Prelude to Mathematics

I bought Prelude to Mathematics when I was 12, it was the first maths book I bought. That was a very long time ago! I thought it was very good, I don't know of another book quite like it. He produced some other good books as well.

Prelude to Mathematics by W.W. Sawyer was written to give students an overview of modern math concepts beyond algebra. Topics include non-euclidian geometry, linear algebra, projective geometry and group theory. Again, for someone with an understanding of algebra. I enjoyed it and think it's in the spirit of what you're looking for. Edit: Introduction to Graph Theory by Trudeau is another that I really liked. Very little was applicable to graphs as programmers think of them. Pure math that is easy to grasp and enjoy.

W. W. Sawyer Mathematician's Delight Prelude to Mathematics What is Calculus About? This is best intro to calculus I ever saw. When I taught introductory calculus, I recommended it to all my students.