Introductory Concepts for Abstract Mathematics

Rating:
Summary: Worth the price!
Review: I have used this text for a Foundations in Mathematics course, and have subsequently found this book among the best that I have read. It would also be good for self-study, as most of the answers are included in the back--which is essential for a good self-study book at this level of Mathematics. Other books I would recommend are: Morash's "Bridge to Abstract mathematics"; "200% of nothing", "An introduction to mathematical reasoning";and "A transition to higher mathematics". Books I would recommend you don't use for self-study are: How to prove it: a structured approach, and any book which doesn't include solutions. (Once one is comfortable with writing and reading proofs, and with higher math in general, then solutions are not always needed.) This book will introduce the reader to many of the topics that one will find in Abstract Algebra and Real analysis: upper and lower bounds, least upper bound, real number system, epsilon-delta proofs, a little number theory, the uncountability of the reals, trans-finite cardinal arithmetic; also has a nice section on the controversial axiom of choice . On the whole, I would recommed this book.

Rating:
Summary: Worth the price!
Review: I have used this text for a Foundations in Mathematics course, and have subsequently found this book among the best that I have read. It would also be good for self-study, as most of the answers are included in the back--which is essential for a good self-study book at this level of Mathematics. Other books I would recommend are: Morash's "Bridge to Abstract mathematics"; "200% of nothing", "An introduction to mathematical reasoning";and "A transition to higher mathematics". Books I would recommend you don't use for self-study are: How to prove it: a structured approach, and any book which doesn't include solutions. (Once one is comfortable with writing and reading proofs, and with higher math in general, then solutions are not always needed.) This book will introduce the reader to many of the topics that one will find in Abstract Algebra and Real analysis: upper and lower bounds, least upper bound, real number system, epsilon-delta proofs, a little number theory, the uncountability of the reals, trans-finite cardinal arithmetic; also has a nice section on the controversial axiom of choice . On the whole, I would recommed this book.