Book Description

This book is an introduction to nonclassical propositional logics. It brings together for the first time in a textbook a range of topics in logic, many of them of relatively recent origin, including modal, conditional, intuitionist, many-valued, paraconsistent, relevant and fuzzy logics. Students with a basic understanding of classical logic will find this an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will be of interest to readers studying logic and, more widely, to readers working in mathematics and computer science. ... Read more

Book Description

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

* Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses.
* Reduced mathematical rigour to fit the needs of undergraduate students ... Read more

Reviews (4)

Very Good.
I read the FIRST EDITION. This is definitely the best introductory mathematical logic book I've seen. It's the most rigorous, most advanced (a reasonably strong form of Godel's theorem is given), and is well-organized and very clearly written. It would be suitable as 1)an introduction for students with some mathematical experience- say a little abstract algebra and perhaps some previous exposure to logic. 2)a refresher for advanced students 3)a nice reference for basic topics. The exposition is great- Enderton always clearly explains what he's doing and why, keeping the reader focused on the big picture while going through the details. He helps to place topics in perspective, and has organized the book so readers can skip some of the more involved proofs and sections on the first reading. Chapter 1 covers propositional logic, with a general-purpose discussion of inductively defined sets, unique readability, and recursion. Many books these days do a sloppy job justifying recursive definition, or dont bother at all- Enderton does it right and is fairly detailed. Chapter 2 begins first order logic and has the most detailed proof of the completeness theorem I've seen. Sect 2.7 concerns translating between theories in different languages, something i hadnt seen developed explicitly before. 2.8 is a great exposure to nonstandard analysis- long enough to give you an idea how it works and why its useful. Chapter 3 begins with an analysis of some reducts of number theory- (N,0,S) (N,0,S,<) and (N,0,S,<,+) and shows how to eliminate quantifiers in them. Next, toward Godel's theorem, a finite set of axioms for a subtheory of number theory is given, and a host of relations and functions are shown to be representable in this theory. In 3.5 we get the fixed-point theorem, Tarskis thm, a weak Godels thm, a stronger Godels thm, and Church's Undecidability thm, and an introduction to the arithmetic hierarchy. 3.6 lifts Godels thm to show set theory is incomplete, and discusses Godels 2cd thm. Chap 4 is 2cd order logic, skolem normal form, many-sorted logic (a first order logic with different sets of variables ranging over different universes), and general 2cd order logic (restrictions are placed on the subsets "X" ranges over in the 2cd order formula \all X \phi). Basic recursion theory is developed throughout the book- Enderton begins with informal notions of computation, then defines a relation R as recursive iff it is representable in some consistent finitely axiomatizable theory, and discusses Church's thesis. 3.8 quickly covers universal computers, partial functions, Kleene normal form, unsolvability of the halting problem, the smn thm, Rice's them, and a register machine model. All this seemed a bit disorganized, so familiarity with computation and automata theory would be a plus. Heres the contents for the first edition, c1972:

Chapter Zero - USEFUL FACTS ABOUT SETS . . . .1
Chapter One - SENTENTIAL LOGIC
1.0 Informal Remarks on Formal Languages 14
1.1 The Language of Sentential Logic . . . . . 17
1.2 Induction and Recursion . . . . . . . . .22
1.3 Truth Assignments . . . . . . . . . . . .30
1.4 Unique Readability . . . . . . . . . . .39
1.5 Sentential Connectives . . . . . . . . . .44
1.6 Switching Circuits . . . . . . . . . . . .53
1.7 Compactness and Effectiveness . . . . . 58
Chapter Two - FIRST-ORDER LOGIC
2.0 Preliminary Remarks . . . . . . . . . .65

2.1 First-Order Languages . . . . . . . . . .67
2.2 Truth and Models . . . . . . . . . . . 79
2.3 Unique Readability . . . . . . . . . . . 97
2.4 A Deductive Calculus . . . . . . . . . .101
2.5 Soundness and Completeness Theorems . .124
2.6 Models of Theories . . . . . . . . . . . 140
2.7 Interpretations between Theories . . . ... 154
2.8 Nonstandard Analysis . . . . . . . . . . .164
Chapter Three - UNDECIDABILITY
3.0 Number Theory . . . . . . . . . . . . 174
3.1 Natural Numbers with Successor . . . . 178
3.2 Other Reducts of Number Theory . . . . 184
3.3 A Subtheory of Number Theory . . . . . . 193
3.4 Arithmetization of Syntax . . . . . . . . .217
3.5 Incompleteness and Undecidability . . . 227
3.6 Applications to Set Theory . . . . . . . .239
3.7 Representing Exponentiation . . . . . . .245
3.8 Recursive Functions . . . . . . . . . . .251
Chapter Four - SECOND-ORDER LOGIC
4.1 Second-Order Languages . . . . . . . . . 268
4.2 Skolem Functions . . . . . . . . . . . . 274
4.3 Many-Sorted Logic . . . . . . . . . . . . 277
4.4 General Structures . . . . . . . . . . . . 281
Index . . . . . . . . . . . . 291

Excellent Textbook with lots of examples
I used this book for self study of Mathematical Logic with the aim of understanding Godel's incompleteness theorem. I also referred to other introductory Mathematical Logic books. In my opinion, this book is by far the best among them. Very readable and contains lots of carefully selected examples.

Excellent introduction to logic
One of the very best introductions to logic, combining readability and depth. An excellent book.

Great Book
This is a great introductory book. Some set theory, sentential logic, first-order logic, metatheory/model theory,number theory, undecidability and Godel's Incompleteness, and Second-Order Logic. You still have to take a lot of time trying to soak in the stuff, but that's because of the complex nature of the material, not the book. The book itself is really good. ... Read more

Book Description

This is the second edition of this text on logistic regression methods. As in the first edition, each chapter contains a presentation of its topic in "lecture-book" format together with objectives, an outline, key formulae, practice exercises, and a test. The "lecture-book" has a sequence of illustrations and formulae in the left column of each page and a script (i.e., text) in the right column. This format allows you to read the script in conjunction with the illustrations and formulae that highlight the main points, formulae, or examples being presented. This second edition includes five new chapters and an appendix. The new chapters are: Chapter 9. Polytomous Logistic Regression Chapter 10. Ordinal Logistic Regression Chapter 11. Logistic Regression for Correlated Data Chapter 12. GEE Examples Chapter 13. Other Approaches for Analysis of Correlated Data Chapters 9 and 10 extend logistic regression to response variables that have more than two categories. Chapters 11-13 extend logistic regression to generalized estimating equations (GEE) and other methods for analyzing correlated response data.

