Analysis: With an Introduction to Proof (4th Edition)

Book Description

By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs. Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises. A thorough reference for readers who need to increase or brush up on their advanced mathematics skills.

Customer Reviews:

Great book.......2007-04-29

Analysis at this level is probably the most challenging class for an undergraduate degree. However, this book made it very manageable. I found the introduction to proof very helpful. I encourage anyone who is using this book to study this chapter ahead of time. It will make the subsequent chapters a lot easier to handle. If it was not for this book and the outsdanting professor I had, I would never have passed this class. Go for it!

good to go.......2005-09-29

The book arrived in good condition and I have not had any problems with it.

Definitely a good first text.......2002-09-05

I bought this book because I have been looking for a Introductory analysis text that isn't too advanced, but yet doesn't gloss over the essential stuff, and I found it in Lay's book. For the self-studier, this book is excellent! I have several books on analysis: Shilov, Kolomogorov, Rosenlicht, Ross,etc... For the beginner, this book is superior to all of them. A plethora of examples. Also, a good range of problems:from straight forward problems requiring only the use of a definition to more advanced problems requiring a little thought. If you already have had some Analysis, then this book is probably not for you. But, if you are a student who wants to learn Analysis on your own, then this book would be hard to beat. After this book, one should be able to tackle "Papa Rudin". For according to Rudin, all that is needed to study his "Real and Complex Analysis" tome, is the first seven chapters of his "Principles of Mathematical Analysis". This book covers all that Rudin covers with the exception of Riemann-Stieltjes integration. On the whole, this is a great start! If proof-based math is new to you, then you will appreciate the first chapter on proofs. Would have given five stars, but I would have liked to seen Riemann-Stieltjes integration. That's really only nit picking, though.

This book was surprisingly good.......2002-07-03

I didn't think this book was going to be very good, but the author has "proved" me wrong ;-) This book starts out so basic that in my class (which was the first analysis course in our math department) we actually skipped the first 1/3 or so of the book. The first 9 or 10 sections consist of stuff like basic set theory, logic, definition of a function, etc. I would think that even the most elementary Analysis books would completely leave this out and expect that the reader is already familiar with this. So if you need it, this book will be a good resource for you.

Then the book goes into a very nice introduction to topology. Basic concepts like open/closed sets, accumulation points, compact sets, etc. Topology can be a little intimidating simply because it's _so_ abstract, but this book makes the basic concepts very easy to understand, and prepares one for a more advanced course in topology. Alot of (good) Elementary Analysis books leave topology out, but I'm glad this book contained it. It is a very interesting subject.

All the material in the book is explained probably about as easily as the concepts CAN be explained. If you still have trouble with it, you might consider a different major. Not to say that this book transforms a very difficult subject into a pathetically easy piece of cake because that's impossible, but the material is presented probably as easily as it can be in order to maintain precision and detail (which is the whole point of Analysis).

The book is definitely not running short in the examples or end-of-section problems department, so that is another plus. The problems at the end of each section range in difficulty from problems that almost exactly match an example worked in detail in the section, to fairly challenging problems. With enough time though the average student could probably do every problem at the end of every section.

I'd recommend this book for self study as well as a supplement to any introductory analysis course. If you have already have exposure to rigorous proof of calculus theorems, then this book will probably be too basic for you.

Book Description

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

* Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses.
* Reduced mathematical rigour to fit the needs of undergraduate students

Customer Reviews:

John Wilson.......2007-07-24

Keen students may find if they study and parse both editions of Enderton's

Logic they may find much of interest. Getting to the root of a problem

can be of use in many situations. So best of luck.

Moderately difficult and very effective.......2006-07-19

This is the most clear book on intermediate level logic that is available. I have many of the logic books that are on its level, and this one is perfect. It covers the most important, difficult concepts in the easiest way possible. It is above all clear (though very terse). It is easier than Mendelson's text but, in my opinion, as it pertains to First Order Logic and Computability Theory, one learns no more through Mendelson's approach.

