  # Student Handbook for Discrete Mathematics with Ducks

## SRRSLEH, 1st Edition

A K Peters/CRC Press

208 pages | 59 B/W Illus.

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### Description

Student Handbook for Discrete Mathematics with Ducks is a Student Reference, Review, Supplemental Learning, and Example Handbook (SRRSLEH) that mirrors the content of the author’s popular textbook Discrete Mathematics with Ducks (DMwD). This handbook provides a review of key material, illustrative examples, and new problems with accompanying solutions that are helpful even for those using a traditional discrete mathematics textbook.

Every chapter in SRRSLEH matches the corresponding chapter of DMwD. Chapters in SRRSLEH contain the following:

• A list of the notation introduced in the corresponding chapter
• A list of definitions that students need to know from the corresponding chapter
• Theorems/facts of note appearing in the corresponding chapter
• A list of proof techniques introduced, with templates and/or examples given for each one
• A selection of examples from DMwD, written out formally and briefly rather than colloquially as in DMwD

A quick refresher for any discrete math student, this handbook enables students to find information easily and reminds them of the terms and results they should know during their course.

Read reviews of DMwD.

### Table of Contents

THE BASICS

Counting and Proofs

Definitions and Notation

Facts and Theorems

Proof Techniques: Direct Proof and Pigeonhole Tips

Some Straightforward Examples

More Problems

More Solutions

Sets and Logic

Definitions and Notation

Facts and Theorems

Proof Techniques: Double-Inclusion, Biconditionals (⇐⇒s), Proving the Contrapositive, and Proof by Contradiction

Some Straightforward Examples

More Problems

More Solutions

Graphs and Functions

Definitions and Notation

Facts and Theorems

Some Straightforward Examples

More Problems

More Solutions

Induction

Definitions and Notation

Facts and Theorems

Proof Techniques: Induction (How Surprising!)

Some Straightforward Examples

More Problems

More Solutions

Algorithms with Ciphers

Definitions and Notation

Facts and Theorems

Some Straightforward Examples

More Problems

More Solutions

COMBINATORICS

Binomial Coefficients and Pascal’s Triangle

Definitions and Notation

Facts and Theorems

Proof Techniques: Overcounting Carefully and Combinatorial Proof

Some Straightforward Examples

More Problems

More Solutions

Balls and Boxes and PIE: Counting Techniques

Definitions and Notation

Facts and Theorems

Some Straightforward Examples

More Problems

More Solutions

Recurrences

Definitions and Notation

Facts and Theorems

Proof Techniques: Showing a Closed Form for a Recurrence Is Correct

Some Straightforward Examples

More Problems

More Solutions

Cutting Up Food: Counting and Geometry

Definitions and Notation

Facts and Theorems

More Problems

More Solutions

GRAPH THEORY

Trees

Definitions and Notation

Facts and Theorems

Some Straightforward Examples

More Problems

More Solutions

Euler’s Formula and Applications

Definitions and Notation

Facts and Theorems

Some Straightforward Examples

More Problems

More Solutions

Graph Traversals

Definitions and Notation

Facts and Theorems

Some Straightforward Examples

More Problems

More Solutions

Graph Coloring

Definitions and Notation

Facts and Theorems

Some Straightforward Examples

More Problems

More Solutions

OTHER MATERIAL

Probability and Expectation

Definitions and Notation

Facts and Theorems

Some Straightforward Examples

More Problems

More Solutions

Fun with Cardinality

Definitions and Notation

Facts and Theorems

Some Straightforward Examples

More Problems

More Solutions

### Subject Categories

##### BISAC Subject Codes/Headings:
COM046000
COMPUTERS / Operating Systems / General
MAT000000
MATHEMATICS / General
MAT036000
MATHEMATICS / Combinatorics