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

Reviews (1)

An overlooked masterpiece of foundational math
A university press should get this back into print pronto! The book is filled with Lewis's tart wit and gentle humor. Had more math been of this nature, I would have majored in math.
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Subjects:  1. Mathematics    2. Philosophy    3. Set Theory    4. Whole and parts (Philosophy)    5. Logic    6. Philosophy of mathematics   

Reviews (2)

A perfect overview
This book is absolutely a good choice for those who want to try to know the wide-spreaded theory or those who have basic knowledge about it and want to know more. It is also squib-style written and easy to be understood. Evene though I only finished the Phonology part (since I'm focusing on Phonology now), I still know that other parts are as wonderful as the phonology part. Just Take It For Yourself!

optimality theory and features
I would like to recommend this book to the readers who are interested in optimality theory .I'm preparing for my dissertation on the features and optimality theory.I couldn't find good papers which deal with thefeatures on the basis of optimality theory. The chapter "optimalityand features" by pulleyblank accounts for a wide range of phonologicalfeatures by the interaction of constraints. Within OT framework, he givesan idea of phonological representations and resolves the complexity offeatural phenomena by the rankingbetween faithfulness and the conflictingconstraints.Though this book lacks specific examples, the contents arequite satisfacory to get an overview on OT ... Read more

Subjects:  1. Grammar    2. Language Arts / Linguistics / Literacy    3. Linguistics    4. Mathematics    5. Optimality theory (Linguistics    6. Optimality theory (Linguistics)    7. Science/Mathematics    8. Set Theory    9. Cognition & cognitive psychology    10. Language & Linguistics   

Reviews (7)

Best Introduction for the Financial Mathematician
This book is, as it were, manna from heaven for the aspiring financial mathematician, especially someone without a first degree in mathematics or a mathematically-based subject. The only prerequisites are a very good understanding of set-theory and some knowledge of the theory of continuous functions (at the level of a first course in real analysis, e.g. Apostol's Mathematical Analysis). The development is patient and there is sufficient help for the beginner (full solutions at the back, and, for practice, unproved propositions in the text with proofs at chapter-ends). The coverage is not overwhelming and anyone with the requisite preparation can digest the book in a term's work. Measure theory on its own is an incredibly dry subject. The authors do a great job of covering the essentials in about 300 pages, while making the subject interesting and applicable at the same time. A very attractive feature of the book is its brief focus on mathematical-finance applications. Most chapters end with a small section on such applications which is very useful for someone simultaneously studying mathematical finance. Particularly, it shows how to conceptualize financial models measure-theoretically. A very useful little volume indeed!

fine book
A correction to one of the previous comments.There is now an 'errata' on Springer's website.A 2nd edition of the book should be coming sometime, so you might want to check on that before buying.

A good introduction to Measure Theory
A good introduction to measure theory. Highly recomended if you are an undergraduate student in Mathematics or a graduate student in subjects such as Mathematical Statistics or Econometrics. Unfortunately, chapter 6 (on product measures) lacks of the clarity of exposition of precedent ones (what may be problem for anyone interested in probability theory). Read more

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

Subjects:  1. Computer Graphics - General    2. Computer Science    3. Computers - General Information    4. Evolutionary computation    5. Evolutionary programming (Comp    6. Evolutionary programming (Computer science)    7. Mathematics    8. Programming - Systems Analysis & Design    9. Science/Mathematics    10. Set Theory    11. Computational Intelligence    12. Computer architecture & logic design    13. Computers / Programming / Systems Analysis & Design    14. Evolvable Hardware    15. Evolvable Machine    16. Hardware Design   

Reviews (1)

The basics and some advanced topics beyond that
A solid foundation in set theory is one of the essential preconditions of being a good, working mathematician. I have taught nearly every course in the undergraduate mathematics curriculum and the basic concepts of set theory crop up on a regular basis. I have also taught nearly every course in the undergraduate computer science curriculum and those same ideas also pop up on a regular basis. Just last week when I was using finite automata to describe language recognizers it was necessary to remind the class about some basic concepts of set theory.
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Subjects:  1. Mathematics    2. Science/Mathematics    3. Set Theory    4. Mathematics / General   

