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Part of a new generation of textbooks for in-service and pre-service teachers at the junior-senior level, this text teaches in three main ways: it extends students' breadth of knowledge beyond, but related to, the topics covered in elementary and middle-grade curriculums; it increases prospective teachers' depth of mathematical understanding by providing problems rich in exploration and mathematical communication; and it models the most current ways of teaching mathematics.Many Section Openers begin with a motivating lesson that introduces a new topic in an understandable, real-world context.Exercise Sets at the end of every section provide more traditional practice and are labeled either Proof Exercises or Writing Exercises.Exploratory Exercises at the end of every section lead students to investigate topics outside the framework presented in the section. The final exercise in each section is a writing exercise.

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• 1 The Language of Logic
• 1.1 An Introduction to Logic
• 1.2 Conditionals and Equivalent Statements
• 1.3 Quantifiers, Venn Diagrams, and Valid Arguments
• 1.4 Thinking About Valid Arguments
• 2 Sets, Functions, and Sequences
• 2.1 Sets
• 2.2 Relations
• 2.3 Functions
• 2.4 Sequences
• 2.5 Recursive Sequences
• 3 An Introduction to Mathematical Proof
• 3.1 Introduction to Mathematical Reasoning
• 3.2 Proving Theorems
• 3.3 Proof by Mathematical Induction
• 3.4 From Mathematical Proof to Number Theory
• 3.5 What Is So Special About Primes?
• 4 Graph Theory
• 4.1 The Highway Inspector and the Traveling Salesman
• 4.2 An Introduction to Graphs
• 4.3 Complete Graphs, Isomorphic Graphs, and Subgraphs
• 4.4 Shortest-Path Problems
• 4.5 Planar Graphs and Euler's Theorem
• 4.6 Coloring Graphs
• 5 Trees and Directed Graphs
• 5.1 Directed Graphs
• 5.2 Introduction to Trees
• 5.3 Spanning Trees
• 5.4 Binary Trees and Tree Traversals
• 6 Combinatorics
• 6.1 There Is More to Counting Than 1, 2, 3
• 6.2 Combinations
• 6.3 Pascal's Triangle and Binomial Coefficients
• 6.4 Permutations and Combinations with Repetitions
• 6.5 The Pigeonhole Principle
• 6.6 The Inclusion-Exclusion Principle
• 7 Probability
• 7.1 Introduction to Probability
• 7.2 Probability with Set Operations
• 7.3 Probability and Combinatorics
• 7.4 Conditional Probability
• 8 Discrete Applications in Political Theory
• 8.1 Expressing Preferences in Voting
• 8.2 Arrow's Paradox and Voting Methods
• 8.3 Weighted Voting Systems
• 8.4 The Problem That Began in 1790
• 8.5 Apportionment Revisited Answers to Odd Questions