Subjects:  1. Computer Books: General    2. Computers    3. General    4. Logic    5. Logic Design    6. Mathematics    7. Programming - Software Development    8. Computers / Programming / Software Development    9. First-order logic    10. Mathematical logic   

Reviews (1)

The Mystery of the Missing Words
Most of the "proofs" in this book will be of moreRead more

Subjects:  1. Charts, diagrams, etc    2. General    3. Mathematics    4. Science/Mathematics    5. Mathematical logic    6. Mathematics / Combinatorics   

Subjects:  1. Automata    2. Computer Books: General    3. Computer Science    4. Computers    5. Computers - General Information    6. General    7. Logic    8. Machine theory    9. Artificial intelligence    10. Computer Programming    11. Computers / Computer Science    12. Mathematical logic    13. applications of computer Science    14. computational complexity    15. formal languages    16. mathematics Logic   

Reviews (4)

Very ambitious project.
This book differs from most books on the theoretical formulations of artificial intelligence in that it attempts to give a more rigorous accounting of machine learning and to rank machines according to their intelligence. To accomplish this ranking, the author introduces a concept called `universal artificial intelligence,' which is constructed in the context of algorithmic information theory. In fact, the book could be considered to be a formulation of artificial intelligence from the standpoint of algorithmic information theory, and is strongly dependent on such notions as Kolmogorov complexity, the Solomonoff universal prior, Martin-Lof random sequences and Occam's razor. These are all straightforward mathematical concepts with which to work with, the only issue for researchers being their efficacy in giving a useful notion of machine intelligence.
The State of the Art as it Exists Today
Artificial Intelligence has proven to be one of those elusive holy grails of computing. Playing chess (very, very well) has proven possible, while driving a car or surviving in the wilderness is a long, long way from possible. Even the definition of these problems has proven impossible.
Theoretical universal AI
Solomonoff's famous inference model solves the inductive learning problem in a universal and provably very powerful way.Many methods from statistics (maximum likelihood, maximum entropy, minimum description length...) can be shown to be special cases of the model described by Solomonoff.However Solomonoff Induction has two significant shortcomings: Firstly it is not computable, and secondly it only deals with passive environments.Although many problems can be formulated in terms of sequence prediction (for example categorisation), in AI in general an agent must be able to deal with an active environment where the agent's decisions affect the future state of the environment.
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Subjects:  1. Algorithms    2. Artificial Intelligence - General    3. Artificial intelligence    4. Computer Books: General    5. Computer Science    6. Computers    7. Computers - General Information    8. Logic    9. Probabilities    10. Adaptive Control Theory    11. Algorithmic Information Theory and Statistics    12. Computers / Artificial Intelligence    13. Reinforcement Learning    14. Sequential Decision Theory    15. Universal Sequence Prediction   

Subjects:  1. Artificial Intelligence - General    2. Computer Books: General    3. Computer Science    4. Computers    5. Computers - General Information    6. Logic    7. Computers / Artificial Intelligence    8. Computing and Information Technology    9. algorithmic learning    10. artificial intelligence    11. artificial neural networks    12. clustering    13. data analysis    14. data mining    15. decision making    16. evolutionary algorithms    17. fuzzy neural systems    18. fuzzy sets    19. genetic algorithms    20. image processing    21. intelligent systems    22. knowledge discovery    23. machine learning    24. multi-agent systems    25. multiple classifier systems    26. neural networks   

Reviews (2)

Worth buying a used copy.
This book is half mathematics and half discussion. Parts 2 & 3 cover the material for an integrated, introductory course in computability theory and logic (the primitive recursive functions, mu-recursive functions and Turing machines and their equivalence, first-order logic, some formal number theory, and Godel's first and second incompleteness theorems). Parts 1 & 4 are given to philosophical discussion and (to a lesser extent) historical background. The longest chapters are one examining Church's thesis and one on intuitionist/constructivist views of mathematics. Overall the book is clearly written and well organized, and it contains interesting selections from the writings of prominent figures in the foundations of mathematics throughout.
when critical thinking, computer and math meet at one
this book takes you into the world of basic pure math. it covers the basic elemects of math such as sets, functions, and proofs. but what is really making this book great and far apart from other similiar books is its elaboration of recursive function and computability, and i find it interesting. ... Read more

