Reviews (3)

Cantor,A Top Mathematician Who Unifies God and Sciene
This is a great book on the work of Georg Cantor.
Philosophy that can be mathematically proven
Some areas of mathematics can be described as philosophy that can be proven, and that certainly applies to the transfinite arithmetic created by Georg Cantor. When his results were first published, they were met with a great deal of opposition by many established and influential mathematicians. Considering the revolutionary aspects of his work, the fact that there was opposition was not surprising and indeed necessary for mathematics to properly advance. However, the opposition to Cantor's main results was so strong that the story that it drove him mad has become a part of the mathematical folklore. As Dauben is careful to point out, his research indicates that Cantor would have suffered from the bouts of depression independent of the degree of opposition to his work and most likely independent of what kind of work he did. In fact, Cantor himself is quoted as stating that his time spent in institutions was some of the most restful and productive of his life. Hard core and worth it
I found this was an excellent memoir of Cantor and his ideas. It goes far more deeply into the mathematics than other discussions of Cantor, and makes you want to read more about both set theory and about the development of topology in the early twentieth century. It also attempts to place Cantor's philosophy and mathematical ideas into a psychological context as well, which is probably appropriate - even essential - in the case of Cantor. Though, in twenty years, this aspect of the book may notwear well. All in all, it is a refreshingly strong and insightful treatment of one of the major historical figures in nineteenth century mathematics. ... Read more

Subjects:  1. 1845-1918    2. Cantor, Georg,    3. History    4. Infinite    5. Mathematics    6. Science    7. Science/Mathematics    8. Set Theory    9. Transfinite numbers    10. Cantor, Georg    11. History of Science and Medicine, Philosophy of Science    12. History of mathematics    13. Philosophy    14. Science / History   

Subjects:  1. General    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Mathematics / General   

Subjects:  1. Calculus    2. Fuzzy integrals    3. Fuzzy measure theory    4. Game Theory    5. General    6. Mathematical Analysis    7. Mathematics    8. Science/Mathematics    9. Set Theory    10. Artificial intelligence    11. Fuzzy set theory   

Subjects:  1. General    2. Logic    3. Logic, Symbolic and mathematical    4. Mathematics    5. Science/Mathematics    6. Set Theory    7. Mathematics / General   

Subjects:  1. Combinatorics    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Mathematical logic    6. Mathematics / Combinatorics   

Subjects:  1. Mathematics    2. Multivariate Analysis    3. Probability & Statistics - Multivariate Analysis    4. Research    5. Science/Mathematics    6. Set Theory    7. Study & Teaching    8. Communication Studies    9. Social Science / Research    10. Social research & statistics   

Reviews (2)

Great book, but too expensive
This is maybe the best book about the subject. The author not only traces the mathematical roots of the new discoveries, showing like no other has done the relationships with the mathematics of the beginning of the XIX century, but he also gives a detailed, and very vivid, description of the characters of the people involved. (Maybe the best part is where he describes the correspondence between Cantor and Dedekind). But there should be a paperback version, for people like me, living in Colombia, the price is terribly high. Even in Spain, where the author comes from, it is inaccesible. There also should be a spanish version (there was one previous version in spanish, but now it is out of the market).

A very thorough, balanced account...
of the complex origins and development of set theory. Riemann's
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Subjects:  1. General    2. Mathematics    3. Science    4. Science/Mathematics    5. Set Theory    6. 20th century    7. History of ideas, intellectual history    8. History of science    9. Mathematics / History    10. Philosophy of mathematics    11. c 1800 to c 1900   

Subjects:  1. Artificial Intelligence - Fuzzy Logic    2. Computer Books: General    3. Computers - General Information    4. Fuzzy Sets    5. Fuzzy logic    6. Mathematics    7. Neural Computing    8. Neural Networks    9. Set Theory    10. Artificial intelligence    11. Computers / Artificial Intelligence    12. Fuzzy set theory    13. Mathematical theory of computation   

Reviews (1)

The missing link
I'm not sure how many of us there are out there, but I am one of a breed of consumers of applied mathematics who learned some pretty sophisticated mathematical technology without the rigor of pure mathematics. Although this book is aimed at freshmen entering mathematics programs who need to be inculturated into the world of pure mathematics, I found it to be the crucial link I needed to advance my own applied mathematical training. I reached a point where I was ready to move from applied texts to the more cryptic world of math texts written for graduate mathematicians. Unfortunately, I was not properly trained to decypher their special language and way of doing things, particularly that of the formal proof. I found reading introductory texts in analysis to be like trying to learn Japanese from books which were themselves written in Japanese. Then I found this wonderful little text. It made things much more accessible to me and helped me crack enough of the code where I could find my way around those analysis texts, which in turn allowed me to move on to the graduate math texts containing the methods I am studying now. The book is a bit high priced for its size, but for me it was well worth it. ... Read more

