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Mathematical Excursions - With CD

Mathematical Excursions - With CD - 04 edition

ISBN13: 978-0618386390

Cover of Mathematical Excursions - With CD 04 (ISBN 978-0618386390)
ISBN13: 978-0618386390
ISBN10: 0618386394
Cover type:
Edition/Copyright: 04
Publisher: Houghton Mifflin Harcourt
Published: 2004
International: No

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Mathematical Excursions - With CD - 04 edition

ISBN13: 978-0618386390

Richard N. Aufmann and Joanne S. Lockwood

ISBN13: 978-0618386390
ISBN10: 0618386394
Cover type:
Edition/Copyright: 04
Publisher: Houghton Mifflin Harcourt

Published: 2004
International: No
Summary

A new text for the liberal arts math course by a seasoned author team, Mathematical Excursions, is uniquely designed to help students see math at work in the contemporary world. Using the proven Aufmann Interactive Method, students learn to master problem-solving in meaningful contexts. In addition, multi-part Excursion exercises emphasize collaborative learning. The text's extensive topical coverage offers instructors flexibility in designing a course that meets their students' needs and curriculum requirements.

  • The Excursions activity and corresponding Excursion Exercises, denoted by an icon, conclude each section, providing opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills. These activities are also ideal for projects or extra credit assignments. The Excursions are designed to reinforce the material that has just been covered in the section in a fun and engaging manner that will enhance a student's journey and discovery of mathematics.
  • The proven 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 method begins with a worked-out example with a solution in numerical and verbal formats to address different learning styles. The matched problem, called Check Your Progress, is left for the student to try. Each problem includes a reference to a fully worked out solution in an appendix to which the student can refer for immediate feedback, concept reinforcement, identification of problem areas, and prevention of frustration.
  • Each Chapter Opener begins with a short introduction to a real data application, which is then highlighted again in one Excursions activity and in the corresponding Excursion Exercises at the end of a section. This specific Excursion will be denoted by an icon. A section-by-section table of contents is accompanied by a brief summary of the topics that will be covered in the chapter.

Author Bio

Aufmann, Richard N. : Palomar College


Richard Aufmann is Professor of Mathematics at Palomar College in California. He is the lead author of two best-selling developmental math series, a best-selling college algebra and trigonometry series, as well as several derivative math texts. The Aufmann name is highly recognized and respected among college mathematics faculty.

Lockwood, Joanne S. : Plymouth State College

Joanne Lockwood is Assistant Professor of Mathematics at Plymouth State College in Plymouth, New Hampshire. She is co-author with Aufmann and Vernon Barker on the hardback developmental series, Business Mathematics, Algebra with Trigonometry for College Students, and numerous software ancillaries that accompany Aufmann titles. She is also co-authoring Mathematical Excursions with Aufmann.

Table of Contents

1. Problem Solving

Section 1.1 Inductive and Deductive Reasoning
Excursion: The Game of Sprouts by John H. Conway
Section 1.2 Problem Solving with Patterns
Excursion: Polygonal Numbers
Section 1.3 Problem-Solving Strategies
Excursion: Routes on a Probability Demonstrator

2. Sets

Section 2.1 Basic Properties of Sets
Excursion: Fuzzy Sets
Section 2.2 Subsets
Excursion: Subsets and Complements of Fuzzy Sets
Section 2.3 Set Operations
Excursion: Union and Intersection of Fuzzy Sets
Section 2.4 Applications of Sets
Excursion: Voting Systems
Section 2.5 Infinite Sets
Excursion: Transfinite Arithmetic

3. Logic

Section 3.1 Logic Statements and Quantifiers
Excursion: Switching Networks
Section 3.2 Truth Tables and Applications
Excursion: Switching Networks--Part II
Section 3.3 The Conditional and the Biconditional
Excursion: Logic Gates
Section 3.4 The Conditional and Related Statements
Excursion: Sheffer's Stroke and the NAND Gate
Section 3.5 Arguments
Excursion: Fallacies
Section 3.6 Euler Diagrams
Excursion: Use Logic to Solve Puzzles

