. And there are ducks!
—Douglas Shaw, Professor of Mathematics, University of Northern Iowa

Editorial Reviews

This book can certainly be used to teach the standard course in discrete mathematics designed for computer science majors. The lighter touch of duck references does amuse you and does not ever overshadow or disguise the mathematical concepts.
—Charles Ashbacher, MAA Reviews, August 2012

When I used Discrete Mathematics with Ducks in class, I assigned readings, and my students came to class full of questions and ideas. Every day we had a good time in one way or another; these classes were a highlight of my teaching career. I give a lot of credit to this book, thanks to the author's skill at blending rigor, great examples, casual humor, and precise writing.
—David Perkins, author of Calculus and Its Origins

I had a lot of fun teaching from Discrete Mathematics with Ducks! ... I think the discovery/exploratory/problem solving approach is ABSOLUTELY the way this course should be taught, and of all the discrete books I have looked at, this text does the best job of supporting that kind of approach to the subject while still giving enough of the material in writing to fill in the gaps. ... I found that the material provided and the instructor notes cut down on my prep time, and I definitely referred to them. Having the in-class activities included is a huge benefit to this book.
—Dana Rowland, Associate Professor of Mathematics, Merrimack College

... an incredible book ... readable by students, useful for instructors, and constructed with style and flair. This book will make it much easier to teach an exciting, student-centered discrete mathematics course that will also serve as an excellent introduction to advanced critical thinking, problem solving, and proofs. And there are ducks!
—Douglas Shaw, Professor of Mathematics, University of Northern Iowa

From the Publisher