The appendix "Computer Programs for Logistic Regression" provides descriptions and examples of computer programs for carrying out the variety of logistic regression procedures described in the main text. The software packages considered are SAS Version 8.0, SPSS Version 10.0 and STATA Version 7.0. ... Read more

Reviews (2)

Good for what it is
This book has a specific goal. It's aim is to give a basic competence in the use of logistic regression, related techniques, and the software that deal with them. This, it does very well. By intent, it leaves many other needs unmet.

The format is 13 chapters, possibly representing the 13 or 14 weeks in a typical school term. Each chapter has a specific statement of teaching goals at the front, a summary outline of the course to date in the back, and a few pages of questions or exercises with answers. There appear to be sample data sets available, formatted for popular stats packages, but I did not figure out how they are made available. Within the main text of each chapter, every page reads like a blackboard lecture: equations on the left and narration on the right. The presentation uses a minimum of math, just a little algebra and exponentials in a few specific forms.

For the aspiring tool-user, this book may be worth a semester's tuition. I can fault it only for an annoying habit of writing out in words equations that appear on the same page ("e raised to the power of the sum of products ... ").

This book is NOT meant for people truly interested in the theory or practice of the exact computations. For example, its use of probability scarely mentions joint or conditional distributions. As a result, some of its formulas (e.g. p.48) come across as rote memorization, instead of natural expressions of the laws of probability. Lacking joint probability, the covariance matrix can not have meaning. It is just something produced, somehow, by an oracular computer program.

The repeated phrase, "according to statisticians ..." makes it very clear that statisticians are a breed distinct from intended audience. What they do is quite alien, but somehow, sometimes leaves the student with formulas to grind through.

Before you buy this book, be very clear about what you expect from it. Beginning students may get a lot from it. Readers already familiar with probability and some stats are likely to be disappointed.

An excellent step-by-step text
When Kleinbaum entitles his book "a self-learning text", this is TRUE ! I'm sure anyone can learn logistic regression with this book. It is cristal-clear, very progressive, with real-data examples... If the best teachers are those who make you feel you're intelligent, certainly the author must be a good teacher... because his book is ! I do recommend it warmly to anyone who has to teach (like me) or learn logistic regression. ... Read more

Book Description

This volume began as a remembrance of Alonzo Church while hewas still with us and is now finally complete. It contains papers bymany well-known scholars, most of whom have been directly influencedby Church's own work. Often the emphasis is on foundational issues inlogic, mathematics, computation, and philosophy - as was thecase with Church's contributions, now universally recognized as havingbeen of profound fundamental significance in those areas. The volume will be of interest to logicians, computer scientists,philosophers, and linguists. The contributions concern classicalfirst-order logic, higher-order logic, non-classical theories ofimplication, set theories with universal sets, the logical andsemantical paradoxes, the lambda-calculus, especially as it is used incomputation, philosophical issues about meaning and ontology in theabstract sciences and in natural language, and much else. The materialwill be accessible to specialists in these areas and to advancedgraduate students in the respective fields. ... Read more

Book Description

First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. Introduction by R. B. Braithwaite.
... Read more

Reviews (9)

The greatest philosopher of the 20th century
When someone upsets your perception of your perception of the world with proof of its fallibility, your only option- really- is to break on one side or the other. As other reviewers have stated, this proof is written for professional mathematicians; but it is accessible to anyone who is really determined. With two years of high school algebra, and a really (really) thorough dictionary, I was still compelled and able to understand the proof fully. This translation is brilliant in itself; as it not only communicates the mathematical implications, but the more day-to-day fallout of flaws in a system's basic structure. All comparisons to a symphony are completely merited, and the introduction by Professor Braithwaite is a piece of artwork. Not only one of the greatest leaps forward in metamathematics and philosophy since Aristotle, but a great piece of literature. When math majors walk around with abstract sexy code puns on their t-shirts, this is why.

From the horse's mouth, 'le text'
Speaking not as a math specialist but one disposed to read a number of the popular explications of Godel's famous proof I can say that it was Godel's original text that did it for me. The reason is that it is the proof and not a lot of verbiage about the proof. And it is short and sweet. One problem is that the more common Turing Machine approach is actually 'easier', where Godel's approach is that of recursive functions which are more obscure, or at least less often discussed. If you can sort of glare at the recursive function issue and proceed with the basics of the proof it will stand out suddenly better than many of the popularizations. At least give it a try.

A Breeze
I enjoyed this book very much. The only problem I had with it was that the material discussed was simply too elementary. I recommend it if you are just beginning study of the philosophy of mathematics. Skip the introductary essay, it's irrelevant...

Fascinating but not good for the recreational reader
I read this over my winter break (2001) from my second year of medical school at UCSF. This is a fun book to try to grasp, but unless you are extremely mathematically gifted (like me) or have spent years plodding away studying philosophy or math, then stay away from this book. If you are a casual reader and want to read great and important philosophy then stick with Heidigger and Kierkegard and such. Being and Time is a lot more fun if you just want some easy reading. Godel is hard stuff and only accessible to a select few. I loved it.

Read the masters!
THE proof as Goedel wrote it (plus typos). I have seen modern proofs of this theorem which are much easier to follow (as an example, a Mir book on mathematical logic by a Russian mathematician whose name I cannot recall), but this one is the REAL thing.

Modern proofs can be much clearer, but the original always has an added value. The writing style is not the best, but by reading this version you get a clearer idea of how Goedel came up with his theorem and the many difficulties he faced. Remember, by the time most of us read or heard about this for the first time, mathematical logic had advanced quite a few decades. ... Read more

Reviews (4)

Graduate student
I think this is a serious Fuzzy Logic book for the serious
graduate students. In other words, it is not a 'Fuzzy Logic
for Dummies'! It is clear and complete. I could learn Fuzzy Logic from this book without any problem in two weeks. There are several errors in the book. However, they are obvious and easy to find. Therefore, they did not disturb me at all.
By the way, examples are useful, and lastly, Chapter 2 is perfect to give the overvall concepts about fuzzy logic. If you have a CS/CENG background, I strongly suggest this book.

