Mathematical Ideas, 15th edition

1. The Art of Problem Solving

• 1.1 Solving Problems by Inductive Reasoning
• 1.2 An Application of Inductive Reasoning: Number Patterns
• 1.3 Strategies for Problem Solving
• 1.4 Numeracy in Today's World
• Summary
• Test

2. The Basic Concepts of Set Theory

• 2.1 Symbols and Terminology
• 2.2 Venn Diagrams and Subsets
• 2.3 Set Operations
• 2.4 Surveys and Cardinal Numbers
• Summary
• Test

3. Introduction to Logic

• 3.1 Statements and Quantifiers
• 3.2 Truth Tables and Equivalent Statements
• 3.3 The Conditional and Circuits
• 3.4 The Conditional and Related Statements
• 3.5 Analyzing Arguments with Euler Diagrams
• 3.6 Analyzing Arguments with Truth Tables
• Summary
• Test

4. Numeration Systems

• 4.1 Historical Numeration Systems
• 4.2 More Historical Numeration Systems
• 4.3 Arithmetic in the Hindu-Arabic System
• 4.4 Conversion Between Number Bases
• 4.5 Arithmetic in Other Bases
• Summary
• Test

5. Number Theory 

• 5.1 Prime and Composite Numbers
• 5.2 Large Prime Numbers
• 5.3 Selected Topics from Number Theory
• 5.4 Greatest Common Factor and Least Common Multiple 
• 5.5 The Fibonacci Sequence and the Golden Ratio
• 5.6 Magic Squares (online)* 
• Summary
• Test

6. The Real Numbers and Their Representations 

• 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 
• Summary
• Test

7. The Basic Concepts of Algebra 

• 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 
• Summary
• Test

8. Graphs, Functions, and Systems of Equations and Inequalities 

• 8.1 The Rectangular Coordinate Systems and Circles
• 8.2 Lines, Slope, and Average Rate of Change
• 8.3 Equations of Lines 
• 8.4 Linear Functions, Graphs, and Models 
• 8.5 Quadratic Functions, Graphs, and Models 
• 8.6 Exponential and Logarithmic Functions, Graphs, and Models  
• 8.7 Systems of Linear Equations
• 8.8 Applications of Linear Systems
• 8.9 Linear Inequalities, Systems, and Linear Programming 
• Summary
• Test

9.  Geometry 

• 9.1 Points, Lines, Planes, and Angles
• 9.2 Curves, Polygons, Circles, and Geometric Constructions
• 9.3 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem
• 9.4 Perimeter, Area, and Circumference 
• 9.5 Volume and Surface Area
• 9.6 Transformational Geometry
• 9.7 Non-Euclidian Geometry and Topology
• 9.8 Chaos and Fractal Geometry 
• Summary
• Test

10. Counting Methods 

• 10.1 Counting by Systematic Listing
• 10.2 Using the Fundamental Counting Principle
• 10.3 Using Permutations and Combinations 
• 10.4 Using Pascal's Triangle
• 10.5 Counting Problems Involving “Not” and “Or”
• Summary
• Test

11. Probability 

• 11.1 Basic Concepts
• 11.2 Events Involving “Not” and “Or”
• 11.3 Conditional Probability and Events Involving “And” 
• 11.4 Binomial Probability
• 11.5 Expected Value and Simulation
• Summary
• Test

12. Statistics 

• 12.1 Visual Displays of Data
• 12.2 Measures of Central Tendency
• 12.3 Measures of Dispersion
• 12.4 Measures of Position
• 12.5 The Normal Distribution
• Summary
• Test

13. Personal Financial Management 

• 13.1 The Time Value of Money
• 13.2 Consumer Credit
• 13.3 Truth in Lending
• 13.4 The Costs and Advantages of Home Ownership 
• 13.5 Financial Investments
• 13.6 Income Tax Liability
• Summary

14. Graph Theory 

• 14.1 Basic Concepts
• 14.2 Euler Circuits and Route Planning
• 14.3 Hamilton Circuits and Algorithms 
• 14.4 Trees and Minimum Spanning Trees
• Summary
• Test

15. Voting and Apportionment 

• 15.1 The Possibilities of Voting
• 15.2 The Impossibilities of Voting
• 15.3 The Possibilities of Apportionment
• 15.4 The Impossibilities of Apportionment 
• Summary
• Test

Answers to Selected Exercises

Credits

Index of Applications

Index