Subjects:  1. Computable functions    2. General    3. Godel's theorem    4. Gèodel's theorem    5. Logic    6. Logic, Symbolic and mathematic    7. Logic, Symbolic and mathematical    8. Mathematical And Symbolic Logic    9. Mathematics    10. Philosophy Of Mathematics    11. Science/Mathematics    12. Mathematical logic    13. Mathematical theory of computation    14. Philosophy / General   

Subjects:  1. Geometry - General    2. Logic    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Calculus & mathematical analysis    7. Mathematics / Mathematical Analysis   

Reviews (1)

Interesting, useful, concise
I have got several ideas from this book. I have never used Mathematica, but one of the most important features of the book, is the fact that is enough clear, and its code can be translated to oher languages veary easy.I recomend this book for every person interested in cellular automataapplications and implementations rather that pure theory. ... Read more

Subjects:  1. Applied    2. Automata    3. Cellular automata    4. Computers - Other Applications    5. Mathematica    6. Mathematica (Computer program    7. Mathematica (Computer program language)    8. Mathematical models    9. Mathematics    10. Philosophy & Social Aspects    11. Physics    12. Programming - General    13. Science/Mathematics    14. Computer modelling & simulation    15. High level programming languages    16. Mathematical logic   

Reviews (3)

Too short on explanation
This text is intended for seniors or beginning grads. The first three of seven chapters form a very quick survey of naive set theory. Since it aims at a more advanced audience, it is not as explanatory as Enderton and the exercises assume more maturity. Chapters 4 - 7 survey some advanced topics that aren't part of the usual introductory set theory course. These chapters have no exercises.
Superb!
Keith Devlin is one of those rare research mathematicians who is able to make recent advances in mathematics understandable and interesting to those whose mathematical education is obsolete or incomplete. I'm in the former category, having done my graduate work in pure math 50 years ago; although I've tried to keep up, constraints of time and other obligations have made it difficult.
At times not so easygoing, but indeed a joy to read ...
Anyone seeking a deeper understanding of the foundations of the mathematics will benefit from reading this excellent book.Read more

Subjects:  1. General    2. Logic    3. Mathematics    4. Science    5. Science/Mathematics    6. Set Theory    7. Mathematics / Logic    8. Mathematics / Set Theory    9. Science-General   

Reviews (7)

focuses on the contributions of Abel to the unsolvability of the quintic
Abel's Proof takes an interesting approach to mathematical writing. The author places all mathematical formulas and derivations in boxes that are separate from the flow of the text so you don't have to do the math if all you want is a knowledge of the history of this era in mathematics. The author does a great job of explaining this history, covering the story of the factoring of polynomials in general but focusing on the unsolvability of the quintic. Abel's life of poverty is covered in detail. There is a lot of mathematics, if you are interested, including how to factor a cubic polynomial and Abel's proof of the unsolvability of the quintic. I found the math somewhat hard to follow but worth the effort of doing so. I found Abel's story to be very sad. The book is worth reading just for his life story alone.

a nice little gem
"Abel`s Proof" is a nice little book which tackles with the unsolvability issue in mathematics within the context of Niels Henrik Abel`s proof of the unsolvability of quintic equations with radicals. The text is an enjoyable account of a rather importantsubject in the whole history of mathematics in some 200 pages, and the quality of writing is laudable. The mathematical details and clarifications are given in boxes along the way, and the book in general is blended with numerous mathematical figures and portraits.
Omar Khayam and Al-Khwarazimi were Persian
Both Omar Khayam and Al-Khwarazimi were undoubtedly Persian and the author did make a mistake referring to them as Arab mathematicians.Both came from the greater Khorasan province, which was a Persian province and populated by a completely Persian speaking population. ... Read more

Subjects:  1. Essays    2. History & Philosophy    3. Logic    4. Mathematics    5. Science/Mathematics    6. History of mathematics    7. Technology / Social Aspects   

Subjects:  1. Applied    2. Computer science    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematical And Symbolic Logic    7. Mathematics    8. Number Theory    9. Science/Mathematics    10. Set Theory    11. Mathematical logic    12. Mathematics / Logic   

Reviews (4)

Very understandable and a bargain
I bought this book to teach myself logistic regression after buying a much much more expensive text . If you've had the experience of trying to learn a stats technique on your own then you know that you'll probably need more than one book.If I could go back, I would buy this one first and then move on to other more expensive and comprehensive texts.I had a good grasp of multiple regression already and found this book's orientation to logistic regression, done by drawing parallels with multiple regression, very understandable.It was easy to read cover to cover and gave great explanations of the background math, without being at all heavy with formulas.If you are taking a logistic regression course and are having a hard time following the explinations in the text assigned for the class, this would likely provide a good alternative for helping you grasp the concepts.