Perhaps its only problem is that it might be just a bit too difficult without an understanding, helpful instructor (or TA) to guide one through the exercises. At any rate an effective progression up to the book might entail: Patty's "Foundations of Higher Mathematics", to Klenk's "Understanding Symbolic Logic", to "Logic, Sets, and Recursion" by Causey. Only after equivalent material has been understood thoroughly can the more hardcore semantics and mathematics of Enderton's book be fully comprehended. And, gone at alone on one's free time such a progression might take up to 2.5 years, maybe more.

Readable but a bit rough.......2005-07-12

It tries to be a readable undergrad introduction and mostly succeeds. Explanations are generally not tight and memorable, proofs seem loose, there are sometimes gaps in the train of thought, and exercises often require a significant conceptual leap from the preceding text. It was particularly annoying the way he suddenly switched to Polish notation for a while and then just as suddenly dropped it, without any obvious benefit. However, it is more accessible than most mathematical logic texts. The main competition for this text would be Ebbinghaus, which I prefer. The benefits of Enderton over that book are that it covers a wider range of topics and has a lot more exercises.

Terrific Book.......2005-01-03

Enderton's writing is the best I've seen in any introductory math textbook; he is lucid, well organised, comfortably paced but free of expository flab. The exercises (judging from chapters 2 and 3) are not terribly difficult, but quite useful in building one's intuition and connecting logic to other mathematics. I had the book for my Logic class as a first-semester sophomore with very little experience with proofs and no abstract algebra, and found it quite accessible. I guess the book starts off with an advantage, being about a subject as interesting as logic, but that does not seriously detract from its merit.

Still the best........2003-09-22

I review the classic FIRST EDITION. If you buy only one book on mathematical logic, get this one. It's by far the best logic book (see my other reviews) that is both 1)introductory and 2)sufficiently broad in scope and complete. The exposition is very clear and succinct- its suitable for beginners without getting wordy. Enderton always clearly explains what he's doing and why, keeping the reader focused on the big picture while going through the details. He helps to place topics in perspective, and has organized the book so readers can skip some of the more involved proofs and sections on the first reading.

Besides being easy to learn from, it's also the most rigorous introductory book I've seen- a rare combination. The proofs are detailed and complete, instead of the usual hand-waving or leaving everything as an exercise for the reader. There are some weak points in it, but overall you're not going to find a better book. It requires a little more 'mathematical sophistication' than most intro books- but if you've had some logic in a computer science course, or a little combinatorics or abstract algebra you'll be more than ready. Familiarity with automata/computability theory will help you in a few of the sections. Although Enderton is very good, it always helps to get several books on a subject- I'd recommend you pick up cheap copies of Boolos & Jeffrey's _Computability and Logic_ and Smullyan's _First-order logic_ as supplements.

Here is the complete table of contents for the first edition, c1972:

Chapter Zero - USEFUL FACTS ABOUT SETS . . . .1
Chapter One - SENTENTIAL LOGIC/ Informal Remarks on Formal Languages 14 /The Language of Sentential Logic 17/ Induction and Recursion 22/ Truth Assignments 30/ Unique Readability 39/ Sentential Connectives 44/ Switching Circuits 53/ Compactness and Effectiveness 58

Chapter Two - FIRST-ORDER LOGIC/ Preliminary Remarks 65/ First-Order Languages 67/ Truth and Models 79/ Unique Readability 97/ A Deductive Calculus 101/ Soundness and Completeness Theorems 124/ Models of Theories 140/ Interpretations between Theories 154/ Nonstandard Analysis 164

Chapter Three - UNDECIDABILITY/ Number Theory 174/ Natural Numbers with Successor 178/ Other Reducts of Number Theory 184/ A Subtheory of Number Theory 193/ Arithmetization of Syntax 217/ Incompleteness and Undecidability 227/ Applications to Set Theory 239/ Representing Exponentiation 245/ Recursive Functions 251

Chapter Four - SECOND-ORDER LOGIC/ Second-Order Languages 268/ Skolem Functions 274/ Many-Sorted Logic 277/ General Structures 281
Index 291

