Subjects:  1. Analysis    2. Biotechnology    3. Life Sciences - Biochemistry    4. Mathematics    5. Nucleic acids    6. Polymerase chain reaction    7. Quantitative genetics    8. Science    9. Science / Biotechnology    10. Science / Chemistry / General    11. Science/Mathematics    12. Set Theory    13. Chemistry - General   

Reviews (2)

The best introduction to probability and measure
The book very nicely develops the basics of measure theory from a probability perspective (e.g. includes Caratheodory extension theorem, Lebesgue-Stieltjes measures, weak convergence and Kolmogorov extension theorem). It then gives a brief introduction to functional analysis and proceeds to probability theory, martingales and concludes with brownian motion and stochastic integration.
Exceptionally Clear
I first used this text in the earlier version, which comprises the first half of the book, in a one-year course in Hilbert Spaces and Lebesgue Measure theory when in the first year of grad school.The material is presented in a clearly written manner and the exposition is some of the clearest mathematical writing I've seen in a subject which is replete with textbooks.Read more

Subjects:  1. Mathematical Analysis    2. Mathematics    3. Measure Theory    4. Probabilities    5. Probability & Statistics - General    6. Science/Mathematics    7. Set Theory    8. Mathematics / General    9. Probability & statistics   

Reviews (4)

Mathematical Proofs
This book is concise, clearly written and easy to understand. However, I would have liked to have seen more examples of new concepts.

Good book for what it is
I am currently using this book for a class right now. I find this book easy to read and work with, but wish there was more examples explaining each kind of proof. Although there are quite a few examples to the proofs, I just need a few more to work with. I am going to purchase another proof writing book to supplement this one, as this is my first dealings with proofs. All in all though, this is a good book.

Mathematical Proofs:A Transition to Advanced Mathematics
I purchased this book as a preparation to take advanced courses in mathematics.It is well laid out and explains the material clearly.I especially liked the chapter on "proofs found in calculus" which explains delta epsilon proofs in a manner that is easy and understandable.Big thumbs up! ... Read more

Subjects:  1. Logic    2. Mathematical And Symbolic Logic    3. Mathematics    4. Philosophy Of Mathematics    5. Proof theory    6. Science/Mathematics    7. Set Theory    8. Mathematics / Advanced   

Reviews (7)

Short and to the point
This book is excellent! It chapters are broken down into short sections and the content in each section is to the point! I also bought the book Proofs and Fundamentals by Ethan D. Bloch but found it to be long and drawn out. If you liked The Nuts and Bolts of Proofs by Antonella Cupillari then this book is for you!

Very well written book
I have a mathematics degree. Like most math majors, I struggled with proofs all through college. This book really has help me understand the art of writing proofs. The book is very well written and easy to read. This is just an awesome book!!!

Now I know how beautiful proofs can be
This book provides a nice introduction to mathematical reasoning and proofs. My intention on purchasing this book was to learn how to perform mathematical proofs. I believe it has achieved that purpose. The text is easy to follow and the author presents the work clearly. ... Read more

Subjects:  1. Logic    2. Mathematics    3. Number Systems    4. Number Theory    5. Proof theory    6. Science/Mathematics    7. Set Theory    8. Mathematical foundations    9. Mathematics / Combinatorics   

Reviews (5)

The ideal introductory book on set theory
In recent months, I read (at least in part) about ten books on set theory, of different levels and styles. Goldrei's book is by far the best on my list. Goldrei has the talent of presenting a fairly difficult and abstract material in a friendly style, with abundant explanations, solved exercises, illustrations, and illuminating comments. I can highly recommend this book as a first reading on set theory, whether for self-study or as a supplementary text for a course on the subject. For the interested readers of this review, here is how I rank some of the other books I've read: Stoll is definitely a second, then Suppes (which goes deeper than both Goldrei and Stoll, but in my opinion is poorly organized and suffers from nonstandard and funny-looking notations), followed by Halmos, Machover, and a few more. And last and least, the incomprehensible "book" by Vaught.

