Mathematics
A Practical Odyssey
8th Edition
Will be published approx. on 1. January 2015
Book
Hardback
1024 pages
978-1-305-10417-4 (ISBN)
Description
Students discover the many ways in which mathematics is relevant to their lives with MATHEMATICS: A PRACTICAL ODYSSEY, 8th Edition and its accompanying online resources. They master problem-solving skills in such areas as calculating interest and understanding voting systems, and come to recognize the relevance of mathematics and to appreciate its creative human aspect.
More details
Edition
8th edition
Language
English
Place of publication
CA
United States
Publishing group
Cengage Learning, Inc
Target group
College/higher education
Dimensions
Height: 35 mm
Width: 218 mm
Thickness: 279 mm
Weight
2060 gr
ISBN-13
978-1-305-10417-4 (9781305104174)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
David Johnson earned a Bachelor's degree in Mathematics and a Bachelor's degree in Psychology (with an emphasis on Learning Theory), from the University of California at Santa Cruz, and a Master's degree in Mathematics from the University of California at Berkeley. After several years working as an academic counselor at Berkeley, he became a Professor of Mathematics at Diablo Valley College (DVC). He has taught DVC's liberal arts math course regularly for about 25 years, using Mathematics a Practical Odyssey. Other favorite courses include Intermediate Algebra, all three semesters of Calculus, and Differential Equations. Thomas Mowry earned a Bachelor's degree and a Master's degree in Mathematics from Michigan Technological University, in Houghton, Michigan. He began his college teaching career at City College of San Francisco and then went on to teach at San Francisco State University, Golden Gate University, and Cogswell College. He has been a professor of mathematics at Diablo Valley College, Pleasant Hill, California since 1985, where he has taught the complete gamut of courses from arithmetic to differential equations. He has served as department chair at DVC for the last seven years. Along with co-author, David Johnson, he created a college-level, transferable mathematics course (at DVC ) designed for students in the liberal arts. As no appropriate textbooks were available for this course, he and David created Mathematics: A Practical Odyssey, which was first published in 1992.
Content
1. LOGIC.
Deductive versus Inductive Reasoning. Symbolic Logic. Truth Tables. More on Conditionals. Analyzing Arguments. Deductive Proof of Validity.
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; Medical Tests and 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 with a TI-Calculator's TVM Application. Payout Annuities.
6. VOTING AND APPORTIONMENT.
Voting Systems. Methods of Apportionment. Flaws of Apportionment.
7. NUMBER SYSTEMS AND NUMBER THEORY.
Place Systems. Addition and Subtraction in Different Bases. Multiplication and Division in Different Bases. Prime Numbers and Perfect Numbers. Fibonacci Numbers and the Golden Ratio.
8. GEOMETRY.
Perimeter and Area. Volume and Surface Area. Egyptian Geometry. The Greeks. Right Triangle Trigonometry. Linear Perspective. Conic Sections and Analytic Geometry. Non-Euclidean Geometry. Fractal Geometry. The Perimeter and Area of a Fractal.
9. GRAPH THEORY.
A Walk through Koeningsberg. Graphs and Euler Trails. 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. MARKOV CHAINS.
Review of Matrices. Review of Systems of Linear Equations. Markov Chains and Tree Diagrams. Markov Chains and Matrices. Long-Range Predictions with Markov Chains. Solving Larger Systems of Equations. More on Markov Chains.
12. LINEAR PROGRAMMING.
Review of Linear Inequalities. The Geometry of Linear Programming. Introduction to the Simplex Model.[online section only] The Simplex Method: Complete Problems. [online section only]
13. THE CONCEPTS AND HISTORY OF CALCULUS. [online chapter only]
Review of Ratios, Parabolas, and Functions. The Antecedents of Calculus. Four Problems. Newton and Tangent Lines. Newton on Falling Objects and the Derivative. The Trajectory of a Cannonball. Newton and Areas. Conclusion.
APPENDICES.
A. Using a Scientific Calculator.
B. Using a Graphing Calculator.
C. Graphing with a Graphing Calculator.
D. Finding Points of Intersection with a Graphing Calculator.
E. Dimensional Analysis.
F. Body Table for the Standard Normal Distribution.
G. Answers.
Deductive versus Inductive Reasoning. Symbolic Logic. Truth Tables. More on Conditionals. Analyzing Arguments. Deductive Proof of Validity.
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; Medical Tests and 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 with a TI-Calculator's TVM Application. Payout Annuities.
6. VOTING AND APPORTIONMENT.
Voting Systems. Methods of Apportionment. Flaws of Apportionment.
7. NUMBER SYSTEMS AND NUMBER THEORY.
Place Systems. Addition and Subtraction in Different Bases. Multiplication and Division in Different Bases. Prime Numbers and Perfect Numbers. Fibonacci Numbers and the Golden Ratio.
8. GEOMETRY.
Perimeter and Area. Volume and Surface Area. Egyptian Geometry. The Greeks. Right Triangle Trigonometry. Linear Perspective. Conic Sections and Analytic Geometry. Non-Euclidean Geometry. Fractal Geometry. The Perimeter and Area of a Fractal.
9. GRAPH THEORY.
A Walk through Koeningsberg. Graphs and Euler Trails. 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. MARKOV CHAINS.
Review of Matrices. Review of Systems of Linear Equations. Markov Chains and Tree Diagrams. Markov Chains and Matrices. Long-Range Predictions with Markov Chains. Solving Larger Systems of Equations. More on Markov Chains.
12. LINEAR PROGRAMMING.
Review of Linear Inequalities. The Geometry of Linear Programming. Introduction to the Simplex Model.[online section only] The Simplex Method: Complete Problems. [online section only]
13. THE CONCEPTS AND HISTORY OF CALCULUS. [online chapter only]
Review of Ratios, Parabolas, and Functions. The Antecedents of Calculus. Four Problems. Newton and Tangent Lines. Newton on Falling Objects and the Derivative. The Trajectory of a Cannonball. Newton and Areas. Conclusion.
APPENDICES.
A. Using a Scientific Calculator.
B. Using a Graphing Calculator.
C. Graphing with a Graphing Calculator.
D. Finding Points of Intersection with a Graphing Calculator.
E. Dimensional Analysis.
F. Body Table for the Standard Normal Distribution.
G. Answers.