Reviews (2)

A well-written, comprehensive introduction to the field
Cellular Automata: A Discrete Universe is a fascinating overview of the wide variety of discrete systems researchers have developed in the past quarter-century, and how these might be used to model a range of natural phenomena, including (in the book's most speculative section) the universe itself.Illustrations are supplied in all the right places--serving to enlighten, rather than overwhelm, the reader.The list of references is superb, making the book not only a great introduction and an important reference, but also a valuable guide to the field of complexity.

disappointing
This book is clearly a labor of love and contains a great wealth of material. However, it sorely lacks focus, the presentation is unclear and the results are often out of date. Here is a selection of more particular criticisms. Many rules remain undefined and the reader has to guess their details. The writer seems to be unfamiliar with the last five years worth of research, so particularly the chapter on probabilistic CA is not worth much. Far too many parts of the book are outlines of original papers (or books) with details omitted. Many claims in the said papers are accepted without scrutiny. (Two examples: (1) There is absolutely no evidence that any cellular automaton studied by Packard and Wolfram has a shape that is close to circular. (2) It has been discovered as far back as 1989 that the famous FHP lattice gas does NOT approach the two-dimensional Navier-Stokes equation, due to the fact that viscosity increases to infinity with increasing size of a finite system.) World Scientific editors need to do a much better job. ... Read more

Subjects:  1. Chaotic Behavior in Systems    2. Computer Bks - General Information    3. Computer Science    4. Computer Simulation    5. Computers    6. Chaos theory    7. Mathematical logic   

Subjects:  1. Discrete Mathematics    2. Mathematical Physics    3. Mathematics    4. Number Systems    5. Physics    6. Science    7. Science/Mathematics    8. Algorithms & procedures    9. Mathematical logic    10. Mathematical theory of computation    11. Mathematics / General    12. Science / Mathematical Physics    13. Science-Physics   

Reviews (23)

Good coverage of material; not enough rigor!
This book gave a good overview of the topics it covered, but it presented ideas and proofs in a very nonrigorous manner.Because of this, readers may find it difficult to create rigorous and correct proofs of the problems presented in the exercise sections.I'd recommend this book as a supplement to a course on the foundations of mathematics, but not as the main text.

One step from greatness.
The main virtue of this book, and which sets it apart from most other modern textbooks I have seen, is that it provides clear and usually illuminating explanations of the philosophical importance of the topics covered. These explanations and clarifications are given in a clear and usually crisp prose and emphasise the philosophical importance of whatever metalogical method or result they concern. I regard it as a very suitable companion or reference-work for the philosophically interested student of logic. For rigorous and very detailed proofs and definitions I normally consult a book like Mendelson's Introduction to Mathematical Logic, but usually I read what Boolos, Burgess and Jeffrey say too. The fact that the book (in its fourth edition at least) is divided into many short chapters makes it all the more useful as a companion. The short 'abstracts' that introduce each chapter deserve special mention. An index is the best way of localising information about something one knows one needs. The abstracts often do the reverse; they help one realise what one needs.
Math majors avoid
If you are a math major, you don't want this book. Get Cutland.
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Subjects:  1. Computable functions    2. General    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematics    7. Philosophy    8. Recursive functions    9. Mathematical logic    10. Philosophy / General   

Reviews (3)

Very usefull book.
I teach students, a mathematical olympic team, and this book will help them to get the training they need in order to have more medalls and achievements in their carreers. It has everything they need to do their exams and practice.

Excellent introduction to problem solving
The last time I competed in a mathematical competition was in elementary school.So when I recently picked up and tried to solve some old Olympiad and Putnam questions I was dumbfounded, to say the least. Then I discovered "The Mathematical Olympiad Handbook." This book is an excellent intro to problem solving.It is an immense help in dealing with the frustration of problems that will not yield.No solutions are given-- only outlines to the solutions(which you should only read part of if you get stuck, as the outlines will easily lead to a solution).This structure was an excellent choice as it gives novice problem solvers a chance to solve problems on their own with a little help if they need it.Highly recommend! A must-buy for problem-solvers.
This book has proven: The olympiad problems are not so hard as they appears. For every problem, there is a valuable solution outline ,teaching us how to attack it in a natural way. Furthermore, here is a good list ofreference books. ... Read more

Subjects:  1. British Mathematical Olympiad    2. General    3. History & Philosophy    4. Logic    5. Mathematics    6. Mathematics (General)    7. Problems, exercises, etc    8. Reference    9. Science/Mathematics    10. Mathematics / Logic    11. United Kingdom, Great Britain    12. c 1960 to c 1970    13. c 1970 to c 1980    14. c 1980 to c 1990    15. c 1990 to c 2000   

Subjects:  1. Algebra    2. Algebra - General    3. Axiom of choice    4. Logic    5. Mathematics    6. Science/Mathematics    7. Mathematical logic   

Subjects:  1. Computer Books: Operating Systems    2. Computer Programming    3. Horn clauses    4. Logic    5. Logic programming    6. Mathematics    7. Programming - General   

Reviews (7)

The Beauty of Equations
The book is very educational and includes numerous equations that represent turning points in humanity'sunderstanding of the world.Equations are in fields such as mechanics, electrodynamics, hydrodynamics, relativity, and quantum mechanics.The book starts with a short introduction to important mathematical concepts.The book appeals to anyone who is interested in physics and mathematics.