The ideal textbook
I went to my university's library and tried to compare Goldrei's book with almost all other popular accounts on Set theory, prior to investing my time learning the basics of the subject. After having almost finished reading it, I believe that this a model of how textbooks in mathematics should be written. Let me be a little bit more specific:
Especially useful for self-study.
This book is especially useful for self study, as it has more worked examples than usual, motivating hints in side bar, and explanitory comments in text. Perhaps the origin of this materical in Open University (I think roughly analogous to what USA schools call "Extension"?) course is reason. Found it helpful where Halmos was a bit concise for someone with fellow students or TA handy. ... Read more

Subjects:  1. Mathematics    2. Science/Mathematics    3. Set Theory    4. Mathematics / Set Theory   

Reviews (6)

A must have
A must have for set theorists. Does a better job than Jech. It's a little weird how you get a sense of the set theorists as people, but the historical stuff is otherwise really great.

Interesting but too much reading
Assumes set theory through forcing and some model theory. He integrates a lot of historical information which is interesting but greatly adds to the reading without adding to the mathematical understanding. The semester is short and I want to learn what I need and get on with life. While it does have more details than Jech, I like Jech's style better and not just because it is shorter. (The 2e is just a corrected reprint of 1e.)

Excellent as a follow-up to Kunen
I'm a graduate student in set theory and I'm finding Kanamori an excellent follow-up to Kunen.The book manages to combine detailed technical exposition with historical insight which is actually useful to understanding the material (not just a list of dates) and gives one a "feel" for the subject.
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Subjects:  1. General    2. Geometry - General    3. Large cardinals (Mathematics)    4. Logic    5. Mathematics    6. Science/Mathematics    7. Set Theory    8. Mathematics / Logic    9. Mathematics / Set Theory    10. Mathematics-Geometry - General    11. Mathematics-Logic    12. infinitary combinatorics    13. large cardinals    14. new axioms for set theory     15. relative consistency results    

Reviews (4)

Actually proves the theorem
The book is wonderful because it actually proves the theorem in a way that a non-expert in mathematical foundations can actually understand.I wish all popular mathematics books were written at this level where the goal is to educate and entertain.Now as I suggested to the author all we need is a book like this one that will explain Godel's and Cohen's results on the independence of the continuum hypothesis.

A fascinating introduction to the Banach-Tarski Paradox
The Pea And The Sun: A Mathematical Paradox is a fascinating introduction to the Banach-Tarski Paradox, a mathematical riddle that asserts it could be possible to create something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again. Written to be accessible to lay readers and non-mathematicians, The Pea And The Sun outlines the history of the paradox, introduces readers to the basics of such matters as set theory, isometrics, scissors congruence and equidecomposability, and walks the reader through the theorem and proof that object duplication is indeed mathematically possible. But just because it is mathematically possible, is it physically possible? The highly counterintuitive nature of the mathematical theorem demands a critical response. A final chapter dwells on speculation as to how the Banach-Tarski Paradox may apply to the modern and future world. Written in a fresh, captivating, friendly style, The Pea And The Sun is remarkably engaging and will appeal to any reader with a discerning, inquisitive mind into the nature of the so-called impossible, regardless of their particular mathematical background.
Perfect blend of math, humor, and information for the layman as well as the math professional
This book gives an incisive look at a fascinating area of science. It is technical enough to hold the attention of the math whiz, while "gentle" enough to carry a complete layman along. I personally learned a great deal about this amazing paradox, and also about the world of higher mathamatics in general. Fascinating, but light hearted reading. Highly recommended for anyone with any interest in this type of field. ... Read more

Subjects:  1. Banach-Tarski paradox    2. History    3. Logic    4. Mathematics    5. Science/Mathematics    6. Set Theory    7. Mathematical logic   

Reviews (1)

Masterwork
"Set Theory and It's Logic" has cast a long shadow since it's first appearance. It is quite simply the crowning work of one of the 20th century's most distinguished philosophers. Sober, clear, and direct (and yet unpretentious and very friendly), it is illuminating to anyone who has the patience to slowly sip it and consider the the way the arguments build up from line to line and page to page a seemingly indestructible house of cards. If one is unprepared for the rigors of the book, that can be easily remedied--Quine also wrote the best introductory book on Logic, "Methods of Logic", which he took through several editions before his death. That book assumes no backround in logic, and a beginner who works her way through the exercises will find herself well-prepared for the magic tricks in "Set Theory and its Logic". I wished we taught this stuff in the public schools, along with mathematics, and (to keep the old dialectic rolling) Homer, Shakespeare, Dante, Tolstoy, Dickinson--the great poets. I might be dreaming, but we may have, at the very least, more ethical scientists, more humane poets, or just plain old more interesting people--who know what the foundations of their thoughts actually assume. A classic. ... Read more

