Mathematics

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MATHEMATICS: A PRACTICAL ODYSSEY, 7E demonstrates mathematics' usefulness and relevance to students' daily lives through topics such as calculating interest and understanding voting systems. Well known for its clear writing and unique variety of topics, the text emphasizes problem-solving skills, practical applications, and the history of mathematics, and unveils the relevance of mathematics and its human aspect to students. To offer flexibility in content, the book contains more information than might be covered in a one-term course. The chapters are independent of each other so instructors can select the ideal topics for their courses.

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Preface. 1. LOGIC. Deductive Logic versus Inductive Logic. Symbolic Logic. Truth Tables. More on Conditionals. Analyzing Arguments. Chapter 1 Review. 2. SETS AND COUNTING. Sets and Set Operations. Applications of Venn Diagrams. Introduction to Combinatorics. Permutations and Combinations. Infinite Sets. Chapter 2 Review. 3. PROBABILITY. History of Probability. Basic Terms of Probability. Basic Rules of Probability. Combinatorics and Probability. Expected Value. Conditional Probability. Independence; Trees in Genetics. Chapter 3 Review. 4. STATISTICS. Population, Sample, and Data. Measures of Central Tendency. Measures of Dispersion. The Normal Distribution. Polls and Margin of Error. Linear Regression. Chapter 4 Review. 5. FINANCE. Simple Interest. Compound Interest. Annuities. Amortized Loans. Annual Percentage Rate with a TI's TVM Application. Payout Annuities. Chapter 5 Review. 6. VOTING AND APPORTIONMENT. Voting Systems. Methods of Apportionment. Flaws of Apportionment. Chapter 6 Review. 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. Chapter 7 Review. 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. Chapter 8 Review. 9. GRAPH THEORY. A Walk through Koenigsberg. Graphs and Euler Trails. Hamilton Circuits. Networks. Scheduling. Chapter 9 Review. 10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Review of Exponentials and Logarithms. Review of Properties of Logarithms. Exponential Growth. Exponential Decay. Logarithmic Scales. Chapter 10 Review. 11. MATRICES AND MARKOV CHAINS. Review of Matrices. Introduction to Markov Chains. Systems of Linear Equations. Long-Range Predictions with Markov Chains. Solving Larger Systems of Equations. More on Markov Chains. Chapter 11 Review. 12. LINEAR PROGRAMMING. Review of Linear Inequalities. The Geometry of Linear Programming. Chapter 12 Review. 12. LINEAR PROGRAMMING (ONLINE). Introduction to the Simplex Method. The Simplex Method: Complete Problems. Chapter 12 Review. 13. THE CONCEPTS AND HISTORY OF CALCULUS (ONLINE). Review of Rations, 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. Chapter 13 Review. APPENDIXES. Appendix A. Appendix B Using a Graphing Calculator. Appendix C Graphing with a Graphing Calculator. Appendix D Finding Points of Intersection with a Graphing Calculator. Appendix E Dimensional Analysis. Appendix F Body Table for the Standard Normal Distribution. Index.

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