Foundations of Higher Mathematics

Rating:
Summary: Great introduction to mathematics
Review: I bought this book for a course in classical algebra. I found the book well explained and well done. It contains a lot of exercise and example of differents difficulty. It covers logic, set, relation, induction, function, combinatorial proofs, countable sets and uncountable sets, groups and some calculus. The book has a lot of subject in it and it make it very flexible. If you want to ontroduce yourself to mathematics, I would recommend this book if you want to spend some money.

Rating:
Summary: A great read to see what lays ahead
Review: I read and worked the problems in this book during my break as I transferred from a community college to a 4-year university, and found it very helpful in introducing me to all the fancy terminology, notation and basic proof writing that I was intimidated by. I found the problems to be hard enough to be challenging, but also neither impossibly hard nor hinging on a silly trick.

If you are a eager HS student, or a curious college student, get this book and work the problems.

Rating:
Summary: An excellent introduction to mathematical logic!
Review: This book provides an excellent introduction to mathematical logic, set theory, graph theory, number theory, and more -- everything which is "neat" in higher math.

I would strongly recommend this book before any proof-based math class. The authors explain methods of proofs very well, and give some principles universally important in mathematics -- Zermelo's thm., Dirichlet's prin., and such.

The exposition in this book is great. If this is your first exposure to, for instance, the proofs by induction, this probably provides an excellent description of what's going on and how it works, why it works.

The book is slim (at least, the 1992 ed.) and not inexpensive. However, the authors' conversational tone makes it very approachable; at the same time, they are mathematically rigorous and very thorough.