Terrible Text
I'd have given it 0 star if that's an option. It's full of errors, "cryptic" sentences encoded in the authors' proprietory RSA encryption algorithm, and "core dumped" information. Can't believe that Prentice Hall would publish such junk.

horrible text
As a graduate student who had to buy and use this book for a class, I strongly discourage using this book for teaching or for beginners to fuzzy logic. The problems created from the errors in problems and theorms causes more difficulty than working the actual problems.

I would have given this book two stars, except for the fact that there are not nearly enough examples to complement the theorms. Neglecting examples and leaving the reader with just a long algorithm (which may or may not have typos) is fine for a reference, but not for a book that presents these concepts to the novice.

I consider this book $95 not well spent.

*LOT* of errors in the book
The book has a lot of errors in it -- some like errors in numbering the problems, are totally inexcusable.

The authors seem to lack a definite approach to teaching Fuzzy Logic. I felt that the book is a whole bunch of (useful) information dumped in front of the reader, and its upto the reader to figure out how the pieces fit together.

There are some topics which need deeper explanations. There are also places where the authors show some concepts, totally assuming that the reader understands the mathematical relations shown.

If you want to buy this book, I suggest you wait for the next edition! I sincerely hope that it will be better. ... Read more

Book Description

Focusing on the formal development of mathematics, this book demonstrates how to read and understand, write and construct mathematical proofs. It emphasizes active learning, and uses elementary number theory and congruence arithmetic throughout.Chapter content covers an introduction to writing in mathematics, logical reasoning, constructing proofs, set theory, mathematical induction, functions, equivalence relations, topics in number theory, and topics in set theory.For learners making the transition form calculus to more advanced mathematics. ... Read more

Book Description

Introduction to Languages and the Theory of Computation is an introduction to the theory of computation that emphasizes formal languages, automata and abstract models of computation, and computability; it also includes an introduction to computational complexity and NP-completeness.Through the study of these topics, students encounter profound computational questions and are introduced to topics that will have an ongoing impact in computer science.Once students have seen some of the many diverse technologies contributing to computer science, they can also begin to appreciate the field as a coherent discipline.A distinctive feature of this text is its gentle and gradual introduction of the necessary mathematical tools in the context in which they are used.Martin takes advantage of the clarity and precision of mathematical language but also provides discussion and examples that make the language intelligible to those just learning to read and speak it.The material is designed to be accessible to students who do not have a strong background in discrete mathematics, but it is also appropriate for students who have had some exposure to discrete math but whose skills in this area need to be consolidated and sharpened. ... Read more

Reviews (20)

Rigorous and cumulative approach to computation
Logic and linguistics interweave and become virtually indistinguishable through the unifying topic of computability. Any serious seeker of knowledge must be familiar with the underlying concepts of computation. Psychology, philosophy, computer science, the physical and metaphysical are all touched upon by this one subject.

The approach of this work is fairly standard. It begins with machines generating or recognizing languages of increasing inclusiveness and generality, and proceeds to further subject matter, computability and complexity. It opens with two introductory chapters covering the basics of set theory, inductive proofs, and linguistic concepts which will be utilized throughout the book. Each topic after this builds upon the previous ones systematically and gradually. Both mathematical/logical, and verbose prose descriptions are employed, to coax the reader through this intricate and immensely important subject.

One must be well grounded in reading mathematics. The introductory chapters will likely be insufficient for the neophyte, who may become frustrated as the material develops, even as gradual as this cumulation is. Rigorous proofs are provided, and the reader is expected to appreciate the underlying implications. One must exert some considerable personal effort to achieve this level.

This work stands at a middle ground in the subject, between the relatively informal approach of the excellent Sipser text, and the extremely thorough work by Hopcraft et al. It expects the reader to approach the subject with seriousness, yet provides gentler guidance through the more complex subtopics than other related works having this level of mathematical rigor.

Lacks educational value
During the course this book has been anything but helpful. The introductory part is a laugh as it takes for given you as a reader is very deep into mathematical lingo and proofs. Indeed the poofs are some of the worst written, many of them using statements as "Clearly it is..." and "It is now easy to see...", well, no, it isn't easy and mostly seems like a shortcut from the author to excuse himself from actual explanations.

Even worse is the examples where solutions reference something form an excercise, here's a hint to Mr Martin, students don't solve all the extremly many excercises unless asked to, so saying something will be clear after a certain excercise doesn't work, how will we ever know if we're right or wrong?

The educational value is very low due to the authors way of writing, never really getting the point across and always assuming the reader knows exactly what's going on. This is certainly not the way to teach people rather complex things. All in all anyone should look elsewhere to have a chance.

Breadth Of Information
I normally don't write reviews. Couple of not very positive reviews could not stop me writing one for this title. In my opinion, this book really presents a breadth of information
on the subject. If one is considering to buy this book, one should have due background in Discrete Mathematics.

Terrible book
This book is awful. Hard to follow along with the reading. Poor examples, lacking and skipping many steps when there actually is an example. Answers to a few of the questions would have been nice, to know if the problems were done correctly. Must be a master of discrete mathmatics to have any understanding what is going on. I have seen many better books.

Good textbook for computation theory starter
I read this book during my preparation for a comprehensive exam, which includes materials about theory of computation. I was bad at theory all the time, but reading this book removes all my confusions. It looks like lots of math at first glance, but all the theorems explained clearly after the declarations. This book is also very helpful to understand the fundamental theory for programming languages. I recommend this book for all new graduate students of computer science. ... Read more

Reviews (2)

A good intro book
Engel begins this book with a general discussion about what logic and argument are/aren't, and about how language impacts the manner in which arguments are formed and understood. He then delves into the informal fallacies, which he divides into three categories: (1) fallacies of ambiguity, which seem to be more misuse/abuse of language than actual fallacies of logic; (2) fallacies of presumption (e.g., hasty generalization, begging the question, slippery slope); and (3) fallacies of relevance (e.g., ad hominem, appeal to authority).

The explanations use clear, simple language that would be appropriate for high-school reading levels and above. As a graduate student, I found this to be an easy but engaging read.

I have two complaints about the book. First, Engel uses many examples from the real world--which is good--but the fallacies in these examples tend to be too obvious. It would be good to start out with obviously fallacious arguments and then move onto more subtle/complicated examples. Second, there are exercises at the end of each chapter where the reader can put his/her new knowledge to work, but answers are given for only a few of the questions in these exercises, which was frustrating.

