Doing Mathematics: An Introduction to Proofs and Problem-Solving

by Steven Galovich

Book Overview

Mathematics majors learn the underlying concepts and how to apply them to problem solving and proofs in this introduction to the fundamentals in mathematical reasoning and the basic properties of the... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0030928001
• ISBN13: 9780030928000
• Release Date: January 1993
• Publisher: Brooks Cole
• Length: 195 Pages
• Weight: 0.70 lbs.
• Dimensions: 0.5" x 6.5" x 9.3"

Customer Reviews

Outline only...

The author gives only Outline of a wide range of topics. No topic is discussed in detail. Not so useful as expected from the title of the book. Although the author has tried his best to pour his all knowledge in this small book. You can read it in one sitting. Overall book is OK SANJAY KUMAR MANAV NEW DELHI INDIA

Really like it

I'm currently using this book for a class, and I really enjoy it. It's interesting, it presents the material in an understandable way, and the author isn't arrogant. Previously, I had purchased two books at a nearby university bookstore with the idea of studying the material on my own. Mathematical Thinking and Writing: A Transition to Higher Mathematics has a LOT of information in it, but it's a bit dry. It's a good reference. Sets, Functions, and Logic: An Introduction to Abstract Mathematics, Third Edition (Chapman Hall/Crc Mathematics Series) is too brief on topics I feel need more explanation. After a very interesting and chatty introduction, the author presents limited explanations, and sometimes repeats, "Read it again!" He also includes no hints or suggestions as to problem solutions. If you check the back of the book for such hints, you'll find a message to this effect: This is where you would normally find answers to selected problems, but you're in higher math now, so you need to figure it out for yourself. Steven Galovich's book makes learning this material much easier.

A treasure

This is an outstanding book that teaches mathematics from the ground up, starting with elementary logic and working its way up gradually through the techniques and notation needed to formulate and rigorously prove theorems. Along the way, it touches on the fundamentals of set theory, number theory, calculus, analysis and linear algebra. There are no prerequisites, making the book suitable for everyone from precocious high schoolers to graduate students. I had the pleasure of using the earlier edition of this book ("Introduction to Mathematical Structures," 1989) for the logic and proofs course required of math majors at Carleton College. After this edition came out, I became the grader for the course. I found the problems in the book to be very well-crafted, challenging yet approachable for the students. Nearly all of them felt both necessary and sufficient. The book is much-improved in its second edition, with a generous number of examples and exercises. I would recommend it to anyone pursuing or even contemplating a degree in mathematics, science or philosophy.

Swell Book

This is a swell introduction to analysis. Plenty of good examples, with a well-ordered approach to the material. I particularly appreciated the section on the mindsets and assumptions that affect how we do mathematics. It's really helpful in seeing that mathematics is creative and intuitive, and not as bluntly algorithmic as so many high school classes seem. A quality read.