Inishgtful, Mesmerizing, Amazing
If you've ever wondered what kinds of formulas physicists deal with to solve complex ideas such as String Theory, look no further than this book.
A Wonderful Compilation of the `Rules of the Game'
The book was heavily wrapped in plastic -- Harvard University Press ?What was the title? `The Equations' ?I opened it in my local bookstore. And there were all the major equations describing mechanics, fluid dynamics, electrodynamics, thermodynamics, quantum mechanics, relativity, quantum chromodynamics, string theory, and more.Like the icons they were, they stood silently ... in the middle of the pages, with some brief explanations about them on the nearby page.
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Subjects:  1. Equations, Theory of    2. History    3. History & Philosophy    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Physics    7. Science    8. Science/Mathematics    9. History of science    10. Mathematical logic    11. Science / Physics   

Subjects:  1. Algebra - General    2. Categories (Mathematics)    3. Category Theory    4. Congresses    5. Geometry - Algebraic    6. Homology Theory    7. Logic    8. Mathematics    9. Science/Mathematics    10. Topology    11. Linear algebra    12. Mathematics / Algebra / General   

Subjects:  1. Developmental - General    2. Logic    3. Mathematical ability    4. Mathematics    5. Methodology    6. Science/Mathematics    7. Study & Teaching    8. Study and teaching    9. Psychology & Psychiatry / Cognitive Psychology   

Reviews (1)

Swell Book
This is a swell introduction to analysis. Plenty of good examples, with a well-ordered approach to the material. I particularly appreciated the section on the mindsets and assumptions that affect how we do mathematics. It's really helpful in seeing that mathematics is creative and intuitive, and not as bluntly algorithmic as so many high school classes seem. A quality read. ... Read more

Subjects:  1. Logic    2. Mathematics    3. Philosophy Of Mathematics    4. Science/Mathematics    5. Set Theory    6. Study & Teaching    7. Mathematics / General   

Reviews (3)

A superb introduction to the glories of Boolean algebra
This book is an undergrad introduction to Boolean algebraic logic and Halmos, who worked hard in the area during the 1950s, is the person to write it. The book includes Halmos's monadic algebra, but remains at the undergrad level because he stops short of his full-blown polyadic algebra (on which, see Halmos's "Algebraic Logic," which AMS keeps in print and is a fine read).
Interesting view on logic
In his "automathography" Halmos described his views on logic which he had in the 1960's.He felt that logic, as usually stated, was very un-profound, unrigorous, combinatorial amusement.He felt additionally that logic could be put on a firm algebraic footing through the theory of Boolean rings.At that time he interpreted many things in logic in terms of Boolean rings.This book is, in some sense, the child of these labors.Halmos created this book in his usual easy to read style, and when he said that few prerequisites were assumed, he meant it.I found the (short) book very interesting, but I also found the introductory pages seemed to drag.Perhaps this is because I already know something about logic, but the rest of the book was interesting and self contained.This book was lighter than most logic books I've seen.These books were mainly written by philosophers in some capacity or other, and they never stopped their thick prose.

A Builder of a Solid Foundation in Mathematics
It can be strongly argued that logic is the most ancient of all the mathematical sub-disciplines. When mathematics as we know it was being created so many years ago, it was necessary for the concepts of rigidanalytical reasoning to be developed. Of the three earliest areas, geometrywas born out of the necessity of accurately measuring land plots and largebuildings and number theory was required for sophisticated countingtechniques.Logic, the third area, had no "practical" godfather, otherthan being the foundation for rigorous reasoning in the other two. In theintervening years, so many additional areas of mathematics have beendeveloped, with logic and logical reasoning continuing to be thefundamental building block of them all. Therefore, every mathematicianshould have some exposure to logic, with the simple history lessonautomatically being included. This short, but excellent book fills thatniche.Read more

Subjects:  1. Algebra - General    2. Logic    3. Logic, Symbolic and mathematic    4. Logic, Symbolic and mathematical    5. Mathematics    6. Science/Mathematics    7. Mathematical logic    8. Mathematics / Combinatorics   