In summary, this is a good, easily-read introduction to logic. It both prepares and encourages the reader to continue studying logical fallacies, but don't expect to be an expert at identifying fallacies when you're done with this book.

The best book about good vs. unfair rhetoric I've seen.
I collect books about fallacies. With Good Reason is definitely the best of the 32 such books I've accumulated so far. His explanations are very clear, and he covers important subject matter ignored by other authors, such as fallacies caused by vagueness and ambiguity. ... Read more

Reviews (13)

An Excellent Intro to Logic
Like other books in Oxford's VSI series, this book sets out to provide -- in a compact book the size of most people's shirt pockets (or at least jacket pockets) -- layman with an introduction and overview of intellectual topics. I gather that it is designed for the intellectually curious layman who always meant to learn more about a certain subject but, due to the stresses of life, never managed to do so.

This book does an excellent job in accomplishing those goals (and more) with regards to to topic of Logic. This books gives an excellent overview of various issues in (formal) logic. There are several things that I found particularly good about this book:

(1) Many people may be scared off by formal logic by the symbolism and mathematical nature of the subject. Graham Priest does an excellent job in guiding the readers through those potential barriers.

(2) Conversely, intellectually curious people don't want to be reading a book that is too 'dumbed down.' This book doesn't insult anyone's intelligence. Symbolic logic is presented to the reader but the book is well written enough so that people who tend to glaze over mathematical symbols will still have a good understanding of what is going on (with some effort, of course).

(3) I really like the fact that Graham Priest gives a few short problems at the end of each chapter (and provides the solutions on the Oxford UP web site). This not only helps in re-assuring readers that they understood (or did not understand) particular topics but also gives even a total layman an opportunity to apply skills in formal logic. Many books of this type, unfortunately, do not provide self-study questions with answers. It's worth 10 stars that this author did provide such a learning tool.

(4) I like the fact that the book tackles probabilistic logic. This topic can be difficult but is often very useful in everyday life (decisionmaking, understanding medical research, etc.).

Bottom line: If you always wanted to learn formal logic and were too busy or too scared to try, buy this excellent book.

By the way, to give this book a rating of anything less than 5 stars is a grave injustice in my opinion and reasons offered by others for not giving this book a perfect mark are not worthy of consideration

Superb, comprehensive Intro to Logic
I am a novice in logic. But I need logic--some of it sophisticated--to understand a philosophy paper I am working with.
I found Graham Priestly's Logic, a Very Short Introduction superb and immensely helpful. I searched full-length texts, but I knew I would never wade through them. I didn't want to take the time for a college course. I searched the Web and found some excellent material, ... However, Graham's book proved far and away the simplest and best.
Here are the advantages I found. Some advantages are simply due to the brevity of the book that suited my needs, but some stand out in any context.
1. The book goes into topics early-truth tables and modal logic, for example. Copi's Introduction to Logic, while undoubtedly very good, and used in many logic courses, does not get to truth tables until Chapter 10 while Priest starts using truth tables in Chapter 2, page 9. Another text, Stephan Layman's The Power of Logic, did not get to modal logic until about page 450. Graham starts the topic in chapter 6, page 38, about 1/3 of the way through his book.
2. The book had every single logic symbol that I needed. I found no one book, full-length text or web source that did this. Equally important every symbol was used and discussed somewhere in the book. Some symbols were missing or introduced very late in other books.
3. Graham doesn't spoon feed the reader with great detail like other books, nor employ elaborate introduction to a topic.
4. Logic, a Very Short Introduction is about 10% the length of other books I looked at (Copi & Layman were about 550-650 pages, for example)-considering Graham's page size is probably ½ that of a normal book. Other books cost roughly 3 to 8 as much.
5. Graham has a very clear, engaging, and often humorous, style. The book is very well organized and written.
6. It is easy to get into meat quickly.
7. In a little over 100 pages, Priest uses a given chapter's logic to analyze a variant form of several classical philosophical questions. For example: the Cosmological Argument for the Existence of God, fatalism, the Ontological Argument for the Existence of God, the Argument from Design for God's existence, etc.
8. The book has an unusual amount of supplemental material-brief history of logic, glossary, list of symbols, problems ..., bibliography, general index and index of names.
9. Every chapter ends with a simple summary of the ideas it covers. There were numerous figures.
10. There were 13 illustrations ranging from cartoons, to art, to famous philosophers.
Of course, this is a short survey and so no one should think that any one topic is covered in depth. Breadth rather than depth is the book's objective.
The book could be used by:
1. Self learners
2. People taking a logic course who want a quick overview or supplement
3. People, who would like rudimentary familiarity with logic for their work, but do not need a college course or a full-length logic book.
...

Difficult but rewarding
On this page, there are negative reviews, saying either that this book is unreadably difficult, or that it is superficial and elementary. Let me start by straightening this out. This book is an introduction. You can't expect it to be tremedously in-depth - it would leave readers new to the subject (those it is aimed at) out of their depth and render a broad overview impossible in the short space available. You can already see some are having difficulty as it is, but this is because Logic is a difficult topic. Having said this, this seems to be as lucid as it could be given the difficulty of the academic discipline.

I read this book because I am considering doing Philosophy at university, and this is an area of Philosophy I am not familiar with. To be honest, it gave me some doubts. I found it hard for an introduction (compared with about 5 other volumes I've read it the same series). Having said this, the author does say there will be times where you have to stop, think and go back over text, and maybe I was being too impatient. So it gave me doubts about the subject.

However, as far as the book itself is concerned, it is excellent. Priest does a magnificent job of making what, in the hands of almost anyone else, could be studiously dull, engaging. He applies logic to everyday problems, questions and scenarios and writes in an engaging style with wide use of examples. The mathematical nature of logic means it is not for everyone, but if you want an introduction, this is the book (I've heard that other so-called 'introductions' to the subject are rather difficult for the layman). It is rewarding when you do understand and master concepts, and it makes you think about different questions and go deeper into basic issues, adding a whole new dimension to philosophical thought.

One of the Greatest Books Ever Written (seriously)
I purchased and read this book a few years ago when I saw someone reading it at a Harvard Square restaurant. I was curious because: (a) I was interested in logic, and (b) because it was in an intriguing new format called "A Very Short Introduction" (more on that later).

