Discrete mathematics with ducks / Sarah-Marie Belcastro.

Enhanced descriptions from Syndetics:

Containing exercises and materials that engage students at all levels, Discrete Mathematics with Ducks presents a gentle introduction for students who find the proofs and abstractions of mathematics challenging. This classroom-tested text uses discrete mathematics as the context for introducing proofwriting.

Facilitating effective and active learning, each chapter contains a mixture of discovery activities, expository text, in-class exercises, and homework problems.

Discrete Mathematics with Ducks offers students a diverse introduction to the field and a solid foundation for further study in discrete mathematics and complies with SIGCSE guidelines. The book shows how combinatorics and graph theory are used in both computer science and mathematics.

Table of contents provided by Syndetics

• The Basics
• Counting and Proofs
• Introduction and Summary Try This! Let's Count
• The Sum and Product Principles
• Preliminaries on Proofs and Disproofs
• Pigeons and Correspondences
• Where to Go from Here
• Sets and Logic
• Introduction and Summary
• Sets
• Logic
• Try This! Problems on Sets and Logic
• Proof Techniques: Not! Try This! A Tricky Conundrum
• Where to Go from Here
• Bonus: Truth Tellers
• Graphs and Functions
• Introduction and Summary
• Function Introduction Try This! Play with Functions and Graphs
• Functions and Counting
• Graphs: Definitions and Examples
• Isomorphisms
• Graphs: Operations and Uses
• Try This! More Graph Problems
• Ramseyness
• Where to Go from Here
• Bonus: Party Tricks
• Bonus 2 Counting with the Characteristic Function
• Induction
• Introduction and Summary
• Induction Try This! Induction
• More Examples
• The Best Inducktion Proof Ever Try This! More Problems about Induction
• Are They or Aren't They? Resolving Grey Ducks
• Where to Go from Here
• Bonus: Small Crooks
• Bonus 2 An Induction Song
• Algorithms with Ciphers
• Introduction and Summary
• Algorithms
• Modular Arithmetic (and Equivalence Relations)
• Cryptography: Some Ciphers
• Try This! Encryptoequivalent Modulagorithmic Problems
• Where to Go from Here
• Bonus: Algorithms for Searching Graphs
• Bonus 2 Pigeons and Divisibility
• Combinatorics
• Binomial Coefficients and Pascal's Triangle
• Introduction and Summary
• You Have a Choice Try This! Investigate a Triangle
• Pascal's Triangle
• Overcounting Carefully and Reordering at Will
• Try This! Play with Powers and Permutations
• Binomial Basics
• Combinatorial Proof Try This! Pancakes and Proofs
• Where to Go from Here
• Bonus: Sorting Bubbles in Order of Size
• Bonus 2 Mastermind
• Balls and Boxes and PIE-Counting Techniques
• Introduction and Summary
• Combinatorial Problem Types Try This! Let's Have Some PIE
• Combinatorial Problem Solutions and Strategies
• Let's Explain Our PIE! Try This! What Are the Balls and What Are the Boxes? And Do You Want Some PIE?
• Where to Go from Here
• Bonus: Linear and Integer Programming
• Recurrences
• Introduction and Summary
• Fibonacci Numbers and Identities
• Recurrences and Integer Sequences and Induction Try This! Sequences and Fibonacci Identities
• Naive Techniques for Finding Closed Forms and Recurrences
• Arithmetic Sequences and Finite Differences
• Try This! Recurrence Exercises
• Geometric Sequences and the Characteristic Equation Try This! Find Closed Forms for These Recurrence Relations!
• Where to Go from Here
• Bonus: Recurring Stories
• Cutting up Food (Counting and Geometry)
• Introduction and Summary
• Try This! Slice Pizza (and a Yam)
• Pizza Numbers Try This! Spaghetti, Yams, and More
• Yam, Spaghetti and Pizza Numbers
• Where to Go from Here
• Bonus: Geometric Gems
• Graph Theory
• Trees
• Introduction and Summary
• Basic Facts about Trees Try This! Spanning Trees
• Spanning Tree Algorithms
• Binary Trees Try This! Binary Trees and Matchings
• Matchings
• Backtracking
• Where to Go from Here
• Bonus: The Branch-and-Bound Technique in Integer Programming
• Euler's Formula and Applications
• Introduction and Summary Try This! Planarity Explorations
• Planarity
• A Lovely Story
• Or, Are Emus Full?: A Theorem and a Proof
• Applications of Euler's Formula
• Try This! Applications of Euler's Formula
• Where to Go from Here
• Bonus: Topological Graph Theory
• Graph Traversals
• Introduction and Summary Try This! Euler Traversals
• Euler Paths and Circuits
• Hamilton Circuits, the Traveling Salesperson Problem, and Dijkstra's Algorithm Try This!-Do This!-Try This!
• Where to Go from Here
• Bonus: Digraphs, Euler Traversals, and RNA Chains
• Bonus 2 Network Flows
• Bonus 3 Two Hamiltonian Theorems
• Graph Coloring
• Introduction and Summary Try This! Coloring Vertices and Edges
• Introduction to Coloring
• Try This! Let's Think about Coloring
• Coloring and Things (Graphs and Concepts) That Have Come Before
• Where to Go from Here
• Bonus: The Four-Color Theorem
• Other Material
• Probability and Expectation
• Introduction and Summary
• What Is Probability, Exactly?
• High Expectations
• You are Probably Expected to Try This!
• Conditional Probability and Independence
• Try This! . . . Probably, Under Certain Conditions
• Higher Expectations
• Where to Go from Here
• Bonus: Ramsey Numbers and the Probabilistic Method
• Fun with Cardinality
• Introduction and Summary
• Read This! Parasitology, The Play
• How Big Is Infinite? Try This! Investigating the Play
• How High Can We Count?
• Where to Go from Here
• Bonus: The Schröder-Bernstein Theorem
• Additional Problems
• Solutions to Check Yourself Problems
• The Greek Alphabet and Some Uses for Some Letters
• List of Symbols
• Glossary
• Bibliography
• Problems and Instructor Notes appear at the end of each chapter