New mathematics often comes about by probing what is already known. Mathematicians will change the parameters in a familiar calculation or explore the essential ingredients of a classic proof. Almost magically, new ideas emerge from this process. This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics. The focus is on exploring the connections between these functions and topics in number theory and combinatorics. There is also an emphasis throughout the book on how current mathematical software can be used to discover and prove interesting properties of these functions. The book provides a transition between elementary mathematics and more advanced topics, trying to make this transition as smooth as possible. Many topics occur in the book, but they are all part of a bigger picture of mathematics. By delving into a variety of them, the reader will develop this broad view. The large collection of problems is an essential part of the book. The problems vary from routine verifications of facts used in the text to the exploration of open questions.
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1 of 1 people found the following review helpful
5.0 out of 5 stars
A great alternative to the same old traditional stifling undergraduate mathematics courses
December 1, 2012
By D Zeilberger
Format:Paperback|Amazon Verified Purchase
Victor Moll, one of the greatest experimental mathematics researchers of our time, is also a very gifted teacher.
Luckily, he wrote up the lecture notes for his innovative classes in experimental mathematics, so that
undergraduate math (and science!) majors can get a glimpse of mathematics that is so much more fun
than the same old lemma/theorem/proof/corollary drivel that turned off so many talented people away from
mathematics, not because they were not capable of mastering it, but because it was no fun.
Exploring mathematics the way Moll does, by experiment, has the potential to attract to math all these
very talented young minds. For the math prof, it should be a case study, and paradigm, of how
to teach math the fun way!
Luckily, he wrote up the lecture notes for his innovative classes in experimental mathematics, so that
undergraduate math (and science!) majors can get a glimpse of mathematics that is so much more fun
than the same old lemma/theorem/proof/corollary drivel that turned off so many talented people away from
mathematics, not because they were not capable of mastering it, but because it was no fun.
Exploring mathematics the way Moll does, by experiment, has the potential to attract to math all these
very talented young minds. For the math prof, it should be a case study, and paradigm, of how
to teach math the fun way!
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