After buying and working through this book, I came away loving almost every bit of the book. Even as the years have gone by since finishing Graham Priest's book, I still feel that it is one of the best books that I have ever read (and I've read quite a few). In fact, as the title of my review suggests, I honestly feel that 'Logic: A Very Short Introduction' is one of the greatest books ever written and that ANY intelligent and educated person -- even if they have little or no initial interest in formal logic, philosophy, or mathematics -- MUST buy and read this book.

So what is this book about. In order to answer that question, I have to discuss the general format of this series of books as well the specifics of this book itself.

Oxford Univ. Press' "A Very Short Introduction" format is a series of books that are designed to INTRODUCE an intellectual discipline to readers that can be considered LAYMAN in that particular subject. These books are brilliant because: (a) they are relatively short and, thus, busy people who have a vague interest in a subject can get an accessible account of it, (b) it is compact so that it can literally fit in a shirt or jacket pocket, and (c) they are INEXPENSIVE (all of them sell for under $10). I put some of the words above in bold letters because some of the other reviewers criticize Graham Priest's book for being too elementary. My response is: No duh, that's what it was INTENDED to be. If you are honestly an expert (as opposed to posing as one), then you probably should be reading another book (but as I will mention below, even experts in the relevant fields can probably get something out of this book).

The content of this book is, as I suggested above, an accessible introduction to formal logic (from the fields of philosophy and, to some extent, mathematics and computer science). It covers most of the standard issues dealt with in a typical logic class PLUS it covers some advanced and/or non-traditional topics such as 'non-classical' logic (modal, multi-valued truth values, etc.) and more inductive (as opposed to deductive) issues such as probability theory and decision theory. To repeat myself, of course this is all at a basic, overview level but it's intended audience (laypeople interested in the field, busy intellectuals, people who need to review of fill in some gaps, etc.) will find this to book to be highly valuable.

Another positive for this book is that Graham Priest is the author. I commend Oxford Univ. Press for choosing him to author the book. He is a very innovative (or controversial depending on your viewpoint) scholar in the field of logic. I appreciate the fact that he has a mathematical background (I think at least one of his degrees was in maths). I think that an implicit objection that some negative reviewers have, based on some of the quirky book recommendations involving religion, is that Mr. Priest is very irreligious and his biases shows up in the book. I'm not an atheist myself and I have to admit that the MINOR little bit where his (lack of) beliefs showed was a bit bothersome for me as well. However, I am enough of an intellectual to get over it and just accept the book for what it is: An excellent introduction to logic. And, to be fair to Prof. Priest, he does play devil's advocate with his own viewpoints and one can't fairly claim that he crams his personal views on his readers because he doesn't do that. So this and any other reasons offered up for trashing this book (and I'm writing this review because I love this book and hate to see the unfair bashing of a book I love) are really not reasonable at all.

A truly magnificent and unique aspect of this book is that "Logic: A Very Short Introduction" has end of the chapter excercises for each chapter with SOLUTIONS to EVERY problem (available on the Oxford UP website for the book). I can't even begin to fully describe how great that is for autodidactic (self-study learners) folks. You can't really learn math (which logic falls under) without solving problems, and you can't be sure you've solved something without the solutions. Graham Priest's book addresses both of those issues. Even more rigourous and formal textbooks on logic sometimes nelgect to offer exercises and usually do not give solutions to all the problems. This aspect of the book alone makes it valuable to potential readers.

What about the more advanced reader? As I've noted above, I think this book offers something for everyone who is smart and curious, including people who have some familiarity with logic. First, it's written by Graham Priest, a scholar with some interesting ideas on logic. Second, it covers some non-classical logics and inductive topics like probability -- things that even those who are familiar with logic may need either review in or a solid introduction to. Third, it offers questions with fully worked out solutions for each and every one of those problems, something that even dedicated texts on the subject often fail to do. Finally, it's cheap and handy so that, even if you don't find any of the above arguments satisfactory justification for buying this book, you can at least give it to your friends, family, or significant other just in case you feel they need to be educated about thinking logically.

Bottom line: This is a solid introduction and overview of logic with some extras that one might not expect in a book such as this. IMHO, it is one of the greatest books ever written. It's cheap and compact. If you haven't bought it and read it, please do yourself a favor and do both.

BTW, Oxford's VSI series has other great books. I would also recommend the books on intelligence (as in IQ) and linguistics.

Save Your Money
Save your money, this book is completely unreadable. If you're hoping (like I was) for a good introduction to this discipline, find another title because this one isn't it. ... Read more

Amazon.com

Gödel's incompleteness theorem--which showed that any robust mathematical system contains statements that are true yet unprovable within the system--is an anomaly in 20th-century mathematics. Its conclusions are as strange as they are profound, but, unlike other recent theorems of comparable importance, grasping the main steps of the proof requires little more than high school algebra and a bit of patience. Ernest Nagel and James Newman's original text was one of the first (and best) to bring Gödel's ideas to a mass audience. With brevity and clarity, the volume described the historical context that made Gödel's theorem so paradigm-shattering. Where the first edition fell down, however, was in the guts of the proof itself; the brevity that served so well in defining the problem made their rendering of Gödel's solution so dense as to be nearly indigestible.

This reissuance of Nagel and Newman's classic has been vastly improved by the deft editing of Douglas Hofstadter, a protégé of Nagel's and himself a popularizer of Gödel's work. In the second edition, Hofstadter reworks significant sections of the book, clarifying and correcting here, adding necessary detail there. In the few instances in which his writing diverges from the spirit of the original, it is to emphasize the interplay between formal mathematical deduction and meta-mathematical reasoning--a subject explored in greater depth in Hofstadter's other delightful writings. --Clark Williams-Derry ... Read more

Reviews (23)

An Abstruse Mathematical Proof Made Fascinating
This is a remarkable book. It examines in considerable detail Godel's proof, a mathematical demonstration noted for its difficulty in its novel logical arguments. The chapter topics - the systematic codification of formal logic, an example of a successful absolute proof of consistency, the arithmetization of meta-mathematics - appear almost unapproachable. And yet, Ernest Nagel and James R. Newman have created a delightful exposition of Godel's proof. I actually read this book in one sitting that took me late into the night. I simply didn't want to stop; it is really a good little book.

