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Mathematical Excursions

Mathematical Excursions - 2nd edition

ISBN13: 978-0618608539

Cover of Mathematical Excursions 2ND 07 (ISBN 978-0618608539)
ISBN13: 978-0618608539
ISBN10: 0618608532
Cover type: Hardback
Edition/Copyright: 2ND 07
Publisher: Houghton Mifflin Harcourt
Published: 2007
International: No

List price: $314.00

Mathematical Excursions - 2ND 07 edition

ISBN13: 978-0618608539

Aufmann, Lockwood, Nation and Clegg

ISBN13: 978-0618608539
ISBN10: 0618608532
Cover type: Hardback
Edition/Copyright: 2ND 07
Publisher: Houghton Mifflin Harcourt

Published: 2007
International: No

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 on Reading and Interpreting Graphs, a section on Right Triangle Trigonometry, and a section on Stocks, Bonds, and Annuities.
  • New! Online algebra review appendix helps students review prerequisite algebra concepts.
  • An Excursion activity and corresponding Excursion Exercises conclude 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, called Check Your Progress, is for the student to try. Each problem includes a reference to a fully worked-out solution in 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/Answer feature 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 Matters feature 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 includes Take 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; and Calculator Notes, providing point-of-use tips.

Table of Contents

1. Problem Solving

1.1 Inductive and deductive reasoning
1.2 Problem solving with patterns
1.3 Problem-solving strategies

2. Sets

2.1 Basic properties of sets
2.2 Complements, subsets, and venn diagrams
2.3 Set operations
2.4 Applications of sets
2.5 Infinite sets

3. Logic

3.1 Logic statements and quantifiers
3.2 Truth tables, equivalent statements, and tautologies
3.3 The conditional and the biconditional
3.4 The conditional and related statements
3.5 Arguments
3.6 Euler diagrams

4. Numeration Systems and Number Theory

4.1 Early numeration systems
4.2 Place-value systems
4.3 Different base systems
4.4 Arithmetic in different bases
4.5 Prime numbers
4.6 Topics from number theory

5. Applications of Equations

5.1 First-degree equations
5.2 Rate, ratio, and proportion
5.3 Percent
5.4 Second-degree equations

6. Applications of Functions

6.1 Rectangular coordinates and functions
6.2 Properties of linear functions
6.3 Finding linear models
6.4 Quadratic functions
6.5 Exponential functions
6.6 Logarithmic functions

7. Mathematical Systems

7.1 Modular arithmetic
7.2 Applications of modular arithmetic
7.3 Introduction to group theory

8. Geometry

8.1 Basic concepts of Euclidean geometry
8.2 Perimeter and area of plane figures
8.3 Properties of triangles
8.4 Volume and surface area
8.5 Introduction to trigonometry
8.6 Non-Euclidean geometry
8.7 Fractals

9. The Mathematics of Graphs

9.1 Traveling roads and visiting cities
9.2 Efficient routes
9.3 Planarity and Euler's formula
9.4 Map coloring and graphs

10. The Mathematics of Finance

10.1 Simple interest
10.2 Compound interest
10.3 Credit cards and consumer loans
10.4 Stocks, bonds, and mutual funds
10.5 Home ownership

11. Combinatorics and Probability

11.1 The counting principle
11.2 Permutations and combinations
11.3 Probability and odds
11.4 Addition and complement rules
11.5 Conditional probability
11.6 Expectation

12. Statistics

12.1 Measures of central tendency
12.2 Measures of dispersion
12.3 Measures of relative position
12.4 Normal distributions
12.5 Linear regression and correlation

13. Apportionment and Voting

13.1 Introduction to apportionment
13.2 Introduction to voting
13.3 Weighted voting systems