This book is a result of a long-term project which originated in courses we taught
to undergraduate students who specialize in mathematics. These students had ı-"
calculus before, but there did not seem to be a suitable comprehensive textbook for
a follow-up course in analysis.
We wanted to write such a textbook based on our courses, but that was not
the only goal. Teaching bright students is about introducing them to mathematics.
Therefore, we wanted to write a book which the students may want to keep after the
course is over, and which could serve them as a bridge to higher mathematics. Such
a book would necessarily exceed the scope of their courses.