Godel's proof is not easy to follow, nor easy to grasp the full implications of its conclusions. Many mathematical texts, overviews, and historical summaries avoid directly discussing Godel's proof as these quotes indicate: "Godel's proof is even more abstruse than the beliefs it calls into question." "The details of Godel's proofs in his epoch-making paper are too difficult to follow without considerable mathematical training. "These theorems of Godel are too difficult to consider in their technical details here." Such is the common reference to Kurt Godel's milestone work in logic and mathematics.

In their short book (118 pages) Nagel and Newman present the basic structure of Godel's proof and the core of his conclusions in a way that is intelligible to the persistent layman. This is not an easy book, but it is not overly difficult either. It does require concentration and a willingness to reread some sections, especially the second half.

"Godel's Proof" begins with an explanation of the consistency problem: how can we be assured that an axiomatic system is both complete and consistent? The next chapter reviews relevant mathematical topics, modern formal logic, and places Godel's work in a meaningful historical context. Following chapters explain Hilbert's approach to the consistency problem - the formalization of a deductive system, the meaning of model-based consistency versus absolute consistency, and gives an example of a successful absolute proof of consistency.

The plot now begins to twist and turn. We learn about the Richardian Paradox, an unusual mapping that proves to be logically flawed, but nonetheless provided Godel with a key to mapping meta-mathematics to an axiomatic deductive system. (I forgot to explain meta-mathematics; you will need to read the story.) And then we learn about Godel numbering, a mind boggling way to transform mathematical statements into arithmetic quantities. This novel approach leads to conclusions that shake the foundations of axiomatic logic!

The authors carefully explore and explain Godel's conclusions. For the first time I began to comprehend Godel's fundamental contribution to mathematics and logic. I am almost ready to turn to Godel's original work (in translation), his 1931 paper titled "On Formally Undecidable Propositions of Principia Mathematica and Related Systems". But first, I want to read this little book, this little gem, a few more times.

Lucid & satisfying: Godel's Proof and modern logic
In 100 lucid and highly readable pages, presents the most important ideas of modern logic: axiomatisation (Euclid), formalization (Hilbert), metamathematical argumentation, consistency, completeness, etc., leading up to Godel's incompleteness result. Elementary from a technical point of view, but technical people should read it to get perspective. Non-technical people will appreciate its workmanlike, substantive exposition, in contrast to the mysticism, obfuscation, and cuteness of a "Godel, Escher, Bach". It is old (1958) and very incomplete (no set theory, no computability, no non-standard analysis, ...), but still essential reading.

(I wrote this review in 1998, but Amazon doesn't know I'm the same person as macrakis@alum.mit.edu.)

Good attempt to explain the proof
This was clearly one of the best attempts at explaining Godel's proof that I have seen, at least superficially speaking. As someone who just wanted to understand what the basic ideas are, I looked over various books and decided on this one because of its high rating. I gave it 4 stars because I was left feeling that there were several times when background knowledge of higher mathematics/logic was assumed and I think more could have been done to explain those parts on a level comprehensible to an interested layperson.

I think the attempt in the book is a good one, but I guess perhaps not enough is said about just how abstract these ideas are and how difficult it is to simply dive in (even with a good book) and expect to understand this proof fully.

I am going to try Godel, Escher, Bach, and Roger Penrose's Shadows of the Mind next, since I have heard that both of them also include explanations of Godel's theorem. But I now have a greater appreciation of why there will never be a "Godel's Proof for Dummies" book!

Don't be intimidated by the subject matter.
The greatest merit of this book is its ability to take a rather arcaic and complicated proof and successfully present it, in a concise and understandable manner, to a broad audience. An otherwise motivated and intelligent person with almost no background in logic should enjoy and understand most of Nagel and Jackson's summarization. One technique that Nagel and Jackson employ is to repeat themselves, presenting crucial points in two or three slightly different ways to insure the idea is grasped. The short length not only makes a one night read a possibility, but makes it easier to grasp the broad structure of the proof itself.

Wish I'd read it first ...
I read Godel's paper in grad school. I wish I had read this first, because it lays out the structure of the argument clearly. N&N are particularly good on clarifying what Godel did and did not prove. This is important because of all the loose mystical obfuscation out there about this theorem.

N&N clearly explain what formal "games with marks" methods are, and why mathematicians resort to them. They then walk through what Godel proved, with a bit on how he proved it. The basic idea of his (blitheringly complex) mapping is explained quite well indeed.

Suitable for mathematicians, or philosophy students tired of mystical speculations. Also goo for anyone with an interest in computability theory or any formal logic. And read it before you read Godel's paper! ... Read more

Book Description

Professor Hodges emphasizes definability and methods of construction, and introduces the reader to advanced topics such as stability.He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference. ... Read more

Reviews (1)

Excellent text, very clearly written
This is an excellent text on the model theory of first-order languages. A condensed version has also been published as: "A Shorter Model Theory."

This book is a classic. Its influence should be comparable to Keisler & Chang's famous book as *the* standard account of the relationship between the language of f.o. logic and mathematical structures. (N.B. Chang & Keisler's last edition is still useful alongside this book since the contents are not identical!)

The text is clear and fluent, as one has come to expect from this remarkable author. The book includes a detailed bibliography and suggestions for further reading. The binding and typesetting are beautifully done as well.

The short-comings are: (1) the large number of typos including an "incorrect lemma" (but with corrections available on the author's homepage), (2) the almost exclusive concentration on (untyped) first-order languages and (3) avoidance of certain speacialized topics.

All in all, this is an excellent book. ... Read more

Book Description

This text introduces students to basic techniques of writing proofs and acquaints them with some fundamental ideas. The authors assume that students using this text have already taken courses in which they developed the skill of using results and arguments that others have conceived. This text picks up where the others left off -- it develops the students' ability to think mathematically and to distinguish mathematical thinking from wishful thinking. ... Read more

Reviews (4)

A great read to see what lays ahead
I read and worked the problems in this book during my break as I transferred from a community college to a 4-year university, and found it very helpful in introducing me to all the fancy terminology, notation and basic proof writing that I was intimidated by. I found the problems to be hard enough to be challenging, but also neither impossibly hard nor hinging on a silly trick.

If you are a eager HS student, or a curious college student, get this book and work the problems.

Great introduction to mathematics
I bought this book for a course in classical algebra. I found the book well explained and well done. It contains a lot of exercise and example of differents difficulty. It covers logic, set, relation, induction, function, combinatorial proofs, countable sets and uncountable sets, groups and some calculus. The book has a lot of subject in it and it make it very flexible. If you want to ontroduce yourself to mathematics, I would recommend this book if you want to spend some money.

