Discrete Mathematics for Teachers : Preliminary Edition

by Wheeler, Ed

• ISBN13: 9780618433926
• ISBN10: 0618433929
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Information Age Pub

Summary

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.

Table of Contents

The Language of Logic

An Introduction to Logic

Conditionals and Equivalent Statements

Quantifiers, Venn Diagrams, and Valid Arguments

Thinking About Valid Arguments

Sets, Functions, and Sequences

Sets

Relations

Functions

Sequences

Recursive Sequences

An Introduction to Mathematical Proof

Introduction to Mathematical Reasoning

Proving Theorems

Proof by Mathematical Induction

From Mathematical Proof to Number Theory

What Is So Special About Primes?

Graph Theory

The Highway Inspector and the Traveling Salesman

An Introduction to Graphs

Complete Graphs, Isomorphic Graphs, and Subgraphs

Shortest-Path Problems

Planar Graphs and Euler's Theorem

Coloring Graphs

Trees and Directed Graphs

Directed Graphs

Introduction to Trees

Spanning Trees

Binary Trees and Tree Traversals

Combinatorics

There Is More to Counting Than 1, 2, 3

Combinations

Pascal's Triangle and Binomial Coefficients

Permutations and Combinations with Repetitions

The Pigeonhole Principle

The Inclusion-Exclusion Principle

Probability

Introduction to Probability

Probability with Set Operations

Probability and Combinatorics

Conditional Probability

Discrete Applications in Political Theory

Expressing Preferences in Voting

Arrow's Paradox and Voting Methods

Weighted Voting Systems

The Problem That Began in 1790

Apportionment Revisited Answers to Odd Questions

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