Mathematical Ideas, 11th Edition

One of the biggest issues college math instructors face is capturing and keeping student interest. Over the years, John Hornsby has refined a creative solution--bringing the best of Hollywood into his mathematics classroom. Mathematical Ideas applies this same strategy of engaging students through descriptions of video clips from popular cinema and television to the textbook. Alongside fresh data and tools, this Eleventh Edition uses up-to-the-minute images as well as old favorites of math being done in Hollywood. In addition, examples are clarified with additional annotations, the margin notes have been freshened, and Chapter 14: Personal Financial Management has been updated to meet the needs of today's students. With great care and effort, Vern Heeren and John Hornsby have crafted this new edition to serve the needs of today's students and instructors.

1.1       Solving Problems by Inductive Reasoning

1.2       An Application of Inductive Reasoning: Number Patterns

1.3       Strategies for Problem Solving

1.4       Calculating, Estimating, and Reading Graphs

Extension: Using Writing to Learn About Mathematics

Collaborative Investigation: Discovering Patterns in Pascal’s Triangle

Chapter 1 Test

2.1       Symbols and Terminology

2.2       Venn Diagrams and Subsets

2.3       Set Operations and Cartesian Products

2.4       Surveys and Cardinal Numbers

2.5       Infinite Sets and Their Cardinalities

Collaborative Investigation: Surveying the Members of your Class

Chapter 2 Test

3.1       Statements and Quantifiers

3.2       Truth Tables and Equivalent Statements

3.3       The Conditional and Circuits

3.4       More on the Conditional

3.5       Analyzing Arguments with Euler Diagrams

Extension: Logic Problems and Sodoku

3.6       Analyzing Arguments with Truth Tables

Collaborative Investigation: Logic Problems and Sodoku Revisited

Chapter 3 Test

4.1       Historical Numeration Systems

4.2       Arithmetic in the Hindu-Arabic System

4.3       Conversion between Number Bases

4.4       Clock Arithmetic and Modular Systems

4.5       Properties of Mathematical Systems

4.6       Groups

Collaborative Investigation: A Perpetual Calendar Algorithm

Chapter 4 Test

5.1       Prime and Composite Numbers

5.2       Selected Topics from Number Theory

5.3       Greatest Common Factor and Least Common Multiple

Extension: Modern Cryptography

5.4       The Fibonacci Sequence and the Golden Ratio

Extension: Magic Squares

Collaborative Investigation: Investigating an Interesting Property of Number Squares

Chapter 5 Test

6.1       Real Numbers, Order, and Absolute Value

6.2       Operations, Properties, and Applications of Real Numbers

6.3       Rational Numbers and Decimal Representation

6.4       Irrational Numbers and Decimal Representation

6.5       Applications of Decimals and Percents      

Extension: Complex Numbers

Collaborative Investigation: Budgeting to Buy a Car

Chapter 6 Test

7.1       Linear Equations

7.2       Applications of Linear Equations

7.3       Ratio, Proportion, and Variation

7.4       Linear Inequalities

7.5       Properties of Exponents and Scientific Notation

7.6       Polynomials and Factoring

7.7       Quadratic Equations and Applications

Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Race-walkers?

Chapter 7 Test

8.1       The Rectangular Coordinate System and Circles

8.2       Lines and Their Slopes

8.3       Equations of Lines and Linear Models

8.4       An Introduction to Functions: Linear Functions, Applications, and Models

8.5       Quadratic Functions, Applications, and Models

8.6       Exponential and Logarithmic Functions, Applications, and Models

8.7       Systems of Equations and Applications

Extension: Using Matrix Row Operations to Solve Systems

8.8       Linear Inequalities, Systems, and Linear Programming

Collaborative Investigation: Living with AIDS

Chapter 8 Test

9.1       Points, Lines, Planes, and Angles

9.2       Curves, Polygons, and Circles

Extension: Geometric Constructions

9.3       Perimeter, Area, and Circumference

9.4       The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem

9.5       Space Figures, Volume, and Surface Area

9.6       Transformational Geometry

9.7       Non-Euclidean Geometry, Topology, and Networks

9.8       Chaos and Fractal Geometry

Collaborative Investigation: Generalizing the Angle Sum Concept

Chapter 9 Test

10.1     Angles and Their Measures

10.2     Trigonometric Functions of Angles

10.3     Trigonometric Identities

10.4     Right Triangles and Function Values

10.5     Applications of Right Triangles

10.6     The Laws of Sines and Cosines: Area Formulas

Collaborative Investigation: Making a Point about Trigonometric Function Values

Chapter 10 Test

11.1     Counting by Systematic Listing

11.2     Using the Fundamental Counting Principle

11.3     Using Permutations and Combinations

11.4     Using Pascal’s Triangle

11.5     Counting Problems Involving “Not” and “Or”

Collaborative Investigation: Solving a Traveling Salesman Problem

Chapter 11 Test

12.1     Basic Concepts

12.2     Events Involving “Not” and “Or”

12.3     Conditional Probability; Events Involving “And”

12.4     Binomial Probability

12.5     Expected Value

Extension: Estimating Probabilities by Simulation

Collaborative Investigation: Finding Empirical Values of π

Chapter 12 Test

13.1     Frequency Distributions and Graphs

13.2     Measures of Central Tendency

13.3     Measures of Dispersion

13.4     Measures of Position

13.5     The Normal Distribution

Extension: How to Lie with Statistics

13.6     Regression and Correlation

Collaborative Investigation: Combining Sets of Data

Chapter 13 Test

14.1     The Time Value of Money

Extension: Annuities

14.2     Installment Buying

14.3     Truth in Lending

14.4     The Costs and Advantages of Home Ownership

14.5     Investing

Collaborative Investigation: To Buy or to Rent?

Chapter 14 Test