Subjects:  1. Artificial Intelligence - General    2. Computer Books: General    3. Computer Science    4. Computers    5. Congresses    6. Formal Language Theory    7. Formal languages    8. General    9. Logic    10. Logic, Symbolic and mathematic    11. Logic, Symbolic and mathematical    12. Mathematical And Symbolic Logic    13. Medical / Nursing    14. Programming - General    15. Computers / Artificial Intelligence    16. Grammatical inference    17. algorithmic learning    18. computatiional linguistics    19. context-free grammars    20. context-free languages    21. learning algorithms    22. machine learning    23. probabilistic grammars    24. statistical learning   

Reviews (4)

Good Biography, a bit heavy on the math
This book has a kind of interesting way of doing a biography. The subject, Godel, is one of the pre-eminent mathematicians of the twentieth century. This biography, written by a mathematician spends a good bit of time on the math that Godel was doing as well as the story of his life.
Excellent.
An excellent biography of Godel. Examines his personal life and mathematical work in an integrated manner. Dawson is thorough, well-researched, and shows a command of the mathematics involved. He provides the most accurate picture available of the real Godel- in contrast to the anecdotal, 'crazy-genius' stories you see elsewhere. This is not a popular account of Godel's work, so the reader will need an understanding of fundamental mathematical logic and Godel's theorem to appreciate much of the book. But Dawson does provide a lot of history of mathematical logic, including a great chapter on developments up to 1928 that could stand by itself. The appendix provides a chronology, genealogy, and "biographical vignettes" of other important logicians.

The definitive biography of Kurt Godel
Knowing what went on in the mind of Kurt Godel will forever be unattainable.Nonetheless, John Dawson comes as close as possible to understanding what made Godel click.Read more

Subjects:  1. Biography & Autobiography    2. Biography/Autobiography    3. History & Philosophy    4. Logic    5. Scientists - General    6. Biography: general    7. Mathematical logic   

Reviews (1)

Poor refrence/class textbook. Good preview, general overview for selected topics in FOM
Having purchased this text (as part of the Springer Undergraduate Mathematics Series), I expected a decent publication. I had purchased and used their Number Theory text (Jones & Jones) and I was satisfied with the overal quality of the problem sets and the exposition.
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Subjects:  1. Categories (Mathematics)    2. Category Theory    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematics    7. Science/Mathematics    8. Set Theory    9. Mathematical logic    10. Mathematics / Logic   

Reviews (2)

the best math textbook I've ever had
This book was the foundational textbook for a 100-level class in symmetry at my university. I recommend it highly to anyone who wants to get a better feel for what mathematicians actually do and think about and work with. Folks who never got into the higher math classes often have a different idea of what mathematics is all about than mathematicians. At the level of introductory algebra and geometry and even some calculus, math education often seems to be mainly about memorizing formulas and recognizing in which situations to apply them. That's an important thing to learn, but it is not useful for imparting an idea and a feel of the field of mathematics as a whole. Farmer's book brings home the understanding that mathematics is, at its heart, about patterns and that mathematics is not so much about memorization and application as it is about discovery.
An excellent primer on abstract algebra
Groups are the first structures encountered in abstract algebra and form the foundation for most of the others. Fortunately, they are also the easiest to physically represent, so in some sense they are the most concrete. In this book, groups are introduced as the motions and structures of geometric figures, so the presentation is largely by diagram rather than formula. Very little previous knowledge of mathematics is required and after reading the book, you will have a solid understanding of what a group is. Read more

Subjects:  1. Group theory    2. Logic    3. Mathematics    4. Pattern perception    5. Science/Mathematics    6. Symmetry (Physics)    7. Theory Of Groups    8. Groups & group theory   

Reviews (2)

Waste of time
I'm quite skeptical of the merits of the analytic philosophers with regard to their labor in mathematical logic.Although much of my early understanding of the sciences and mathematics came from mathematical logicians, such as Russell, Carnap, Reichenbach, Hahn and Weyl, I discovered that knowledge to be a foundation built on sand.D'Abro notes that Russell never contributed anything productive to the development of mathematics.He never "created" any.Similarly, Weyl tackles the age old problem of founding the real numbers in a manner independent of geometrical methods.The latter would be circular reasoning since it is precisely that which we wish to depart from since sets are deemed more mathematically "pure" than geometrical lines.However, if, as Poincare says, the reasoning of Frege and hence of Dedekind leads to unwelcome paradoxes or contradictions, then Weyl's task is monumental indeed.
a fascinating detour
I first learned of this book from Eves and Newsom back in the early 1960's. It sounded fascinating but I couldn't read German. Now we're lucky to have it in Englsh translation with an introduction that relates Weyl's notation and terminology to the current one. (Or, if you're really out of date like me, you can use it in reverse to catch up on the modern field of foundations studies).
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Subjects:  1. Calculus    2. Foundations    3. Mathematical analysis    4. Mathematics    5. Philosophy & Social Aspects    6. Science/Mathematics    7. Calculus & mathematical analysis    8. Mathematical logic    9. Mathematics / General   