Reviews (1)

Great Introduction to Measure Theory
This book is great. As an undergraduate I did an independent study using this book and learned lots of stuff. The exposition is nicely done and allows for a clear presentation of some very complicated ideas. There are also lots of great examples and applications, which can be really helpful when dealing with something as abstract as measure theory. The exercises mix well with the exposition and contain interesting results. You can learn a great deal from this book without needing to go to lectures, but it does help a lot to be able to ask somebody questions as the material gets quite tricky sometimes.
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Subjects:  1. Calculus    2. Mathematics    3. Measure Theory    4. Probabilities    5. Science/Mathematics    6. Set Theory    7. Mathematics / Calculus    8. Mathematics / Mathematical Analysis    9. Probability & statistics    10. Probability Theory   

Subjects:  1. Computer Books: General    2. Computer Science    3. Computers    4. Computers - General Information    5. Expert Systems    6. Expert systems (Computer scien    7. Expert systems (Computer science)    8. Fuzzy Sets    9. Fuzzy systems    10. Set Theory    11. Artificial intelligence    12. Computers / Expert Systems    13. General Theory of Computing   

Subjects:  1. Algebraic Geometry    2. Functional Analysis    3. Geometry - Algebraic    4. Group Theory    5. Homology Theory    6. Mathematics    7. Probability & Statistics - General    8. Science/Mathematics    9. Set Theory    10. Sheaf theory    11. Weil conjectures    12. Algebra    13. Deligne's Fourier transform    14. Deline's theory of weights and of purity    15. Etale cohomology    16. Hard Lefschetz Theorem    17. Mathematics / Geometry / Algebraic    18. Mathematics-Group Theory    19. Mathematics-Probability & Statistics - General    20. Springer representations Weyl groups    21. estimates of exponential sums    22. generalized Weil conjecture    23. middle perverse sheaves   

Reviews (1)

The New Standard for Measure Theory Books
This is a fantastic book on measure theory.The focus is on measure theory on its own right and not on probability.I was lucky to come across this book while canvassing the measure theory books at our library.I looked at the books by Billingsley, Halmos, Chung, Resnick, Rao, Rudin, Pollard, Dudley, Nielson, Stroock, Williams, Pitt, and many others.Hand-down, Vestrup is the best.Read more

Subjects:  1. Calculus    2. Integral Calculus    3. Integrals, Generalized    4. Mathematical Analysis    5. Mathematics    6. Measure Theory    7. Science/Mathematics    8. Set Theory    9. Calculus & mathematical analysis    10. Mathematics / Statistics    11. Probability & statistics   

Editorial Review

The search for infinity, that sublime and barely comprehensible mystery, has exercised both mathematicians and theologians over many generations. Jewish mystics, in particular, labored with elaborate numerological schema to imagine the pure nothingness of infinity, while scientists such as Galileo, the great astronomer, and Georg Cantor, the inventor of modern set theory (as well as a gifted Shakespearean scholar), brought their training to bear on the unimaginable infinitude of numbers and of space, seeking the key to the universe.Read more

Reviews (54)

engaging story of Cantor and his problems
I thoroughly enjoyed this book. It blends history, mysticism, mathematics and psychological interest into an engaging story. Though some of the mystical emphasis might be a little hokey, this was an excellent and very readable account of how Cantor came to his 'continuum hypothesis' and his deterioration into madness. Having an MS in abstract mathematics, and being an actuary by profession, I thought the author made the technical issues very conceptual and stimulating, retaining the accuracy they deserve. But, he did not just present technical material - he wove the psychological aspects related to the issue right into the mix. This made it quite fascinating. Not to be left hanging, he brings the story to a conclusion with Gödel's and Cohen's roles in solving the problem that drove Cantor (and presumably Gödel) mad. I highly recommend this title to anyone interested in the history of math, it's foundations, the continuum hypothesis or a story on how an important intellectual problem was brought to light and tackled over a period of centuries.