Excellent Over view
Prof Scott Menard must be commended for writing an excellent book on Logistic Regression. Explaining it in the context of commercially available software packages is a very good idea. I was able replicate some his analysis using SAS on the data set used in this book (available on line from ICPSR, Univ of Michigan). A Nice Overview
A good, cheap overview of logistic regression analysis.Read more

Subjects:  1. General    2. Logic    3. Logistic distribution    4. Mathematics    5. Probability & Statistics - General    6. Regression analysis    7. Research    8. Science/Mathematics    9. Probability & statistics    10. Social Science / Research    11. Sociology, Social Studies   

Reviews (3)

Boolean Algebra and Its Applications
This is by far one of the best math books in the Dover catalogue. While the prose is admittedly dry, the clarity of the exposition is flawless. The author begins his discussion with a chapter on set theory and wisely takes an intuitive appraoch rather than a theoretical one. This makes the second chapter, which gives an axiomatic account of the fundamentals of Boolean algebra, much easier to digest. Once you master the first two chapters, the rest of the books is smooth sailing. From here the author gives detailed, yet succinct, accounts of the applicatons of Boolean algebra to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. Although the book is aimed primarily at math, computer science, and electrical engineering majors, it accessible to anyone who is comfortable with college level mathematics. It is especially helpful to the philosophy student who wishes to learn about symbolic logic and its applications to the foundations of computer science.

Boolean Algebra
Though written with dry prose, this book is very much worth studying toanyone with an interest in the subject. dry
This book fell to the floor where it was pounced upon and chewed by my nieces 3 pounddog who `forthwith' lost 10 pounds of the nectar of life. We shall be suing Dover for her wrongful death by dehydration. BooleanAlgebra is a fine subject but this book ... the most turgid bit of writingsince `OG the trog-dude' first scratched a mark on a cave wall. ... Read more

Subjects:  1. Algebra - General    2. Algebra, Boolean    3. Mathematics    4. Science/Mathematics    5. Mathematical logic    6. Mathematical theory of computation    7. Mathematics / General   

Reviews (9)

Concise and pleasant
Smullyan gives an introduction to logic borrowing central ideas from Henkin, Herbrand, and Gentzen. The tableau method using his unifying notation is very simple and provides an analytic proof method for first-order logic. Various completeness and soundness proofs are given (e.g. using maximal consistent sets, truth sets, axiom systems). Gentzen systems, linear logic, and Hintikka block tableaux (like Smullyan tableaux using sets of formulas) are also covered. His unifying principle (generalized by P. Andrews for type theory) and the fundamental theorem of quantification theory are neat.
Great stuff.
First, this isn't one of Smullyan's popular puzzle books- its a serious mathematics text. Second, don't use this as your first exposure to first-order logic (note the title doesnt say "Introduction to ...")- although logically self-contained, it requires some experience to appreciate what a neat little book this is. An Oddity But a Good-ity. Wait, that's terrible.
The reviewer from Illinois gave a very good characterization of Smullyan's style here: Read more

Subjects:  1. First-order logic    2. Logic    3. Mathematics    4. Science/Mathematics    5. Mathematical logic    6. Mathematics / General   

Reviews (1)

A very good one. Misses some of the more advanced techniques
This book is a very useful one, if not a must. ... Read more

Subjects:  1. Algorithms    2. Recursion theory    3. Regression Analysis    4. Mathematical logic   

Reviews (1)

alternatives to Euclid
For some 2000 years, Euclid's postulates of geometry were considered the final word. As axioms, they seemed unassailable. Yet this neat little book describes how one mathematician stumbled on equally valid alternatives. Gray shows how Bolyai started by looking at Euclid's most controversial axiom. That two parallel lines in a plane will not intersect. An alternative formulation of which is that the angles of a triangle will always sum to pi radians.
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Subjects:  1. General    2. Geometry - Non-Euclidean    3. History    4. History & Philosophy    5. Logic    6. Mathematics    7. Reference    8. Science/Mathematics    9. History of mathematics    10. History of science    11. Non-Euclidean geometry    12. Science / History   

Subjects:  1. Artificial Intelligence - General    2. Computer Science    3. Computers - General Information    4. Logic    5. Mathematics    6. Science/Mathematics    7. Computers / Artificial Intelligence    8. General Theory of Computing    9. Mathematical logic    10. Mathematics and Science   

Subjects:  1. General    2. Logic    3. Mathematics    4. Operads    5. Science/Mathematics    6. Algebraic topology    7. Theoretical methods   

Reviews (19)

Laws of Form
An Excellent book. It contains the information from the original at a much more affordable price.