Introduction to Algorithms: A Creative Approach

Average customer rating:

A great supplement and right sized for travel too!
thought that this book was wonderful, but...
Great on algorithm design, not that good on analysis
Not good for beginners
fantastic

Introduction to Algorithms: A Creative Approach
Udi Manber
Manufacturer: Addison Wesley
ProductGroup: Book
Binding: Paperback

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ASIN: 0201120372

Customer Reviews:

A great supplement and right sized for travel too!.......2007-01-25

I really like this book as a supplement to the algorithm bible (Introduction to Algorithms, Thomas Cormen et al). This book is tiny and portable yet every major algorithm is covered. Basics, like mathematical induction are reviewed and illustrated with relevant examples.

One of the ways that Udi Manber packs so much information into such a small package is by keeping verbosity to a minimum. In his proofs, only the most complicated steps are justified or explained. As a result the reader may find herself spending time justifying steps in the proofs that are unrelated to the problem at hand. I did not mind doing this; others may. Regardless, the persistent reader will find that within the pages of this book lies all of the information required to understand all of the algorithms covered (and of course, it never hurts to keep a notebook, pencil and several erasers handy).

I would not recommend this book as a reference; rather, it provides a refreshingly new perspective on algorithms that may seem old and dusty. I've spent more time and energy per page on this book than any other CS book I've had but the ROI has been well worth the effort.

thought that this book was wonderful, but..........2006-04-10

...I changed my mind after trying to use this book alone to implement FFT. Its description is quite clear and simple, much simpler than the Rivest et al book or wikipedia. Unfortunately, though clear, it is not complete and it is not possible to actually implement FFT using this book alone. I ended up having to use the Rivest et al book (which I had on CD via DDJ) along with this book to implement it. (Wikipedia was truly hopeless for trying to understand the FFT algorithm.) I was able to implement FFT in a single page of Python code because of Manber's description.

For giving very simple explanations of a number of algorithms, this book is fantastic. Just don't rely on it for the technical details.

Great on algorithm design, not that good on analysis.......2005-04-25

I like this book a lot. I think it's a good reference and introductory text, maybe as a supplement. It's much easier to read than Cormen's, but not half as deep.

Pros:
- Easy to read. You can understand an algorithm much faster if you go to this book first.
- Good examples and pictures.
- Explain the ideas that lead to efficient algorithmic designs.

Cons:
- Doesn't go into enough details about the proofs of correctness and complexity.
- The approach is different than most books and may take some time to get used to.

Not good for beginners.......2004-07-08

The book is complete and correct, no argument there. However, I had a lot of trouble learning from it. I had to re-read the same paragraph a number of times in order to derive comprehensive meaning from the author's scant explanations. The author usually walks through a sample problem, but then provides little or no guidance for solving an arbitrary problem of the same type. Likewise, although the book centers on induction, it was extremely difficult to follow with no prior induction education.

The author often presents the answer to some given problem with words like "obviously" or "clearly" without making things at all clear or obvious to the student. I kept wishing that the author wouldn't be so tight-lipped and would spend some extra time clarifying the issues at hand.

fantastic.......2003-10-25

It's a very perfect book to become familiar with main
methods of producing effective algorithms.

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

Average customer rating:

This book is adequate but needs improvement
Do not buy this book!
Big Improvement in Second Edition
Great Introduction to proofs
YOUR FIRST BOOK IN MATHEMATICS

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes
Daniel Solow
Manufacturer: Wiley
ProductGroup: Book
Binding: Paperback

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ASIN: 0471406473

Book Description

This book categorizes, identifies and explains the various techniques that are used repeatedly in all proofs and explains how to read proofs that arise in mathematical literature by understanding which techniques are used and how they are applied.

Customer Reviews:

This book is adequate but needs improvement.......2004-10-19

I have an older edition of this book. It is well-written and has a good selection of homework problems, but it lacks clarity and does not emphasize practice. Most proof books are good for learning the basics of proofs but aren't sufficient to do proofs in a specific area of math. My website focuses on how to practice doing proofs, fsc729.ifreepages.com.

