1st Edition

Student Handbook for Discrete Mathematics with Ducks SRRSLEH

By sarah-marie belcastro Copyright 2016
    208 Pages 59 B/W Illustrations
    by A K Peters/CRC Press

    208 Pages
    by A K Peters/CRC Press

    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.

    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

    Biography

    sarah-marie belcastro