Subjects:  1. General    2. Mathematics    3. Philosophy    4. Set Theory    5. Mathematical foundations    6. Philosophy / General   

Reviews (3)

The best introduction on the subject
I can't stress how reader friendly this book is.It is by far the best introduction on component analysis.It is written in such a way that those with a weaker math background can understand it while those with years of experience will not be bored, at certain times it even reads like a story.
James Stone's monograph: 'Independent Component Analysis'
James Stone's monograph is a refreshing new book amongst the many other `new books' on Independent Component Analysis (ICA). The author brings his teaching experience to present the theory and practice of ICA in a highly accessible form using a duplication of words and straight-forward mathematics.
An Excellent Introduction
Independent Component Analysis (ICA) is one of the emerging technologies that ever more powerful computers are becoming more available. Basically it is a set of mathematical techniques that are used to pull a little bit of information out of a large mass of data.
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Subjects:  1. Artificial Intelligence - General    2. Cognitive Psychology    3. Computers - General Information    4. General    5. Mathematics    6. Multivariate analysis    7. Neural networks (Computer scie    8. Neural networks (Computer science)    9. Neuropsychology    10. Psychology    11. Science/Mathematics    12. Set Theory    13. Neural networks    14. Psychology & Psychiatry / Cognitive Psychology   

Reviews (1)

Good Reference
This is an EXCELLENT reference manual. Its a "bit" mathematical, but does need to be updated regarding turbo codes. ... Read more

Subjects:  1. Coding Theory    2. Computers - General Information    3. Discrete Mathematics    4. Information Theory    5. Mathematics    6. Number Theory    7. Programming - Systems Analysis & Design    8. Science/Mathematics    9. Set Theory    10. Algebra    11. Algebraic geometry    12. Algebraic number theory    13. Applied mathematics    14. Combinatorics & graph theory    15. Mathematics / Number Theory   

Subjects:  1. Logic    2. Mathematical And Symbolic Logic    3. Mathematics    4. Philosophy Of Mathematics    5. Proof theory    6. Science/Mathematics    7. Set Theory    8. Mathematics / Advanced   

Reviews (5)

Fast entry to notation
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.
Breezy Intro to Fuzzy Logic
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.
Excellent starting point
This book gives you an excellent introduction to Fuzzy Logic Concepts, Reasoning and Applications.
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Subjects:  1. Artificial Intelligence - Fuzzy Logic    2. Computers - General Information    3. Fuzzy Sets    4. Fuzzy logic    5. Logic    6. Mathematical And Symbolic Logic    7. Mathematics    8. Science/Mathematics    9. Set Theory    10. Automatic control engineering    11. Computers / Artificial Intelligence    12. Fuzzy set theory    13. Mathematics-Logic   

Reviews (3)

For better or worse it's the standard
For a graduate course on set theory, I don't think there is any serious competition for Kunen. It assumes you have already had a basic course and starts right in using the concepts of axiomatic set theory and the properties of cardinals and ordinals, although it does start with a terse recap of logic and ZFC. The whole book is narrowly focused on leading up to the technique of forcing to prove consistency results under ZFC. It mostly avoids large cardinals, the Axiom of Choice, descriptive set theory, and model theory.
Kunen is the master expositor
This is the most widely used textbook for graduate -level set theory, andwith good reason. Kunen manages to cover all the essentials of set theoryin a quick 300 pages--and he does so with exceptional clarity and depth. Excellent graduate level text
An excellent text leading to a clear explanation of forcing and what it is good for.Tough going without someone to question for this advanced non-student (almost a math minor but 20 years ago.)This was recommended in sci.math as the best approach to forcing and I believe it ... Read more

Subjects:  1. General    2. Mathematics    3. Science/Mathematics    4. Set Theory   

Subjects:  1. Arithmetic    2. Foundations Of Mathematics    3. Logic    4. Mathematics    5. Predicate calculus    6. Science/Mathematics    7. Set Theory    8. Mathematical logic    9. Mathematical theory of computation   

Reviews (1)

Where is the data ?
While i do not deny the contribution at providing a more or less complete treatment of neurofuzzy techniques for data modeling, i'm still wondering where the non-theoretical chapters dealing with how to cope with real data with these techniques are hidden. The few examples in the book are mostly artificial and very limited in their scope. i'm not sure people dealing with data have an interest at reading this book, it's more about neurofuzzy techniques than data modelling.Read more