4. Numeration Systems and Topics from Number Theory

Section 4.1 Early Numeration Systems
Excursion: A Rosetta Tablet for the Traditional Chinese Numeration System
Section 4.2 Place-Value Systems
Excursion: Subtraction via the Nines Complement and the End-Around Carry
Section 4.3 Different Base Systems
Excursion: Information Retrieval via a Binary Search
Section 4.4 Arithmetic in Different Bases
Excursion: Subtraction in Base Two via the Ones Complement and the End-Around Carry
Section 4.5 Prime Numbers and Selected Topics from Number Theory
Excursion: The Distribution of the Primes
Section 4.6 Additional Topics from Number Theory
Excursion: A Sum of the Divisors Formula

5. Applications of Equations

Section 5.1 First-Degree Equations
Excursion: Body Mass Index
Section 5.2 Rate, Ratio, and Proportion
Excursion: Earned Run Average
Section 5.3 Percent
Excursion: Federal Income Tax
Section 5.4 Second-Degree Equations
Excursion: The Sum and Product of the Solutions of Quadratic Equations

6. Applications of Functions

Section 6.1 Rectangular Coordinates and Functions
Excursion: Dilations of a Geometric Figure
Section 6.2 Properties of Linear Functions
Excursion: Negative Velocity
Section 6.3 Finding Linear Models
Excursion: A Linear Business Model
Section 6.4 Quadratic Functions
Excursion: Reflective Properties of a Parabola
Section 6.5 Exponential Functions and Their Applications
Excursion: Chess and Exponential Functions
Section 6.6 Logarithmic Functions and Their Applications
Excursion: Benford's Law

7. Mathematical Systems

Section 7.1 Modular Arithmetic
Excursion: Computing the Day of the Week
Section 7.2 Applications of Modular Arithmetic
Excursion: Public Key Cryptography
Section 7.3 Introduction to Group Theory
Excursion: Wallpaper Groups

8. Geometry

Section 8.1 Basic Concepts of Euclidean Geometry
Excursion: Preparing a Circle Graph
Section 8.2 Perimeter and Area of Plane Figures
Excursion: Slicing Polygons into Triangles
Section 8.3 Similar Triangles
Excursion: Topology
Section 8.4 Volume and Surface Area
Excursion: Water Displacement
Section 8.5 Non-Euclidean Geometry
Excursion: Find Geodesics
Section 8.6 Fractals
Excursion: The Heighway Dragon Fractal

9. The Mathematics of Graphs

Section 9.1 Traveling Roads and Visiting Cities
Excursion: Pen-Tracing Puzzles
Section 9.2 Efficient Routes
Excursion: Extending the Greedy Algorithm
Section 9.3 Planarity and Euler's Formula
Excursion: The Five Regular Convex Polyhedra
Section 9.4 Map Coloring and Graphs
Excursion: Modeling Traffic Lights with Graphs

10. The Mathematics of Finance

Section 10.1 Simple Interest
Excursion: Treasury Bills
Section 10.2 Compound Interest
Excursion: Consumer Price Index
Section 10.3 Consumer Loans
Excursion: Leasing versus Buying a Car
Section 10.4 Home Ownership
Excursion: Home Ownership Issues

11. Combinatorics and Probability

Section 11.1 The Counting Principle
Excursion: Decision Trees
Section 11.2 Permutations and Combinations
Excursion: Choosing Numbers in Keno
Section 11.3 Probability and Odds
Excursion: The Value of Pi by Simulation
Section 11.4 Addition and Complement Rules
Excursion: Keno Revisited
Section 11.5 Conditional Probability
Excursion: Sharing Birthdays
Section 11.6 Expectation
Excursion: Chuck-a-luck

12. Statistics

Section 12.1 Measures of Central Tendency
Excursion: Linear Interpolation and Animation
Section 12.2 Measures of Dispersion
Excursion: A Geometric View of Variance and Standard Deviation
Section 12.3 Measures of Relative Position
Excursion: Stem-and-Leaf Diagrams
Section 12.4 Normal Distributions
Excursion: Cut-Off Scores
Section 12.5 Linear Regression and Correlation
Excursion: An Application of Linear Regression

13. Apportionment and Voting

Section 13.1 Introduction to Apportionment
Excursion: Apportioning the 1790 House of Representatives
Section 13.2 Introduction to Voting
Excursion: Variations of the Borda Count Method
Section 13.3 Weighted Voting Systems
Excursion: Blocking Coalitions and the Banzhaf Power Index

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