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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 Königsberg. 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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Anatole Manniste
reviewed Mathematics: A Practical Odyssey on December 30, 2016
Mathematics
Mathmatics and the Unexpected takes a look at three changes in mathmatics and how these affected how people thought about what could be solved through mathmatics. More a cultural study than a math text book, the examples used show the evolution of mathmatic in application. It is written for someone who has a strong grasp on college level mathmatics (calculus and statistics), but is written for easy consumption, not rigorous proofs.
I really liked this book. As I'm behind on my book goal for the year, I thought a short but intense book might be warrented for once, and this one was really quite facinating. I'll be the first to admit I have a good gradp on the mechanics of math, but I fail to understand the possibilities of thier application, so a book dedicated to following the application of these processes I've been studying was really eye opening. With the added element of historical context, it probided a well rounded evolution of certain ideas and how those ideas affected thier societies.
My favorite chaper is probably the first one (calculous and determinism), though the ideas in the second are really interesting(chaos theory and probability). I'm not sure I followed the third chapter particularly well, as catastrophe theory seems too open ended to really mean anything. It's a near idea, but I don't think I understand how it's supposed to be used, beyond a new way to take notes on a phenomenon.
I though short, it is dense with ideas, as it tries to explain the questions past mathmatians faced and the experiments they used to try to solve them. I recommend this to anyone interested in mathmatics, or someone who wants to know the limitations of these tools they learned about in college.
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Add Mathematics: A Practical Odyssey, Users discover the many ways in which mathematics is relevant to their lives with MATHEMATICS: A PRACTICAL ODYSSEY, 7E and its accompanying online resources. They master problem-solving skills in such areas as calculating interest and understanding voting, Mathematics: A Practical Odyssey to the inventory that you are selling on WonderClubX
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Add Mathematics: A Practical Odyssey, Users discover the many ways in which mathematics is relevant to their lives with MATHEMATICS: A PRACTICAL ODYSSEY, 7E and its accompanying online resources. They master problem-solving skills in such areas as calculating interest and understanding voting, Mathematics: A Practical Odyssey to your collection on WonderClub |