John G.

Do not buy this book!.......2003-10-22

I had one of my math courses at Macalester College use this book in addition to the main textbook. It is one of the most boring readings in math ever. If you want a beginning book that would teach you how to do problem-oriented math, you had better consider George Polya's How to Solve It or consult a math teacher near you;-) In order to further underscore my poit, I will just say that it was not only I but the whole class that disgruntled against the book and we hated it so much that the professor does not use it anymore.

Big Improvement in Second Edition.......2002-02-15

Contrary to the review by the person from Louisiana I feel the second edition is better than the first. The typesetting is greatly improved, and there are a few new tools for your toolbag in the second edition.

As to the criticism that the second edition only has solutions for the odd numbered problems, the reviewer failed to mention that there are twice as many problems in the new edition and that all the problems from the first edition were carried into the second (along with their solutions). I found it more satisfying working through the second edition knowing that the problems were correctly solved - not because the answer matches the back of the book - but because the arguments are compelling and demonstrably correct.

I heartily recommend this book to anyone who feels mystified at the process of writing proofs.

Great Introduction to proofs.......2001-09-21

When I order this book it was not at all clear if I would like it, because of it low grades contain and examples. I was very surprised when I received it, because the book is written very clearly. The author make a great job when he explains the technics of proof. The exercises and the examples are definitely too easy for an undergraduate or graduate but you must take a look at it just for the explanation that the author gives for the technics of proof. The examples and exercises are mostly for high school students. The price of the book make it very affordable. It worth the price. I would recommend this book to anyone who want to introduce himself into the basic of proofs.

YOUR FIRST BOOK IN MATHEMATICS.......2001-06-04

YOU REALLY NEED THIS BOOK IF YOU ARE TRYING TO STUDY ABSTRACT MATHEMATICS BY YOURSELF OR WITH A TEACHER. LIKE ELECTRONIC ENGINEERING THAT LIKE TO DO MATHEMATICS THIS BOOK REALLY HELP ME TO UNDERSTAND HOW TO READ PROOFS AND MADE MY OWNS.

Friendly Introduction to Mathematical Logic, A

Average customer rating:

Most Accessible Undergraduate Text Covering Incompleteness

Friendly Introduction to Mathematical Logic, A
Christopher C. Leary
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Hardcover

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ASIN: 0130107050

Book Description

This user-friendly introduction to the key concepts of mathematical logic focuses on concepts that are used by mathematicians in every branch of the subject. Using an assessible, conversational style, it approaches the subject mathematically (with precise statements of theorems and correct proofs), exposing readers to the strength and power of mathematics, as well as its limitations, as they work through challenging and technical results. KEY TOPICS: Structures and Languages. Deductions. Comnpleteness and Compactness. Incompleteness--Groundwork. The Incompleteness Theorems. Set Theory. : For readers in mathematics or related fields who want to learn about the key concepts and main results of mathematical logic that are central to the understanding of mathematics as a whole.

Customer Reviews:

Most Accessible Undergraduate Text Covering Incompleteness.......2006-08-24

I have used this text in both graduate and undergraduate courses as well as tutorials and independent studies. It is the best text for a one semester course that introduces formal logic and has as its goal the Incompleteness Theorems of Godel. Students have reported it to be very readable and the array of exercises is excellent. Moreover, the author is a really nice fellow.