We Take the Form of Distinction for the Form
I take the key sentences in Spencer-Brown's Laws of Form to be the first two sentences at the beginning of Chapter 1: "We take as given the idea of distinction and the idea of indication, and that one cannot make an indication without drawing a distinction. We take therefore the form of distinction for the form." This book is a carefully crafted and beautifully written account of how the act of imagining a distinction gives rise to worlds of multiplicity from a unity where no distinction is actually possible. The first mathematics that so arises is remarkably close to the boolean mathematics with which all logicians, engineers and philosphers are familiar. Once discovered it is easy to exhibit. Let < > stand for a typographical distinction between outside < inside > outside.Note that in imagining distinctions using linear typography, one must make extra cuts between right and left. Drawing circles in the plane is easier (and C. S. Peirce did this long before Spencer-Brown). Spencer-Brown uses a planar notation that is simple to write and less easy to type. In any case, we make a mathematics from the distinction < >.Think of < >as an "elementary particle" that can interact with itself in two ways. 1. It can interact with itself and produce itself, or it can produce two copies of itself from itself. < > ----- < > < > Read the dotted line in either direction. 2. It can interact with itself to cancel to nothing, or a pair of two copies of the particle can emerge from nothing. < < > > ----- Yes that's nothing on the right hand side, but maybe you would like a symbol for nothing. Ok. Let # stand for nothing. This means that you can erase # or put it in whenever you want to, and that means anywhere. Then we have < < > > ----- # With these modes of particle interaction we have an arithmetic of distinctions. For example < < > < > > -----< < > > -----# The patterns of this arithmetic have their own algebra, and when one makes the critical distinction between < > as an operator, and < > as a value, this algebra gives rise to the patterns of boolean algebra. There is much more, but the key point is the simplicity of this approach. This simplicity can be applied to many complex systems to locate the key patterns that make them tick. The mark < > is itself an imaginary boolean value. At the outset the mark could be any imagined distinction at all, and the reader will have to ask how those distinctions managed to appear so solid and real. Two marks in a line do not create an inside and an outside. You the reader accomplished that trick. Then again, the mark was not boolean until the context became boolean, and operators separated from operands. This separation is a departure from the beginning. Later considerations in Chapter 11 of Laws of Form about imaginary values are related to this original imaginary state. The temporal interpretation of values i such that < i > = i calls the state of distinction into question, and either returns us to the imaginary source or propels us into temporality. Chapter 11 shows how digital circuitry has the structure of that apparently metaphysical discussion. And the theory of types? Well take a look at your Godel-Bernays set theory and realize that the usual resolution is to imagine sets and classes, with classes a bit more imaginary than sets. (A set is a member of a class. A class is never a member of anything.) The usual technical solution is to introduce imaginaries in the "right" place and to tell the users what they can say and what they cannot say. Spencer-Brown is rude enough and honest enough to admit this situation right in the beginning. There is no need for the theory of types because it is a matter of creativity just how you make your distinctions, and how you want to avoid inconsistency. How will you behave when the next new clever inconsistency in formal mathematics is discovered? A good reader of Laws of Form will be happy and ready to explore the anomaly.

An intriguing exposition of the foundations of logic
Yes, Spencer-Brown probably got a lot from Peirce, and yes, his "system" is isomorphic to older systems, and yes, it's NOR gates. But his notation is as elegant as you can get to express zeroth order logic, and I think his claim is correct about developing a "natural" arithmetic for logic.Read more

Subjects:  1. General    2. Logic    3. Mathematics    4. Philosophy    5. Algebra, Boolean   

Reviews (1)

Very useful reference
This is a great collection of seminal papers by Goedel, Church, Turing, Rosser, Kleene, and Post on the topic of undecidability. It is an extremely handy reference.Read more

Subjects:  1. Advanced    2. Computable functions    3. Godel's theorem    4. Gèodel's theorem    5. Logic    6. Mathematics    7. Recursive functions    8. Science/Mathematics    9. Turing machines    10. Unsolvability (Mathematical lo    11. Unsolvability (Mathematical logic)    12. Mathematics / General