Mathemagic
"The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity" assures us that a linkage between the mystical and the purely logical will at least be explored. Thus, Amir D. Aczel's book is aptly titled I think, attempting as it does to encompass the antipodes of the mind grappling with a great unknown. Indeed, the mathematical quest for infinity may lead us to the very limits of human understanding. Science and rationality can aid us in this search, but at some juncture we are speculating upon the purely ineffable. We are beyond empiricism, peering into the magical realm of mathematics with Pythagoras, Plato, and Einstein.
Trying to hard to ride the Kabbalah trend
It is highly ironic that at the start of this book the author chides those celebrates who like to play Kabbalah just because of its new found trendyness because this is exactly what seems to be going on in this book.
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Subjects:  1. 1845-1918    2. Biography / Autobiography    3. Cabala    4. Cantor, Georg,    5. Infinite    6. Logic    7. Mathematical Physics    8. Religious    9. Science    10. Science/Mathematics    11. Scientists - General    12. Set Theory    13. Spirituality - General    14. Biography: general    15. History of mathematics    16. Popular science   

Reviews (1)

Excellent book as an advanced introduction.
My opinion is that this is the most readable and user friendly advanced book on Set Theory today. Especially the treatment of (Cohen's) Forcing is valuable, since other expositions on this subject were not suitable for beginning graduate students (Kunnen - very good, but very sophisticated,Jech - also good, but presents Forcing via Boolean Algebra, which is less widely used today, and the book is too long as an advance introduction).Read more

Subjects:  1. Combinatorics    2. General    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematical And Symbolic Logic    7. Mathematics    8. Science/Mathematics    9. Set Theory    10. Mathematical logic    11. Mathematical theory of computation    12. Mathematics / Combinatorics   

Subjects:  1. Geometry - Algebraic    2. Hodge theory    3. Mathematics    4. Science/Mathematics    5. Set Theory    6. Algebraic geometry    7. Algebraic topology    8. Applied mathematics    9. Complex analysis    10. Fields & rings    11. Quantum physics (quantum mechanics)   

Reviews (1)

first text to provide software for implementation of theory
This book provides a nice introduction to the mathematical theory of rare events and extreme values.It takes the point process approach to rare events using the empirical point process defined by the crossing of a high or low level to employ an approximate Poisson process.This approach has broad applicability and the authors use it to consider rare and extreme events for stochastic processes including Gaussian processes, Poisson point processes, extreme value models and nonparametric regression.Read more

Subjects:  1. Mathematics    2. Probability & Statistics - General    3. Science/Mathematics    4. Set Theory    5. Mathematics / Statistics    6. Probability & statistics    7. probability theory    8. statistics   

Reviews (1)

Great book for everybody (about Russian edition).
Everybody who has some interest to mathematics can understand this remarkable book. I was 17 when I read it first time. Now I have PhD in mathematics and often use examples from the book formy students and my children. Some things seem to be impossible(the curve covering a square, ...) but after reading this bookone can feel it, not only understand. ... Read more

Subjects:  1. General    2. History Of Mathematics    3. Infinite    4. Mathematics    5. Science/Mathematics    6. Set Theory    7. Mathematics / Logic    8. Mathematics / Set Theory    9. Philosophy of mathematics    10. Science: General Issues   

Subjects:  1. Advanced    2. Mathematics    3. Science/Mathematics    4. Selection theorems    5. Set Theory    6. Functional analysis    7. Mathematics / Advanced   

Subjects:  1. Computer algorithms    2. Engineering - General    3. Fuzzy sets    4. General    5. Heuristic programming    6. Mathematical Analysis    7. Mathematical optimization    8. Mathematics    9. Programming - Algorithms    10. Science/Mathematics    11. Set Theory    12. Mathematics / Applied    13. Optimization   

Subjects:  1. Borel sets    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Mathematical logic    6. Mathematics / Logic    7. Mathematics / Set Theory   

Subjects:  1. Mathematics    2. Set Theory   

Reviews (1)

not worth it
This book costs around $50 and the "chapters" are only one page long! This book looks like a rough draft to a book that should have never been published. There are very few problems and solutions. If you like to blow your hard earned money, this book is for you. ... Read more

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