Introduction to Logic: Propositional Logic (3rd Edition)

Average customer rating:

The most user-friendly book for Propositional Logic

Introduction to Logic: Propositional Logic (3rd Edition)
Howard Pospesel
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Paperback

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ASIN: 0130258490

Book Description

Designed to make logic interesting and accessible—without sacrificing content or rigor—this classic introduction to contemporary propositional logic explains the symbolization of English sentences and develops formal-proof, truth-table, and truth-tree techniques for evaluating arguments. An accompanying computer tutorial program, PropLogic, is available on CD-ROM in two versions: one version can be installed and run off a hard drive; one (identical) “portable” version can be run off the CD-ROM itself (allowing students/instructors flexibility on when/where they use the program). An appendix in the text describes program details. Tutors readers on formula construction, symbolization, formal proofs, full and brief truth tables, and truth trees. Also provides additional practice exercises. Content organized around natural-deduction formal-proof procedures, truth tables, and truth trees. Gradual presentation of logical statement connectives. Shows students how to symbolize sentences containing the connective and how to use proof rules involving that connective before introducing additional connectives. Examples of actual arguments similar to those readers encounter, and to which they can readily relate. Draws examples and exercises from newspapers, magazines, television, books, textbooks, term papers, posters, comic strips, television programs, films, records, and conversations. Increases students' awareness of the arguments they read and hear every day. Extensive exercise sets throughout provide solutions to about one-quarter of the exercises (in an appendix). Provides ample opportunities for assignments and practice.

Customer Reviews:

The most user-friendly book for Propositional Logic.......2004-10-10

This is a easy to use text for learning the basics of Propositional Logic. The rule set is simple and symmetrical, easy to use. The CD gives important feedback to the student and contains the answers to almost every exercise in the book plus additional practice exercises. I would recommend this textbook to any professor wishing to teach Propositional Logic.

Average customer rating:

An Introduction to Substructural Logics
Greg Restall
Manufacturer: Routledge
ProductGroup: Book
Binding: Paperback

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ASIN: 041521534X

Book Description

This is the first book to systematically survey new areas of substructural logics. This book is geared to introduce the topic to advanced students. An Introduction to Substructural Logics covers the area of logic that is crucial to developments in computing, philosophy and linguistics.

Introduction to Mathematical Structures and Proofs

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Introduction to Mathematical Structures and Proofs
Larry J. Gerstein
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387979972

Book Description

"...Gerstein wants-very gently-to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. For instance, after his discussion of cardinals he has a section entitled Languages and Finite Automata. This allows him to illustrate some of the ideas he has been discussing with problems that almost anyone can understand, but most importantly he shows how these rather transparent problems can be subjected to a mathematical analysis. His discussion of how a machine might determine whether the sequence of words "Celui fromage de la parce que maintenant" is a legitimate French sentence is just delightful (and even more so if one knows a little French.)...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge.

- Steven Krantz, American Mathematical Monthly

"This very elementary book is intended to be a textbook for a one-term course which introduces students into the basic notions of any higher mathematics courses...The explanations of the basic notions are combined with some main theorems, illustrated by examples (with solutions if necessary) and complemented by exercises. The book is well written and should be easily understandable to any beginning student."

- S. Gottwald, Zentralblatt

This textbook is intended for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, etc. It contains a wide-ranging assortment of examples and imagery to motivate and to enhance the underlying intuitions, as well as numerous exercises and a solutions manual for professors.

An Introduction to Fuzzy Logic for Practical Applications

Average customer rating:

Good introduction, with some errors
Fast entry to notation
Breezy Intro to Fuzzy Logic
Excellent starting point
Excellent

An Introduction to Fuzzy Logic for Practical Applications
Kazuo Tanaka
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 0387948074

Book Description

Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of human knowledge and experience to behave in a manner similar to a human controller. Throughout, the level of mathematical knowledge required is kept basic and the concepts are illustrated with numerous diagrams to aid in comprehension. As a result, all those curious to know more about fuzzy concepts and their real-world application will find this a good place to start.

Customer Reviews:

Good introduction, with some errors.......2007-08-03

This 136 page book provides a brief introduction to fuzzy logic and applications. However, I have to disagree with the comment that symbols are always defined when used, as many are not.

Also, I think the book may have suffered in translation, as there are quite a few errors, especially in the translation of formulas. For example, on page 27 is an incontrovertable mangling of De Morgan's laws. In other places, symbols are left out, subscripts and superscripts are inexplicably moved around, and shading for graphs and tables is mentioned many places in the text but mysteriously not present in the graphs and tables referred to.

