UK  Germany 
Home  Books  Science  Mathematics  Pure Mathematics  Logic  Help 
120 of 200 1 2 3 4 5 6 7 8 9 10 Next 20 
click price to see details click image to enlarge click link to go to the store
1. Introduction to Automata Theory, Languages, and Computation (2nd Edition) by John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman  
list price: $108.20
our price: $108.20 (price subject to change: see help) Asin: 0201441241 Catlog: Book (20001114) Publisher: Addison Wesley Sales Rank: 22942 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Reviews (29)
Very useful book for GRE CS Subject preparation (part III)
A very good book for theory of computing
first edition is a classic, the second one unremarkable Sadly, the second edition misses a great deal of the first edition. Many chapters were removed. Important lemmas and theorems are missing. I would gladly exchange my second edition for the first one, if it wasn't out of print. J.
Excellent introductory text, but has several weaknesses The topics of complexity classes and NPCompleteness, as well as the chapter on Turing Machines are rather succint and do not cover the full depth. Papadimitriou's "Computational Complexity" does a better job in this respect, even though it is not at all flawless. Some might say that there is a reason why this book is introductory, but I argue that instead of doing a poor job, the authors should have maybe just made another book dealing with the abovementioned topics. PS: My professor told me that the first edition was much better  maybe you could find it somewhere in the library, if interested.
Could be better 
2. Introduction to the Theory of Computation by Michael Sipser  
list price: $103.95
our price: $103.95 (price subject to change: see help) Asin: 053494728X Catlog: Book (19961213) Publisher: Course Technology Sales Rank: 36260 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Amazon.com Reviews (35)
Life saver The main thing that made this book stand out above the rest is that it's written in language that is easily understood, while other text books burden you down with a multitude of symbols and equations. The proof ideas are very helpfull in understanding concepts Thank you Mr. Sipser!
BEST Computer Theory book My advice is read this book if you an undergrad student, even though instructor might be using a different book. If you are a grad student this books makes an excellent reference for refreshing your knowledge of Computer Theory. Computer Theory is not my area of interest, but this book makes it very interesting and fun area; which is quiet unusual for Computer Theory books. I am a grad student taking advanced "Computer Theory" class. I have bought couple books including this one, and checked out from library another 6. This book in an introductory book and it has excellent coverage of the basics, and it has some brief but very good coverage of advanced topics as well. I read this book every time to refresh my knowledge before I go on to more in depth topics. The only thing that I wish, is that the undergrad course that I have taken a number years ago was using this book; and/or I read this book when I was an undergrad.
Probably the best computation theory text for students
A Near Perfect Computer Theory Textbook
An EXCELLENT Automata/Theory of Computation book One of the greatest things about this book is its focus on developing an intuitive understanding of the concepts and proofs. Other books do a better job of formal proofs but this book is light years ahead of any other in terms of helping you develop an intuitive understanding of why a given proof or construction is correct. It's a lot better than the memorize/regurgitate model necessitated by the emphasis on minutiae of other books. Lastly, this book provides great tips on how to approach problem solving (especially proofs). ... Read more 
3. How to Prove It : A Structured Approach by Daniel J. Velleman  
list price: $28.99
our price: $28.99 (price subject to change: see help) Asin: 0521446635 Catlog: Book (19941125) Publisher: Cambridge University Press Sales Rank: 193781 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (16)
A good start on writing proofs, but falls short!
An excellent book
Starts off good, and then goes off on a tangent.
