I came across a really interesting thread in the Internet where the author was asking for fun, but serious Maths book recommendations. I saw plenty of excellent books being recommended there and thought I'd start a similar thread over here :)
Some characteristics the books should have
They should be readable and friendly.
They should be dealing with topics that are not commonly taught at the school or undergraduate level.
I don't want books dealing with very commonly taught topics like differential equations, or Calculus by Spivak, which though elegant is not what I'm looking for.
Here are some examples of books I liked to make myself clearer:
Visual Complex Analysis by Tristan Needham - I like this book for the simplicity and the sheer beauty of it all.
Cauchy-Scwhartz Inequalities by Micheal Steele - Mathematical inequalities are not a very advanced topic, yes. But, it's also not taught extensively.the author describes this book as a master class where mathematicians come to fine tune their skills, and that's exactly what it is. I loved it.
Concrete Mathematics by Graham Knuth and Patashnik - Again a very readable book. It doesn't deal with mathematics that is very advanced, but then again it gives a very beautiful and new treatment to it.
- Flatterland _ Ian Stewart A wonderfully readable book.
I hope this gives you a clear idea. If you have any questions regarding what I'm looking for, you could ask in addition to your recommendations. I don't mind books on problem solving and the history of mathematics too.