Fortunately, Tanaka goes over the same topic from multiple prespectives, in most cases allowing the reader to figure out what is going on. As an introduction, this book would definitly have benefited from a table of symbols. However, overall, a good introduction to (or review of) the topic.

Fast entry to notation.......2006-08-17

I purchased this book to gain enough information to read a technical paper. Fuzzy logic is new to my industry (petroleum) and my 1970's education did not provide any background. The book took less than an evening to absorb and provided more than enough understanding of the notation and basic operations that I was able to read my paper and start building an interest in deploying Fuzzy logic in my daily work. Other books are needed to fully apply the methodology. However, sufficient demonstration of basic fuzzy arithmetic was provided to know that 2 times 3 divided by 2 is not necessarily 3.

I shared the book with a mathematically oriented associate and she had similar experiances.

Overall, a great introduction with just enough information for a cursory review and enough detail to help determine need or interest for a more detailed presentation.

Breezy Intro to Fuzzy Logic.......2006-07-30

I was impressed by the fact that most symobology used in the book is defined during its first use. There are a few symbols like 'sup' on page 38 that I'm still unclear about.

There are five basic chapters in the book:
1 Introduction
2 Fuzzy Set Theory
3 Fuzzy Relations
4 Fuzzy Reasoning
5 Fuzzy Logic Control

Chapter 1 is a brief two page intro to the concept. The chapter on Fuzzy Set Theory gets into the basics. I've read the descriptions of Fuzzy Logic in MathLab's Fuzzy Logic module and so was prepared for most what is in this chapter. As such, I'm still somewhat unclear as how Cartesion Products and Extension Principles are applicable to the whole concept of Fuzzy Logic.

In the chapter on Fuzzy Relations, further use of extensions is used along with the properties of composition. Simple matrix math is used in some cases to arrive at results in some of the examples.

The fourth chapter, which is about Fuzzy Reasoning, includes reasoning based upon Mamdani's Direct Method, Takagi & Sugeno's Fuzzy Modelling, and the Simplified Method. It is in this chapter where the earlier mechanisms of composition are utilizied. Defuzzification, which is final step of any fuzzy logic process, is lightly described with a brief reference to the standard centroid calculation.

The final chapter is light on formulas, and offers up a high level description of the superiority of fuzzy logic over PID controllers, and how the former can help the latter obtain better control in some situations.

After having taken a first read of this book, I'll have to go through it again to see if I can better relate Fuzzy Relations to the remainder of the book. In addition, now that I've got a better grasp on fuzzy symbology, I believe I'm ready to move on to the more heavy duty books of the subject area.

Excellent starting point.......2006-07-10

This book gives you an excellent introduction to Fuzzy Logic Concepts, Reasoning and Applications.

I am a Practitioner of Industrial Process Control, and was looking for a book to learn about Fuzzy Logic. The book did it in a simple way, with many examples and explanation for every topic to make even easier my introduction to this area.

Excellent.......2006-02-01

You'll find one of the simpler introductions to fuzzy logic here. Unlike many more technical fuzzy logic books, much of the symbolism used gets explained. The diagrams of projection and cylindrical extension also help understand these notions in an intuitive manner. The book does have a slight error in that it claims a proof of a general theorem through the use of a single numerical example. But, the plethora of simple examples in this books make it a pleasure and an ease to read. You'll also find encoruagement if you have doubts about pursuing this field, as Niimura indicates that Zadeh had his original paper on fuzzy sets finished for two years prior to its publication, and it only got published, because he edited the journal.

An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Applied Logic Series)

Average customer rating:

used early draft as grad text

An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Applied Logic Series)
Peter B. Andrews
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 1402007639

Book Description

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability.

The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory.

Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises.

Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.

Customer Reviews:

used early draft as grad text.......2005-12-07

I took a great graduate course from Prof. Andrews, way back in the 1970's, where his class lecture notes were titled "To Truth Through Proof", so I assume that was a very very early draft of this book.

If so, this must be a very good book, because his notes were wonderful even back then.

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