Breakthrough and Original ...... Velleman uses structured style as a technique. Two columns are prepared. The left column is Givens and right Goal. By restructuring Givens and Goal using relationships and definitions, some parts of Goal statement is moved to Givens, like peeling skins of onion. This process iterates until one finds the proving obvious. The whole process is a "scratch work" and a reader is able to see how the author structures the proof step by step, both from Goal and Givens viewpoints. In past, there was only a Macintosh proofing program, but now Java version called Proof Designer is out. So Windows and Linux users alike can now enjoy this little program in conjunction with the book. Two disappointments with Proof Designer are that the output is only in the form of a traditional proof style which does not expose "the scratch work" and that the program does not use the two column style used in the book. There are additional materials such as supplementary exercises, documentation, and a list of proof strategies (which is also available at the end of the book as a good reminder and reference), all available from author's site for free. [search in google like this: velleman "how to prove it" inurl:amherst] After completion of this book, don't throw it away! Advance to Rudin's Principles of Mathematical Analysis and keep Velleman aside. Now one can work on complete proof of materials in Rudin with rigor and study how he constructs logical structures step by step in your own "structured" words!
Probably the best book out there but not perfect 
4. The Art and Craft of Problem Solving by PaulZeitz  
list price: $65.95
our price: $65.95 (price subject to change: see help) Asin: 0471135712 Catlog: Book (19990209) Publisher: Wiley Sales Rank: 38955 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (14)
General Problem Solving Strategies. This particular book has very clear explanations of the main problem solving strategies illustrated with carefully sample problems. Reading this book brings to my memory the works of Polya. One of the only things I think the book is lacking is on strategies to solve Geometry problems in particular or to use the same strategies in the book to solve more Geometrically flavor problems. Nevertheless is a Joy to read.
One of the best Now this maybe is the first book written by a member of former MO team, and now a training lecturer. (The author himself won the USAMO and IMO in 1974, and helped train several USA IMO teams, including the 1994 "perfect score team"). So here is the precious experience! Besides, the ratio between the harder problems and the easier problems is really good. In my opinion this is an excellent textbook for ambitious beginners (both teachers and students), for selfstudys and problemsolving fans. Highly recommended.
Essential for budding (and experienced) problemsolvers It contains hundreds of problems from various levels of competition, from AIME problems all the way through some of the toughest Putnam problems (which, if you know anything about the Putnam, are about as hard as competition problems come). But the biggest help are the vital insights and exciting ways of looking at these problems. Don't take my word for it many past IMO contestants have suggested this book too. You don't have to be a math competition buff to gain from this book, however. If you're simply interested in mathematical puzzles and problems, and looking to expand your repertoire, this book will help you. Anyone with a good dose of intelligence and motivation will benefit. For an additional problem book, check out Mathematical Olympiad Challenges by Andreescu and Gelca. For purely Putnam treatment, there are several volumes written by Kedlaya. And if you're a CS student, looking for honing those CS math skills to be razor sharp, you should definitely look into Concrete Mathematics by Graham, Knuth, and Patashnik. Happy solving.
The Book I wish I had in High School This book is for the exceptionally brilliant and the mentally tough. It is absolutely necessary to approach this book in a different way from a standard math textbook. You MUST attempt the examples BEFORE looking at the example solutions, NO MATTER HOW DIFFICULT OR FRUSTRATING. You may be bamboozled by the problems, but even trying to understand the problems before looking at the solutions and thinking about how a solution might proceed will pay huge dividends in the long run. For example, in the first chapter Zeitz presents an example asking the reader to prove that the product of four consecutive integers cannot be a perfect square. The solution involves some clever algebraic trickery not visible to the inexperienced, but persistence and getting your hands dirty is key. If you persist in spite of the considerable difficulty, you will find that you get better very, very quickly. You will also notice that it isn't just contest problems it helps you solve. I have found that I have solved my homework sets in the Berkeley graduate engineering program much more easily since working these problems. You will start to see creative and clever solutions where they exist in everything problem oriented. PATIENCE PATIENCE PATIENCE!