Subjects:  1. General    2. Logic, Symbolic and mathematical    3. Mathematics    4. Science/Mathematics    5. Set Theory    6. Mathematics / General    7. Number theory   

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

Reviews (2)

First systematic exposition of the Anti-Foundation Axiom
As the title suggests, this is the first systematic exposition of classic set theory without the axiom of foundation. What replaces it, the anti-foundation axiom, allows sets to be members of themselves and it is this type of circularity that, as the authors claim, lies at the heart of understanding knowledge in interacting systems (like computing machines or game-theoretic agents or Liar-type sentences that refer to themselves).
Fasciniating look at a new extension of set theory
This book discusses recent advances in the general field of set theory.The authors study a variant of ZF in which the axiom of foundation is replaced by a new axiom allowing non-well-founded sets.Just as thenaturals can be extended to the integers, and the integers to therationals, and the reals to the complex numbers, in each case by positingnew numbers that are the solutions to a class of equations, so this bookposits an extension to any model of set theory consisting of the solutionsto a class of (systems of) equations having no solutions in ZF. Thesimplest example is the equation Read more

Subjects:  1. Cycles    2. Hypersets    3. Mathematics    4. Science/Mathematics    5. Set Theory    6. Mathematical logic    7. Mathematics / Combinatorics    8. Mathematics / Set Theory   

Subjects:  1. Item response theory    2. Mathematics    3. Nonparametric statistics    4. Probability & Statistics - General    5. Research    6. Science/Mathematics    7. Set Theory    8. Statistical methods    9. Social Science / Research    10. Social research & statistics   

Subjects:  1. Information Theory    2. Mathematical Analysis    3. Mathematics    4. Probabilities    5. Probability & Statistics - General    6. Science/Mathematics    7. Set Theory    8. Characteristic functions    9. Convergence of random series    10. Markov dependence    11. Mathematics / Statistics    12. Random Fourier series    13. Weak limit laws   

Reviews (1)

OK
Books for transitional mathematics courses are becoming more common and this book falls short of most of them.The writing style is nice and dry, but the topics in the book don't flow well.The author doesn't develop foundational material in the first three chapters (no axiomatic set theory or predicate calculus).Also, there isn't enough discussion of proof techniques (existencial and universal arguments, indirect proofs, etc.).The abstract algebra and analysis chapters aren't enough to give a full treatment, but are beyond the scope of good "bridge" course.
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Subjects:  1. General    2. Logic    3. Logic, Symbolic and mathematic    4. Logic, Symbolic and mathematical    5. Mathematical Analysis    6. Mathematical And Symbolic Logic    7. Mathematics    8. Philosophy Of Mathematics    9. Proof theory    10. Science/Mathematics    11. Set Theory    12. Mathematical foundations    13. Mathematics / General   

Subjects:  1. Advanced    2. Computer simulation    3. Mathematical models    4. Mathematics    5. Probability & Statistics - General    6. Probability & Statistics - Multivariate Analysis    7. Probability & Statistics - Regression Analysis    8. Science/Mathematics    9. Set Theory    10. Stochastic processes    11. Mathematical modelling    12. Probability & statistics    13. Stochastics   

Subjects:  1. Calculus    2. Integral Calculus    3. Lebesgue integral    4. Mathematics    5. Measure Theory    6. Science/Mathematics    7. Set Theory    8. Applied mathematics    9. Functional analysis    10. Integral equations    11. Mathematics / General    12. Numerical analysis   

Subjects:  1. Applied    2. Engineering - Industrial    3. Game Theory    4. Mathematics    5. Science/Mathematics    6. Set Theory    7. Technology & Industrial Arts    8. Mathematics / Applied    9. Operational research    10. Operations Research    11. Optimization Methods    12. Optimization Research   

Subjects:  1. Data processing    2. Fractal Geometry    3. Functional Analysis    4. Geometry - Algebraic    5. Graphic methods    6. Invariant sets    7. Mathematical & Statistical Software    8. Mathematics    9. Number Theory    10. Science/Mathematics    11. Set Theory    12. WInSet    13. Fractals    14. Mathematical logic    15. Non-linear science   

Subjects:  1. Algebra - General    2. General    3. Logic    4. Mathematics    5. Model theory    6. Science/Mathematics    7. Set Theory    8. Algebra    9. Mathematical logic    10. Mathematical modelling    11. Mathematics / Set Theory   

Subjects:  1. Mathematical Analysis    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Complex analysis    6. Mathematics / Mathematical Analysis    7. Operator theory