Books to release our inner Ubermensch with calculus?

Solution 1:

Here are three book recommendations which might get the attribute ''interesting'' in OPs sense.

Each of these books has analysis at the core but also invites the reader to look outside the box. They are sometimes rather challenging but many parts will be accessible and the other parts might invite the reader to do some further research for his own benefit.

• Real Infinite Series by Daniel D. Bonar and Michael J. Khoury

  A first impression of the content can be found in this answer.

The other two books have many subjects in common, are both focused at analysis and number theory, but provide completely different approaches. Both are IMO treasures of knowledge and fun.

• Experimentation in Mathematics - Computational Paths to Discovery by J. Borwein, D. Bailey and R. Girgensohn

  You might have a look at the table of contents or the summary, but this is rather misleading as it does not give you a proper insight about the content. Since there are so many different nice things to discover, I suggest to take this book from somewhere and skim through it in order to get a first impression.

• Euler Through Time - A New look at Old Themes by V.S. Varajarajan

  The intention of this book is not to cover all of Euler's work, but instead focus at important contributions to analysis and (analytic) number theory. The fascinating thing here is, the author does not stick at the past but instead examines his work and its relation to current mathematics.