Brilliant Note: I also bought ProblemSolving Strategies by Arthur Engle. Those, perhaps more advanced, problemsolvers that want even more of a challenge should purchase this book as well (as both books give very challenging problems, but Engel's is undoubtedly more advanced). ... Read more 
5. Symbolic Logic (5th Edition) by Irving M. Copi  
list price: $95.33
our price: $95.33 (price subject to change: see help) Asin: 0023249803 Catlog: Book (19790401) Publisher: Prentice Hall Sales Rank: 435910 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Reviews (4)
Great, But Outdated That said, I do not recommend this book as a text for those attempting to learn logic today. The symbolic language that is used and the mode of problemsolving demonstrated by Copi in this work is long since outdated and using this text will only confuse a logic amateur when they move on to more current and complicated logic.
a classic textbook on logic Re the logical structure of English sentences, I would like to note that I used many of the exercises from this book in a logic class I taught a few years ago, and was stunned to see the difficulties students were having: Difficulties in comprehending the logical structure of a sentence in English and then expressing this structure using Boolean connectives and quantifiers. I found this discovery both alarming and curious.
This is "the" book to use.
Excellent text dealing with 2nd order predicate calculus. Most programmers never get beyond the firstorder (unquantified) predicate calculus introduced in the standard finite math course. This text goes to the next level in formal logic, teaching how to prove or disprove that a quantified expression follows logically from a group of premises. Copi's notation is concise, leads to elegant proofs, and to proofs which are much shorter than many of the tree methods. Even if you don't feel that you have the stamina to take on quantified logic, the book is an excellent text to unquantified rules of inference. But the real wealth here is the treatment of UI, UG, EI, and EG. To become fluent with this notation requires diligently working the host of example problems in each chapter, but the result will be problemsolving abilities that are much more flexible than the abilities of mathematics alone. You may find yourself becoming addicted to formal logic! Steve ... Read more 
6. Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter  
list price: $22.00
our price: $14.96 (price subject to change: see help) Asin: 0465026567 Catlog: Book (19990101) Publisher: Basic Books Sales Rank: 2752 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Amazon.com Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers. The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. Richard Dragan Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and nonEuclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; selfreference and selfrepresentation; Turing test for machine intelligence. ... Read more Reviews (197)
Multifaceted Thesis
Essential reading The book explores a number of themes  one of the most important is joining together disparate forms of 'strange loops'  paradoxical self referential constructs that pop up in in art (Escher and Bach fugues), mathematics (Godel's theorem), religion (Zen buddhism), AI and various other places. I agree with another reviewer  everything in GEB leads towards an understanding the mind (Hofstadter's field is of course AI/cog science)  it's not just a random romp  but it's a misleading exagerration to say GEB is trying to provide a bottomup theory! It is true, some of the foundations of AI such as propositional logic are explored and various metaphors for the mind are developed as well as the importance of circular selfreferentiality, and emergence of complex behavior from simple primitives  but the implications for AI and cognitive science are always rather vague and the HOW is mostly left as an openended question. This openendedness perhaps contributes to the rambling feeling of the book. Of course these questions are great mysteries and it's not surprising that GEB doesn't provide a neat theory to tie it all together. At it's size it is a rather daunting book to read in one go, but since a lot of chapters are rather independent it is possible to dip into it from time to time, i find myself picking it up occasionally and rereading random chapters, usually i notice something new to ponder on. For me the most unique contribution of this book is the pointing out the importance of 'strange loops' in so many areas of thought (although they're never formally defined). I found myself constantly linking this idea to other things  for example Jacques Derrida's notion of deconstruction seems to me most easily understood as about creating a linguistic strangeloop to point out the limitations of language and philosophy itself. I don't think the book has really dated much at all the central ideas are timeless and AI and cognitive science haven't advanced to a point that invalidates anything, although Fermat's theorem has now been solved.
