Calculus: A Liberal Art
Calculus: A Liberal Art by W.M. Priestley, published by Springer New York in May 1998, is a comprehensive exploration of calculus designed to engage readers in the nature and development of mathematics. This second edition spans 404 pages and is presented in English. The book addresses the concept of mathematical maturity and emphasizes the importance of speculation and inference in learning mathematics, inviting readers to approach the subject with curiosity and openness.
In this edition, readers will find a gentle introduction to calculus that encourages them to engage with the material through exercises that promote guessing and exploration. The early chapters are structured to foster an investigative spirit, allowing readers to speculate on mathematical truths without the pressure of needing to guess correctly. The content focuses on mathematical analysis and algebra, providing a unique perspective on calculus that highlights the interplay between learning and the invention of mathematics.
Official synopsis Publisher
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.
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