Reviews (2)

An easy and practical approach to fuzzy set theory
The book gives a clear and intuitive description of fuzzy math and its application. The discussions are done neatly and nicely. It doesn't get into hardcore math discussions very much; instead, it focuses on applications and practice. Therefore, it doesn't take much time to get the idea, and you are not bothered with very complex math proofs. The level of the theory is also limited to what needed in application. To my belief this is one of the best books for engineers and applied mathematicians.

Review about Zimmermann's Book !
This book is a kind of essential book. The growth in Fuzzy Science has showed more and more possibilities in applications of its concepts. The book shows the vast applicability of Fuzzy in details and how this new approach can be useful in domains with high degree of uncertainty. Read more

Subjects:  1. Applied    2. Artificial Intelligence - General    3. Fuzzy Sets    4. Mathematics    5. Operations Research    6. Operations Research (Engineering)    7. Science/Mathematics    8. Set Theory    9. Computers-Artificial Intelligence - General    10. Fuzzy set theory    11. Mathematics / Logic    12. Mathematics / Set Theory    13. Mathematics-Applied   

Editorial Review

Could it be true that Whitehead and Russell's Read more

Reviews (14)

A monumental tower of Babel
Poor Whitehead and Russell, trying to build a perfect, complete, self-consistent foundation for mathematics instead built one enormous, convoluted monstrosity that led to a spectacular collapse at the hands of G�del.Using cold logic (in a horribly arcane notation) they set upon themselves the task of ridding mathematics from ambiguity and counter-intuitive paradoxes such as the Banach-Tarski Paradox of 1924.Using the Zermalo-Fraenkel Axioms upon which modern mathematics is conventionally based, the Banach Tarski Paradox, resulting principally from the Axiom of Choice, states that if S and T are solid three-dimensional spheres of possibly different radii, (one a golf ball, one a basketball say), then S and T are equivalent by finite "cut and paste" decomposition.Clearly we believe this is nutty, but we are forced to live with this paradox because so many theorems of non-paradoxical mathematics depend on the Axiom of Choice.
ludicrously quixotic work
I have not read this book.I tried, having been fascinated by logic and mathematics since high school, but it has absolutely nothing to offer most people.in fact I find it hard to believe anyone has ever read this book.The 4 and 5 star reviews on this page should be taken as evidence there are some people out there with very different taste from mine, and I bet yours. In fact I have difficulty believing they are serious.
A Hallmark in the History of Mathematics and Philosophy.

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Subjects:  1. Foundations Of Mathematics    2. General    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematics    7. Philosophy    8. Philosophy Of Mathematics    9. Science/Mathematics    10. Mathematical logic    11. Mathematics / Combinatorics    12. Mathematics--Philosophy   

Reviews (2)

Standard by default
Almost four decades after being written, this is still the standard graduate survey text. A large part of the reason is that there is little competition, but it is also a good book on its own merits. The author writes with a clarity and concision you rarely see in a math (or any) textbook. Proofs are straighforward, not tricky or convoluted. There are many excercises and with detailed setup. The exercises are often quite hard, requiring significant extension from the text.
Rock-solid introduction to Mathematical Logic
Since my first contact with mathematical logic, I've always seen it as a kind of brainwashing, forcing one's mind to work based on several little pieces of thought. Nevertheless, it can be described as "a necessary evil", because the mindless use of mathematical logic throughout mathematics is very treacherous, as it can be seen in the problems regarding the axiom of choice, the Banach-Tarski paradox inmeasure theory, the issues about the undecidability of certain assumptions in set theory, and the very limitations of mathematical logic.Read more

Subjects:  1. Logic    2. Logic, Symbolic and mathematic    3. Logic, Symbolic and mathematical    4. Mathematics    5. Science/Mathematics    6. Mathematical logic   

Reviews (3)

He hasn't yet given up on the 'paradoxes'
You'll notice that although GG still lists Cantor's "paradox" in his index, in the text he doesn't quite bring himself to say that there is such a thing.Why not?Because he has read Garciadiego's BERTRAND RUSSELL AND THE ORIGINS OF THE SET-THEORETIC 'PARADOXES,' which shows quite clearly that there is no such thing as Cantor's paradox, or the Burali-Forti paradox, or Russell's for that matter.The so-called "set-theoretic paradoxes" were for the most part inventions of Russell, and not a single one from the period, comes out as anything but a meaningless formulation.