Introduction to Advanced Mathematics (2nd Edition)

Rating:
Summary: Initial Impressions
Review: I will teach a course this summer using this text - which I didn't choose. These are intial impressions and I will follow up in August.

The binding is poor. My copy, which was used by other instructors the past two semesters is falling apart.

This is a book with a lot of exercises and very little excess verbiage. There is little in the way of motivation or enlightenment. Of course, the instructor may want to stamp his personality on the course.

I think the first half of the book needs a section on permutations and combinations. In general counting is slighted.

I also question the choice of optional topics in the second half of the book. I would like to see the construction of Q from the integers and some material on algebraic completenes of C. The choice of rings and integral domains over groups as an introduction to abstract algebra is puzzling.

Finally, at my university, half the students taking the transitions course are future secondary teachers. I doubt that this is unusual. This book seems to ignore this audience completely.