Read more
reason for delaying its study has to do with the question of mathematical maturity. * No use is made here of trigonometric, logarithmic, or expo nential functions except in occasional optional material indicating how such functions can be handled. A perceptive remark made by George P6lya suggests how we can simultaneously learn mathematics and learn "about" mathematics-i.e., about the nature of mathematics and how it is developed: If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference. The reader will find plenty of opportunity here for guessing. The early chapters go at a gentle pace and invite the reader to enter into the spirit of the investigation. Exercises asking the reader to "make a guess" should be taken in this spirit-as simply an invitation to speculate about what is the likely truth in a given situation without feeling any pressure to guess "correctly". Readers will soon realize that a matter about which they are asked to guess will likely be a topic of serious discussion later on.
List of contents
1. Tokens from the Gods Variables, Functions, and Limits.- 2. Rational Thoughts The Rise of Mathematics and the Liberal Arts.- 3. To Measure Is to Know More Pre-calculus Mathematics.- 4. Sherlock Holmes Meets Pierre de Fermat Derivatives.- 5. Optimistic Steps Techniques of Optimization.- 6. Chains and Change Instantaneous Rates.- 7. The Integrity of Ancient and Modern Mathematics Integrals and Antiderivatives.- 8. Romance in Reason Seventeenth-century Mathematics.- Appendices.- Answers to Selected Problems.
