Synopses & Reviews
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.
Synopsis
Discover the many ways mathematics is relevant to your life with MATHEMATICS: A PRACTICAL ODYSSEY and its accompanying online resources. You'll 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 human aspect. Included with your purchase is access to the CengageNOW, an online tutorial that allows you to work with real math notation in real time, with unlimited practice problems, instant analysis and feedback, and streaming video to illustrate key concepts and Personal Tutor with SMARTHINKING a live, online mathematics tutor.
Synopsis
MATHEMATICS: A PRACTICAL ODYSSEY is a market leader, well known for its clear writing and unique variety of topics, including its accessible chapters on logarithms and exponential functions, calculus and Markov chains. Johnson and Mowry's text emphasizes the practical applications and the history of mathematics. It illustrates to students how mathematics is relevant to their education, human history, and culture. The authors effectively demonstrate how learning algebraic concepts allows students to understand more about how logic, probability, statistics, finance, geometry, matrices, logarithms, calculus, and other topics are vital to everyday life.
About the Author
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.
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. AVAILABLE ON THE WEB: LINEAR PROGRAMMING. Introduction to the Simplex Method. The Simplex Method: Complete Problems. THE CONCEPTS AND HISTORY OF CALCULUS. The 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.