by David B. Johnson and Thomas A. Mowry
List price: $250.00
Well known for its clear writing and unique variety of topics, MATHEMATICS: A PRACTICAL ODYSSEY demonstrates how mathematics is usable and relevant to students. Throughout the book, the authors emphasize problem solving skills, practical applications, and the history of mathematics. Students encounter topics that will be useful in their daily lives, such as calculating interest and understanding voting systems. They are encouraged to recognize the relevance of mathematics and appreciate its human aspect. To offer flexibility in content, the book contains more information than could be covered in a one-term course. The chapters are independent of each other so instructors can select the ideal topics for their courses.
1. LOGIC.
Deductive vs. Inductive Reasoning.
Symbolic Logic.
Truth Tables.
More on Conditionals.
Analyzing Arguments.
2. SETS AND COUNTING.
Sets and Set Operations.
Applications of Venn Diagrams.
Introduction to Combinatorics.
Permutations and Combinations.
Infinite Sets.
3. PROBABILITY.
History of Probability.
Basic Terms of Probability.
Basic Rules of Probability.
Combinatorics and Probability.
Expected Value.
Conditional Probability.
Independence; Trees in Genetics.
4. STATISTICS.
Population, Sample, and Data.
Measures of Central Tendency.
Measures of Dispersion.
The Normal Distribution.
Polls and Margin of Error.
Linear Regression.
5. FINANCE.
Simple Interest.
Compound Interest.
Annuities.
Amortized Loans.
Annual Percentage Rate on a Graphing Calculator.
Payout Annuities.
6. VOTING AND APPORTIONMENT.
Voting Systems.
Methods of Apportionment.
Flaws of Apportionment.
7. NUMBER SYSTEMS AND NUMBER THEORY.
Place Systems.
Arithmetic in Different Bases.
Primes and Perfect Numbers.
The Fibonacci Sequence and the Golden Ratio.
8. GEOMETRY.
Perimeter and Area.
Volume and Surface Area.
Egyptian Geometry.
The Greeks.
Right Triangle Trigonometry.
Conic Sections and Analytic Geometry.
Non-Euclidean Geometry.
Fractal Geometry.
The Perimeter and Area of a Fractal.
9. GRAPH THEORY.
A Walk Through Konigsberg.
Graphs and Euler Paths.
Hamilton Circuits.
Networks.
Scheduling.
10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Review of Exponentials and Logarithms.
Review of Properties of Logarithms.
Exponential Growth.
Exponential Decay.
Logarithmic Scales.
11. MATRICES AND MARKOV CHAINS.
Review of Matrices.
Introduction to Markov Chains.
Systems of Linear Equations.
Long-Range Predictions.
Solving Larger Systems of Equations.
More on Markov Chains.
12. LINEAR PROGRAMMING.
Review of Linear Inequalities.
The Geometry of Linear Programming.
Appendices:
Using a Scientific Calculator.
Using a Graphing Calculator.
Graphing with a Graphing Calculator.
Finding Points of Intersection with a Graphing Calculator.
Dimensional Analysis.
Body Table for the Standard Normal Distribution.
Answers to Selected Exercises.
David B. Johnson and Thomas A. Mowry
ISBN13: 978-0495012733Well known for its clear writing and unique variety of topics, MATHEMATICS: A PRACTICAL ODYSSEY demonstrates how mathematics is usable and relevant to students. Throughout the book, the authors emphasize problem solving skills, practical applications, and the history of mathematics. Students encounter topics that will be useful in their daily lives, such as calculating interest and understanding voting systems. They are encouraged to recognize the relevance of mathematics and appreciate its human aspect. To offer flexibility in content, the book contains more information than could be covered in a one-term course. The chapters are independent of each other so instructors can select the ideal topics for their courses.
Table of Contents
1. LOGIC.
Deductive vs. Inductive Reasoning.
Symbolic Logic.
Truth Tables.
More on Conditionals.
Analyzing Arguments.
2. SETS AND COUNTING.
Sets and Set Operations.
Applications of Venn Diagrams.
Introduction to Combinatorics.
Permutations and Combinations.
Infinite Sets.
3. PROBABILITY.
History of Probability.
Basic Terms of Probability.
Basic Rules of Probability.
Combinatorics and Probability.
Expected Value.
Conditional Probability.
Independence; Trees in Genetics.
4. STATISTICS.
Population, Sample, and Data.
Measures of Central Tendency.
Measures of Dispersion.
The Normal Distribution.
Polls and Margin of Error.
Linear Regression.
5. FINANCE.
Simple Interest.
Compound Interest.
Annuities.
Amortized Loans.
Annual Percentage Rate on a Graphing Calculator.
Payout Annuities.
6. VOTING AND APPORTIONMENT.
Voting Systems.
Methods of Apportionment.
Flaws of Apportionment.
7. NUMBER SYSTEMS AND NUMBER THEORY.
Place Systems.
Arithmetic in Different Bases.
Primes and Perfect Numbers.
The Fibonacci Sequence and the Golden Ratio.
8. GEOMETRY.
Perimeter and Area.
Volume and Surface Area.
Egyptian Geometry.
The Greeks.
Right Triangle Trigonometry.
Conic Sections and Analytic Geometry.
Non-Euclidean Geometry.
Fractal Geometry.
The Perimeter and Area of a Fractal.
9. GRAPH THEORY.
A Walk Through Konigsberg.
Graphs and Euler Paths.
Hamilton Circuits.
Networks.
Scheduling.
10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Review of Exponentials and Logarithms.
Review of Properties of Logarithms.
Exponential Growth.
Exponential Decay.
Logarithmic Scales.
11. MATRICES AND MARKOV CHAINS.
Review of Matrices.
Introduction to Markov Chains.
Systems of Linear Equations.
Long-Range Predictions.
Solving Larger Systems of Equations.
More on Markov Chains.
12. LINEAR PROGRAMMING.
Review of Linear Inequalities.
The Geometry of Linear Programming.
Appendices:
Using a Scientific Calculator.
Using a Graphing Calculator.
Graphing with a Graphing Calculator.
Finding Points of Intersection with a Graphing Calculator.
Dimensional Analysis.
Body Table for the Standard Normal Distribution.
Answers to Selected Exercises.