Mathematical Excursions

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2006-01-17
  • Publisher: Brooks Cole
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By presenting problem solving in purposeful and meaningful contexts,Mathematical Excursions,2/e, provides students in the Liberal Arts course with a glimpse into the nature of mathematics and how it is used to understand our world. Highlights of the book include the proven Aufmann Interactive Method and multi-part Excursion exercises that emphasize collaborative learning. An extensive technology program provides instructors and students with a comprehensive set of support tools. New!Content new to this edition includes a subsection onReading and Interpreting Graphs,a section onRight Triangle Trigonometry,and a section onStocks, Bonds, and Annuities. New!Online algebra review appendix helps students review prerequisite algebra concepts. AnExcursionactivity and correspondingExcursion Exercisesconclude each section, providing concept reinforcement and opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills. Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples, the first of which is a completely worked-out example with an annotated solution. The second problem, calledCheck Your Progress,is for the student to try. Each problem includes a reference to afully worked-out solutionin the back of the text. A section on Problem Solving Strategies in Chapter 1 introduces students to the inductive and deductive reasoning strategies they will use throughout the text. Question/Answerfeature encourages students to pause and think about the current discussion and to answer the question. For immediate reinforcement, the Answer is provided in a footnote on the same page. Carefully developed exercise sets emphasize skill building, skill maintenance, concepts, and applications. Icons are used to identify various types of exercises, including writing, data analysis, graphing calculator, and web exercises. Extension exercises at the end of each exercise set include Critical Thinking, Cooperative Learning, and Explorations, which may require Internet or library research. Math Mattersfeature throughout the text helps to motivate students by demonstrating how and why math is applicable to contemporary, real-life situations. Variety of supporting margin notes includesTake Note,alerting students to a concept requiring special attention;Point of Interest,offering motivating contextual information;Historical Notes,providing background information or vignettes of individuals responsible for major advancements in their field; andCalculator Notes,providing point-of-use tips. Chapter-ending resources include aChapter SummarywithKey WordsandEssential Concepts; Chapter Review Exercises(answers available in a special section), and aChapter Test.

Table of Contents

Preliminary Contents
Problem Solving
Inductive and deductive reasoning
Problem solving with patterns
Problem-solving strategies
Basic properties of sets
Complements, subsets, and venn diagrams
Set operations
Applications of sets
Infinite sets
Logic statements and quantifiers
Truth tables, equivalent statements, and tautologies
The conditional and the biconditional
The conditional and related statements
Euler diagrams
Numeration Systems and Number Theory
Early numeration systems
Place-value systems
Different base systems
Arithmetic in different bases
Prime numbers
Topics from number theory
Applications of Equations
First-degree equations
Rate, ratio, and proportion
Second-degree equations
Applications of Functions
Rectangular coordinates and functions
Properties of linear functions
Finding linear models
Quadratic functions
Exponential functions
Logarithmic functions
Mathematical Systems
Modular arithmetic
Applications of modular arithmetic
Introduction to group theory
Basic concepts of Euclidean geometry
Perimeter and area of plane figures
Properties of triangles
Volume and surface area
Introduction to trigonometry
Non-Euclidean geometry
The Mathematics of Graphs
Traveling roads and visiting cities
Efficient routes
Planarity and Euler's formula
Map coloring and graphs
The Mathematics of Finance
Simple interest
Compound interest
Credit cards and consumer loans
Stocks, bonds, and mutual funds
Home ownership
Combinatorics and Probability
The counting principle
Permutations and combinations
Probability and odds
Addition and complement rules
Conditional probability
Measures of central tendency
Measures of dispersion
Measures of relative position
Normal distributions
Linear regression and correlation
Apportionment and Voting
Introduction to apportionment
Introduction to voting
Weighted voting systems
Table of Contents provided by Publisher. All Rights Reserved.

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