Subjects:  1. Artificial Intelligence - General    2. Computer Bks - General Information    3. Computer Books: General    4. Computer Science    5. Computers    6. Computers - General Information    7. Fuzzy Sets    8. Information Storage & Retrieval    9. Neural Computing    10. Neural Networks    11. Set Theory    12. Computers / Artificial Intelligence    13. Empirical Modeling    14. Mathematical theory of computation    15. Neurofuzzy Modeling    16. Nonlinear Identification    17. Pattern Recognition   

Reviews (3)

Very questionable science, and many errors in text
I bought this book for a readings class this semester.I don't have a suitable vocabulary to describe how poor it is.The text is inconsistent and full of errors.The author blathers on without concluding much.He references his previous work and that of PhD theses (which I can only assume are his own students).I question the underlying assumptions of his theory but it is never fleshed out in sufficient detail to be understood and examined.
What is important here?
One of great emerging ideas in the past 20 years is that there are tools to help in the design of robust products and systems.There are other approaches: TRIZ, QFD and other heuristic-based methods.There are also references to Dr. Taguchi's robust design methods (DFSS). The point is that the author here has made his point - DFSS as applied to multi-requirement products and systems... and that includes just about every product/system we use and need... has an overlooked flaw.Read this book to understand what that flaw is and how to address it. A False Science
Is design a science? Or, can design be a science?Read more

Subjects:  1. Axiomatic set theory    2. Design, Industrial    3. Drafting & Mechanical Drawing    4. Engineering - Mechanical    5. Industrial Design    6. Industrial Design - General    7. Methodology    8. Science/Mathematics    9. Set Theory    10. Technology    11. Technology & Industrial Arts    12. Engineering & Technology | Electrical & Computer Engineering    13. Engineering: general    14. Mechanical engineering    15. Systems analysis & design    16. Technology / Engineering / Mechanical   

Reviews (5)

Clear and comprehensive
The author tried to cover everything a set theorist should master plus a representative selection of topics of current interest. That makes for a lot of ground to cover, but Jech did a great job. The writing is very well organized and clear. Every short chapter has many exercises, often with hints. There are extensive sections on applications of forcing. The indexes are really good.
A good but unreadable book
It's really a good book for researchers in set theory. But it is NOT an introduction for students who want to know what is set theory. You will feel you are so stupid if you read this book without any set theoretical background. I recommand Kunnen's book for those people who are interested in set theory but have no any (or only a little) set theory knowledge.

This edition has been completely revised!
Just wanted to point out that all the reviews here dated before Feb 2003 are referring to older editions.The new one has been totally revised (no laundry list of corrections at the end) and also expanded -- lots of material from the last 25 years of set theory research is now included. Most notable among these is material on proper forcing and pcf theory.(There is even a section on my research interest, mutually stationary sets, and this is a notion which was just published for the first time 2 years ago!)The book is still just as informative and readable as the previous editions. ... Read more

Subjects:  1. Logic    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Mathematics / Logic    6. Mengenlehre   

Subjects:  1. Congresses    2. Field theory (Physics)    3. Geometry - General    4. Homology theory    5. Mathematics    6. Quantum Theory    7. Quantum gravity    8. Science    9. Science/Mathematics    10. Set Theory    11. String models    12. Topology - General    13. Geometry    14. Mathematics / Applied    15. Relativistic quantum mechanics & quantum field theory    16. Topology   

Reviews (2)

WOW!!!!
This book is like no other. Its short and to the point which means that the busy math major can actually sit down and read it! We all know how hard it is to try and read a wordy book on how to write proofs while at the same time trying to study abstract algebra! We dont need a full 100 pages on informal logic! Antonella Cupillari seems to understand this and sums up everything we need to know concerning logic in under 12 pages! Excellent book! Well worth the $32.95!

I own a previous edition
I own the second edition of this book and find it incredibly well done. I am a math major, and this book was recommended to me by a caring professor to help aid my transition between computational mathematics and the more abstract area of Mathematical Proofs.
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Subjects:  1. Econometrics    2. General    3. Mathematics    4. Proof theory    5. Science/Mathematics    6. Set Theory    7. Mathematical logic    8. Mathematics / Applied   

Subjects:  1. Advanced    2. General    3. Mathematics    4. Mathematics (General)    5. Science/Mathematics    6. Mathematics / Set Theory