A wonderful read for all aspiring thinkers
A readable Mobius strip
Pseudoscience at best 
7. An Introduction to Formal Languages and Automata by Peter Linz  
list price: $93.95
our price: $93.95 (price subject to change: see help) Asin: 0763714224 Catlog: Book (20001001) Publisher: Jones & Bartlett Publishers Sales Rank: 128009 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (25)
Not an "Introduction" It is clear that the author isn't writing this book as a tutorial for students, but as a reference for professors. It seems like he is trying to show off his proofwriting ability throughout the book and has no concern for the poor student who might be struggling to understand new concepts. That's why I give it a low rating. I was lucky to have an excellent instructor for this class so that after her lectures I could read this book and understand most of it. But, it would be almost impossible to learn anything from this book by self study only. So my advice, like others who have posted is: Unless this book is required for a class, don't buy it!
Simply godawful Linz' utter ineptitude towards writing is what gives this book 1 star. Examples throughout chapters are sparse and relatively worthless. Sample problems at the end of the chapter, in contrast, are ridiculously difficult, and the solutions in the back don't offer any explanation whatsoever towards the answers. This is the only book I have ever read that actually made me feel dumber for reading it. It's simply demeaning. Rather than explaining or justifying his logic, as he should to the target audience of this book, he simply uses "it's obvious that..." repeatedly for sample problems and solutions. A ridiculously complex problem's solution in the back of the book will be whittled down to two lines at best, half of which says something along the line of "It's blatantly obvious that the answer is ___, and you're stupid for not realizing it." If you're actually assigned graded work from this book, may god have mercy on your soul.
Boring subject
Not a good book
for the brainy one 
8. The Logic Book with Student Solutions Manual by MerrieBergmann, JamesMoor, JackNelson  
list price: $80.00
our price: $80.00 (price subject to change: see help) Asin: 0079130836 Catlog: Book (19970301) Publisher: McGrawHill Humanities/Social Sciences/Languages Sales Rank: 211344 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description The third edition incorporates many new and updated exercises and expanded discussions on evaluating arguments and symbolization in predicate logic. A free Student Solutions Manual is packaged with every copy of the textbook. Two logic programs, Bertie III and Twootie, are available as a free download from the University of Connecticut Philosophy Department’s Web site. The Web address for downloading the software is http://www.ucc.uconn.edu/~wwwphil/software.html. Bertie 3 is a proof checker for the natural deduction method and Twootie is a proof checker for the truth tree method. ... Read more Reviews (8)
not concise, but still a good learning aide
Was Moriss Thinking? Contrary to my compatriot from Lubbock,though, I find the time spent on truth trees to be entirely beneficial. While the derivations are definitely the grandest exercise in formal logic, their focus on the validity or invalidity of an argument leaves them to fail to show the one thing that truth trees reveal, that is, the truth conditions of any given proposition. Please do not let the naysayers detract you from using this book as a text if you are undertaking the task of teaching logic. It is rather common that symbolic logic is the ruination of many a philosophy major's GPA. For me, however, I found this book extremely easy to follow and comprehend. The ample exercises, most with answers and explanations provided, only add to the worth of this classic text. Few logic books can compare with this fine instrument.
One of the worst written books I came across
Not a Classic for No Reason My experience with this text and (perhaps, therefore) with my undergraduate logic class in general was considerably more enjoyable than Mr. Morriss's experience. Certainly my professor was very good at presenting the material, but presumably he was not making up for a poorly written book. For, when I needed to consult the text, I found it actually to be quite clear and helpful. Turning to the book itself, since I am not a fan of truth trees, when I have the opportunity to teach my own logic course, I will utilize proofs. I have viewed many undergraduate logic texts, and the proof method presented in this text seems the clearest. Furthermore, as my logic professor told me and his professor told him: Logic is not in the head; it's in the fingers. Therefore, I think that the considerable amount of exercises contained in this text is greatly beneficial. Third, definitions of terms and important points are presented clearly in text boxes throughout the book. Students will benefit greatly by committing these terms and points to memory. Finally, although the price is prohibitive (hence, four stars), Bergmann, Moor, and Nelson's text has withstood the test of time. (In fact, the 4th edition is supposed to be out this summer.) Such evidence is not conclusive, but it suggests that perhaps lying behind Mr. Morriss's frustration is a cause more complex than merely this classic text.
