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Schaum's Outline of Set Theory and Related Topics, by Seymour Lipschutz
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Confusing Textbooks? Missed Lectures? Not Enough Time?
Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
This Schaum's Outline gives you
- Practice problems with full explanations that reinforce knowledge
- Coverage of the most up-to-date developments in your course field
- In-depth review of practices and applications
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!
Schaum's Outlines-Problem Solved.
- Sales Rank: #252630 in Books
- Published on: 1998-07-22
- Original language: English
- Number of items: 1
- Dimensions: 11.00" h x .35" w x 8.00" l, .95 pounds
- Binding: Paperback
- 200 pages
From the Back Cover
Master set theory with Schaum's--the high-performance study guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams!
Students love Schaum's Outlines because they produce results. Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study guides. Get the edge on your classmates. Use Schaum's!
If you don't have a lot of time but want to excel in class, this book helps you: Brush up before tests Find answers fast Study quickly and more effectively Get the big picture without spending hours poring over lengthy textbooks.
Schaum's Outlines give you the information teachers expect you to know in a handy and succinct format--without overwhelming you with unnecessary details. You get a complete overview of the subject. Plus, you get plenty of practice exercises to test your skill. Compatible with any classroom text, Schaum's lets you study at your own pace and reminds you of all the important facts you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams.
Inside, you will find: 530 detailed problems with step-by-step solutions Clear, concise explanations of set theory, relations and functions, cardinal and ordinal numbers, and more Help with partially and totally ordered sets and the axiom of choice Answered exercises for improving your problem-solving skills
If you want top grades and thorough understanding of set theory, this powerful study tool is the best tutor you can have!
About the Author
He is a Ph.D and a Professor of Mathematics in Temple University
Most helpful customer reviews
16 of 16 people found the following review helpful.
The Front Door to Abstract Mathematics
By Jason Dowd
This book has been in print for over 45 years, and there's a good reason for it. It's excellent.
Whether you are a math student or a student in another discipline struggling with the mathematics necessary in your field (anything beyond calculus), you should read this book. Immediately.
Set Theory is the foundation of modern mathematics, and if you don't understand the basics of it you simply don't understand math. At all. Really.
This makes it all the more amazing that it is possible to get a PhD in mathematics without ever taking an actual class in set theory, and during my education I found that even professional mathematicians would sometimes make elementary mistakes with set theory.
Don't let this happen to you! By this book. Study it. Carefully. If you are a math student, it will strengthen you. If you are a student from another discipline, you will likely find that many of your previous mathematical difficulties begin to melt away.
I have seen many books on set theory over the years, and I have never seen one that I would recommend before this one. Never. In fact, for anyone interested in or forced to work with higher mathematics, I'd recommend this as the very first book they read.
However, for anyone reading this book, there is an important error which I will discuss because you may find it helpful. The definition of an ordered pair (a,b) is given as {{a},{a,b}}. You are told that with this definition (a,b)=(c,d) if and only if a=c and b=d.
But if you try you will find that you are not able to prove this. Indeed, set theory as developed in this book is insufficient to allow you to prove this result. In more advanced treatments of set theory, you will find out that this result relies on the Axiom of Foundation. Or you can just take the author's word for it, which is the only sensible course of action at this point.
The issue is that set theory becomes a deeply technical subject, full of subtle distinctions and formal logic. Fortunately, it isn't necessary to know it that well unless you really become interested in set theory for its own sake, and after reading this book you just might! The author is mostly very clear about the issues with this development of set theory. For example, there is a section completely devoted to showing you a variety of ways in which set theory as developed in this book is logically inconsistent. And this is exactly how things happened historically: after mathematics was set up on the basis of set theory, it was found that set theory itself -- as they understood it at the time -- was deeply flawed. This necessitated a careful, difficult, axiomatic overhaul of the subject which is of little practical value to people who actually just want to USE set theory to help them with other math, like engineers, physicists, or even most mathematicians. And those are the people this book is aimed at.
That said, the omission of the Axiom of Foundation from this treatment is perfectly understandable. However, it would have been nice if the author at least informed the reader that the set theoretic definition of ordered pair given requires additional set theory to completely justify.
So this book is not perfect, but in spite of its flaws it is an outstanding book, and after a short discussion of the ordered pair business I have recommended it to many people over the years. And now I am recommending it to you. Reading it will give you a new found power when dealing with abstract mathematics no matter who you are, and the mathematical prerequisites for this book are essentially non-existent. Set theory is where abstract mathematics starts, and this is the best first book on the subject I have ever seen.
22 of 24 people found the following review helpful.
Way Too Many Mistakes!
By David Clark
I went through the first chapter and worked all of the problems.
First, the typos:
On Page 10: About half way down it says "(a) on list or B"; it should be "(a) on list A or B"
On Page 33: The answer for 1.68 says "a is an element of X or a is not a subset of X." After the or it should be "not an element of X."
Second, the incorrect answers:
1.61: (b) should be 65 and (c) should be 25
1.63: They drew the Venn diagram correctly but then got (d) and (e) wrong. (d) should be 8 and (e) should be 12.
Third, the incorrect problems:
1.74: The right side formula is incorrect, I don't know what the correct formula should be.
1.75: The right side should be n/(2n+1) not 1/(2n+1). I checked this with n = (1,2,3) and the proof by induction worked with n/(2n+1).
If someone points our where I am wrong I will change or delete my review. As it is, six mistakes in one chapter is a a lot in my estimation, especially when the problems are incorrect. The whole point of Schaum's is to provide lots of example problems. If lots of the sample problems have mistakes it really cuts down on the usefulness of the book.
14 of 17 people found the following review helpful.
Well presented with excellent problems!
By A Customer
The material is well presented with numerous problems that drive home the concepts in the book. The reader must be a little careful as there a few errors in the Problem Solutions though. Overall, this is an excellent text.
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