Includes index (684-691 p.)

Includes references (682-683 p.)

1 Puzzles Patterns, and Mathematical Language

1 First examples

9 Number Puzzles and sequences

24 Truth-tellers, Liars and propositional logic

40 Predicates

53 Implications

68 Excursion Validity of Arguments

81 A Primer of Mathematical writing

82 Mathematical writing

98 Proofs about numbers

110 Mathematical induction

122 More about induction

132 Contradiction and the pigeonhole principles

150 Excursion Representations of Numbers

166 Excursion Modular Arithmetic and Cryptography

181 sets and Boolean Algebra

181 Set Definition and Operation

198 More Operations on Sets

210 Proving set Properties

221 Boolean Algebra

229 Excursion Logic Circuits

248 Functions and Relations

249 Definitions Diagrams and Inverses

283 Properties of functions and set Cardinality

301 Properties of relations

313 Equivalence Relations

324 Numerical Functions in Discrete math

334 Excursion Iterated functions and Chaos

345 Excursion Growth of functions

368 Combinations

369 Introduction

386 Basic Rules for Counting

398 Combinations and the Binomial Theorem

408 Binary Sequences

418 Recursive Counting

423 Excursion Solving Recurrence Relations

440 Probability

440 Introduction

448 Sum and Rules for Probability

460 Probability in Games of Chance

466 Expected Value in Game of Chance

475 Excursion Recursion Revisited

excursion Matrices and markov chains

505 Graphs and Trees

506 Graph Theory

519 Proofs About Graph and trees

533 Isomorphism and Planarity

546 Connections to Matrices and Relations

567 Graph in Puzzles and Games

581 Excursion Binary Trees

596 Excursion Hamiltonian Cycles and the TSP

613 A Rules of the Game

613 Cards

614 Sports

615 Miscellaneous Games

618 B Matrices and their Operations

618 Matrix Operation

620 Matrix Arithmetic with Technology

625 Selected Answers and Hints

682 References and Further Reading