An excellent introduction to mathematical logic!
This book provides an excellent introduction to mathematical logic, set theory, graph theory, number theory, and more -- everything which is "neat" in higher math.

I would strongly recommend this book before any proof-based math class. The authors explain methods of proofs very well, and give some principles universally important in mathematics -- Zermelo's thm., Dirichlet's prin., and such.

The exposition in this book is great. If this is your first exposure to, for instance, the proofs by induction, this probably provides an excellent description of what's going on and how it works, why it works.

The book is slim (at least, the 1992 ed.) and not inexpensive. However, the authors' conversational tone makes it very approachable; at the same time, they are mathematically rigorous and very thorough.

Clear and concise book on math and more
This book is well done. Not only is well done but the explanations are clear and concise. The book offers different approaches. I use it for class and find most revealing. Hope you enjoy too. M. ... Read more

Book Description

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.

Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism. ... Read more

Reviews (14)

A passionate introduction to the theme of infinity
The book mentiones : Infinity commenly inspires feelings of awe, futility and fear. Reading of the book makes one agree to it. The book is written for a reader who is philosophically curious and patient in reading. After introducting the various context ( spatial, temporal , physical) where one encounter the issue of infinity, the author explain clearly the debate of potential vs actual infinity. Here author points out about the Greek philosophical tendencies. Chapter two discusses the revolution brought by Cantor's works. He explains the concept using a lot of symbols, diagrams and illustrations. The reader is made to understand the notion of transfinite number. The chapter ends with an extract from his novel White Light which deals with the idea of the chapter. Next chapter discusses the kind of paradoxes one encounter in thinking the theme of infinity within modern mathematical logical framework. Chapter four discusses the implications of Godel's theorems in question of Robot consciousness. He gives details about his personal interactions with Godel. He mentiones about his dream about Godel the day before Godel's death. This is most humanistic chapter. Last chapter discusses the abstract philosophical reflections. There are two well written excursion chapters : one on Cantor's set theory and one on Godel's Incompleteness theorems. Every chapter has well thought puzzles and paradoxes section.

Infinity made simple and understandable
In many ways, infinity is the most abstract concept of all. Many of the advances in understanding how to manipulate infinities had unpleasant consequences. As the legend goes, the first one to announce that there are infinite non-repeating decimals was rewarded by being drowned. Georg Cantor, the first to prove that there are different levels of infinity, faced extreme criticism and ultimately went mad. Fortunately, Rudy Rucker provides a gentle introduction to this concept, one that can be read by most with the only consequence being enlightenment.
The entire range of infinities (what a phrase!) is covered in this book. From the simplest infinity (omega), to the multi-universe theories of quantum theory. All are put forward in a very readable style, although there are times when one must slow down and read very carefully if one is to understand. Rucker's encounters with Kurt Godel is a welcome contrast with the common depiction that he was a dry, humorless man. It is refreshing to hear that he laughed and had a sense of humor.
Many different test scenarios have been put forward to determine if a computer is indeed intelligent. At this time, I would propose that any machine that can understand the concept of infinity must be considered intelligent. Any human wishing to pass that test need only read this book. It should be required reading in all undergraduate mathematics programs.

Published in Journal of Recreational Mathematics, reprinted with permission.

At the intersection of parallel lines...
Rudy Rucker, son of a cleric and mathematics whiz kid, produced this book on 'Infinity and the Mind' years ago, but reading and re-reading it, I continue to get insights and the chance to wrap my mind around strange concepts.

'This book discusses every kind of infinity: potential and actual, mathematical and physical, theological and mundane. Talking about infinity leads to many fascinating paradoxes. By closely examining these paradoxes we learn a great deal about the human mind, its powers, and its limitations.'

This book was intended to be accessible by those without graduate-level education in mathematics (i.e., most of us) while still being of interest to those even at the highest levels of mathematical expertise.

Even if the goal of infinity is never reached, there is value in the journey. Rucker provides a short overview of the history of 'infinity' thinking; how one thinks about divinity is closely related often, and how one thinks about mathematical and cosmological to-the-point-of-absurdities comes into play here. Quite often infinite thinking becomes circular thinking: Aquinas's Aristotelian thinking demonstrates the circularity in asking if an infinitely powerful God can make an infinitely powerful thing; can he make an unmade thing? (Of course, we must ask the grammatical and logical questions here--does this even make sense?)

Rucker explores physical infinities, spatial infinities, numerical infinities, and more. There are infinites of the large (the universe, and beyond?), infinities of the small (what is the smallest number you can think of, then take half, then take half, then take half...), infinities that are nonetheless limited (the number of divisions of a single glass of water can be infinite, yet never exceed the volume of water in the glass), and finally the Absolute.

'In terms of rational thoughts, the Absolute is unthinkable. There is no non-circular way to reach it from below. Any real knowledge of the Absolute must be mystical, if indeed such a thing as mystical knowledge is possible.'

At the end of each chapter, Rucker provides puzzles and paradoxes to tantalise and confuse.

* Consider a very durable ceiling lamp that has an on-off pull string. Say the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed?

Rucker explores the philosophical points of infinity with wit and care. He explores the ideas behind and implications of Gödel's Incompleteness Theorem, and leads discussion and excursion into self-referential problems and set theory problems and solutions.

He also discusses, contrary to conventional wisdom, the non-mechanisability of mathematics. We tend to think in our day that mathematics is the one mechanical-prone discipline, unlike poetry or creative arts and more 'human' endeavours. But Rucker discusses the problems of situations which require decision-making and discernment in mathematical choices that no machine can (yet!) make.

* Consider the sentence S: This sentence can never be proved. Show that if S is meaningful, then S is not provable, and that therefore you can see that S must be true. But this constitutes a proof of S. How can the paradox be resolved?

