Schaum's Outline of Set Theory and Related Topics

by Seymour Lipschutz

Book Overview

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,...

• Format: Paperback
• Language: English
• ISBN: 0070381593
• ISBN13: 9780070381599
• Release Date: July 1998
• Publisher: McGraw-Hill Companies
• Length: 288 Pages
• Weight: 1.20 lbs.
• Dimensions: 0.6" x 8.1" x 10.8"

Customer Reviews

The Front Door to Abstract Mathematics

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

schaum' s outline, set theory and related topics

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All you need and more

Like the other books of the Schaum's Outline series, "Theory and Problems of Set Theory and Related Topics" provides you with hundreds of problems, which have been worked out step by step, to show you how the theory works. This is similar to a professor in college showing you the problems on the board, but these don't get erased and are much more legible.In addition to the solved problems, there are supplementary problems to test your understanding of the material. At the end of each chapter, the answers are printed for you to check your work.The discussions of set theory include definitions to ensure that you are familiar with the lingo. There are also plenty of examples to illustrate the author's meaning. With all the information on set theory, there are also chapters on quantifiers, boolean algebra, logical reasoning, and the algebra of propositions.This book provides some good assistance in learning set theory.

Provides essential knowledge to e-commerce security pros

This is an excellent introductory text on set theory. It provides a fast and thorough coverage of the basics in an economical, if terse, style. If you diligently go through this short 200 page book you will have a solid grasp of set theory that you can immediately use on the job. I am an IT consultant so, although this book has a much wider audience, I am focusing my review on how this book applies to IT. Because many e-commerce systems are being designed using role-based access controls that are independent of any specific application it is essential that the designers have a thorough understanding of set theory. As such, I think this book is an indispensable quick reference guide for IT security specialists, system architects and QA team members who need to brush op on the subject. These folks design, validate and verify systems that require strong security from within and outside of their organizations. This type of work requires a provably correct design that can only be approached with set theory. Moreover, the testing of the design, as implemented, also requires an understanding of this subject in order to develop a viable test strategy and produce test cases. Given the fact that most IT professionals are not versed in set theory, this book is one of the quickest ways to get up-to-speed. Among the highlights of this book are: the paradoxes in set theory, which is "must reading" regardless of how you intend to use the knowledge and skills that this book provides, algebra of propositions and logical reasoning. This book is clearly written, however, the material requires a strong dedication to learning because the subject is complex and dry. No author, regardless of his or her writing skills can change that. If you need to understand set theory and don't know where to begin, this book is one of the best starting points I have come across.

excellent book for non-mathematicians

This is THE book to learn set theory if you are not a mathematician or mathematics major. Set theory is presented in a non-axiomatic manner. All the basics are covered: elementary set theory, cardinal and ordinal numbers, axiom of choice, and a brief intro to logic. The number of examples is huge. If you need examples when learning, then this is the book for you!