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Student Handbook for Discrete Mathematics with Ducks

SRRSLEH

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## Book 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 BASICSCounting 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

**COMBINATORICSBinomial 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 THEORYTrees**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 MATERIALProbability 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