This is a beautifully complex and intriguing book on the edges of mathematics and philosophical thinking, which is nonetheless accessible and intellectually inviting. You'll wonder why math class was never this fun!

a mind-blowing trip to the infinite
What is infinity? How do we train our minds to understand the idea? This one of the hardest questions to answer for non-professional mathematicians, and one that Rucker address superbly - and, believe it or not entertainingly in this excellent book. And once you think you grasped that, how about a higher level infinity? Next one? Infinite series of higher level infinities? Sound very scary, and it is. It takes an amazing capacity to explain these concepts to a (relative) layman, and Rucker has it in abundance. An exhilarating intellectual tour de force, perhaps comparable to climbing mount Everest - infinite number of times, with deep philosophical, and perhaps, religious connections, presented in a light, funny, and yet rigorous manner. The book also provides a history of the concept of the infinite, and interesting people who developed it. A must read for a curious mind.

A perfect book for someone like me
I know very little about any of the subjects discussed in this book, although I do have a degree in philosophy of science, and I liked this book a lot.

I can't believe I made it through 7 years of senior school and 2 years of degree level maths and nobody ever bothered to tell me about infinity, transfinite numbers, set theory and its relationships with, and underpinning of other branches of mathematics in a way I could understand rather than simply regurgitate. Rucker on the other hand manages to do this in 362 pages.

I slso found the stuff about Godel and the impossibility of complete formulisms very useful, not only philosophically, but also just for my own peace of mind. ... Read more

Book Description

Now in its fourth edition, this classic work clearly and concisely introduces the subject of logic and its applications. The first part of the book explains the basic concepts and principles which make up the elements of logic.The author demonstrates that these ideas are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning.The second part of the book shows the applications of logic in mathematical theory building with concrete examples that draw upon the concepts and principles presented in the first section.Numerous exercises and an introduction to the theory of real numbers are also presented.Students, teachers and general readers interested in logic and mathematics will find this book to be an invaluable introduction to the subject. ... Read more

Book Description

[Man] invented a concept that has since been variously viewed as a vice, a crime, a business, a pleasure, a type of magic, a disease, a folly, a weakness, a form of sexual substitution, an expression of the human instinct. He invented gambling.
Richard Epstein's classic book on gambling and its mathematical analysis covers the full range of games from penny matching, to blackjack and other casino games, to the stock market (including Black-Scholes analysis). He even considers what light statistical inference can shed on the study of paranormal phenomena. Epstein is witty and insightful, a pleasure to dip into and read and rewarding to study. ... Read more

Reviews (9)

Disappointing and Often Uninsightful
Some parts are interesting, and the writing can be entertaining, but the book is short on insight and clarity and long on tedious tables and uninterpreted computations.

Buy this if you already know probability and would like to see -some- applications and cute games.

Don't buy it if you want insight into particular games; especially, the blackjack and bridge sections (and meager poker section) have virtually no value.

I am a graduate student in mathematics, and enjoy probability theory and games: I should be the ideal audience.
The math is no problem for me, but much is boring, and much time is spent writing huge tables without giving much insight.

Research articles in statistics are easier to read, and far more informative.

The math background is awful: if you don't already know it, don't learn it here.
[Instead, see "The Cartoon Guide to Statistics", or Feller's "Intro to Probability"]
The writing is willfully obscure and florid (though, admittedly,
entertaining): gymkhana, panjandrum, kubiagenesis?

My main objection is the lack of insight: the author does (mostly) correct computations and statements but seldom shows much depth of understanding and rarely conveys any to the reader.

Rather than answering questions or giving examples that convey the meaning of the theory, how it lets you understand questions, Epstein does many unillustrative examples.

This book won't teach you to understand games and gambling, which it could do, and should do.

At best, it provides a basis from which you can (after too much work) begin to understand games. This is not because the subject is that hard (at least not what Epstein covers) -- it's because the material is undigested and Epstein is a poor expositor.

If you want to get something out of this book, be prepared to do the work that Epstein hasn't, and to look at more modern and insightful references.

Here's an example: how many times do you need to shuffle a deck before it's essentially random? Very natural question, of big interest in gambling. Epstein gives a very slick argument, one of the gems of the book (measure entropy of a shuffle) that you need at least 5 shuffles -- but beyond that just writes some equations for 2 shuffles of a 4-card deck and says that a computer would help, and instead tabulates that 18 perfect shuffles of a 58-card deck return it to the original state.

The rest of the book is like this: some question begging for study, perhaps an insight, and then irrelevant and pedantic computations and tables.

There are gems in here (it's a grab-bag), and the writing is often amusing, but it's a frustrating read: it could be so much better.

Very Hard to Find Info
Don't read this book if you're a poker player who knows how to divide your outs by number of unseen cards but never took any serious math courses. This is a serious mathematical treatment of gambling.

If you want a more rigorous treatment of the general statistical theory involved in gambling (in general, not just for poker) then this is a book you MUST read. Are you a full or part-time mathematician? Are you someone who took some math courses and is interested in learning about how to mathematically describe different games that involve gambling? Are you wanting to write a computer program to simulate statistical games based on solid mathematics and understand your program? This book is something you don't want to overlook if you answered "yes" to any of those questions. If you answered with a resounding "no" to all of them and are just interested in a particular game and aren't mathematically inclined then you want to look elsewhere.

Kubeiagenesis
To the reader who was frustrated by the title of Chapter one, 'Kubeiagenesis', and could not find a definition.

-genesis, is first defined as a suffix, meaning 'origin'.
Kubeia comes from The New Testament Greek Lexicon.

Kubeia (koo-bi'-ah). Definition 1. dice playing 2. metaphor for the deception of men, because dice players sometimes cheated and defrauded their fellow players.

Translated to english in Ephesians as both 'sleight' (KJV) and 'trickery' (NAS).

Clearly, Kubeiagenesis is meant to be the origin of sleight, trickery, and deception.

That it is the first word of the text may be to inform the reader that what follows may be nonintuitive -- but is well defined, documented, and referenced. You may find yourself reading several of the referenced texts before completing the book if you are going to absorb it all.

This book is the Bible on the subject. The author brilliantly interweaves relevant stories, and shows connections to disciplines outside mathematics and gaming. If you simply want answers and don't care how they were calculated, try some of the other texts offered. If you want to understand the subject -- buy this book.

For what it is, it's a great book
I would mostly echo the positive reviewers of this book. This book is indeed a classic in the field of probability theory and applied statistics. It is also a great book for people who want a serious, math-intensive treatment of gambling.

I am writing this review mostly to deal with the criticism that this book has received from some of the other reviewers. I would agree with those critics that this book is not for the faint of heart. This book does require a certain comfort level with mathematics.

However, I don't think it's all that fair to bash this book for those alle