Good text, but of course with some flaws 
9. Fuzzy Sets and Fuzzy Logic: Theory and Applications by George J. Klir, Bo Yuan  
list price: $93.33
our price: $93.33 (price subject to change: see help) Asin: 0131011715 Catlog: Book (19950511) Publisher: Prentice Hall PTR Sales Rank: 563139 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (3)
First bible of fuzzy systems theory since Dubois and Prade. The applications section presents theory which could be useful in applications rather than the applications themselves. References are given, but no distinction is made between theoretical work and realworld applications, and many of the references are old and outofdate. For a reference book on fuzzy mathematics, this book is superb; as a pointer to realworld applications, it leaves something to be desired.
Robust treatment of fuzzy logic has interdisciplinary appeal
One of the most important book to learn about fuzzy logic 
10. An Introduction to Probability and Inductive Logic by Ian Hacking  
list price: $24.99
our price: $24.99 (price subject to change: see help) Asin: 0521775019 Catlog: Book (20010702) Publisher: Cambridge University Press Sales Rank: 54352 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (3)
Hacking gets everything right except for Keynes
For anyone, any thinker I bought this book while working on a particular problem in machine learning, at a point where I had started realizing that I was losing clarity on my definition of probability. I was using the mechanics, but didn't clearly understand why the use was valid. This seemed an odd and embarrassing circumstance at the time, how could I not understand what "probability" means? As it turns out this confusion is one shared broadly in history of science, and in current applications of statistical mechanics. Prof Hacking's writing is clear and entertaining, clearly aimed at engaging the reading audience.
What do you mean, "probably"? Some readers will be disappointed by this book. Since the book concentrates on the conceptual basis of probability and inductive logic, it does not give the reader enough technical tools to really do much applied mathematics. On the other hand, by the time Hacking gets around to discussing what students of philosophy will likely view as the big philosophical payoff of probability theory (i.e. Bayesian and frequentist contributions to the problem of justifying induction) he devotes to them a mere 20 pages of not terribly deep discussion. ... Read more 
11. An Introduction to Kolmogorov Complexity and Its Applications (Graduate Texts in Computer Science) by Ming Li, P. M. B. Vitanyi  
list price: $79.95
our price: $67.96 (price subject to change: see help) Asin: 0387948686 Catlog: Book (19970101) Publisher: SpringerVerlag Sales Rank: 441701 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (6)
A must The authors are careful to place the development of the theory in its historical context, give a face to the main players in the field and explore frictions with other lines of thought. But the main storyline is the mathematical world of Kolmogorov complexity. Neccessary background knowledge is provided, most proofs are given and the open problems are presented. Most chapters are more or less self sufficient, making it possible to skip those that are of less relevance to you. In the later chapters much thought is given to the different fields of application. A third edition is in the making which will include recent advances. But since the authors make new discoveries available on the web, the present edition will continue for a long time to hold a prominent place in the book shelves of many computer scientist.
Excellent if you have the math... The reviews below give more than enough information so I won't belabour the Kolmogorov complexity here. Suffice it to say you won't find the subject detailed more fully in any other reference work in existence today. However, this book does need to be revised and updated. There has been a lot of development in the field and the sections overviewing Solomonoff's work, in particular, could be expanded. Also, I found it hard to believe that nothing about the 'philosophical' importance of the whole induction question  this is at the core of many very important questions and should not be treated trivially. There should also be some overview of two other areas that, in combination with the theory outlined in this text, are starting to form the nexus of a "new kind of science" (definitely not Wolfram's pathetic attempt). I refer to some information regarding nonclassical logical systems as well as anticipatory computing systems. Both will, I predict, become core areas in addition to extensions to Kolmogorov/Chaitin complexity in the future. All textbooks should be as clear and concise as this example.
The only one of its kind....
Comprehensive and Excellent
Careful and clear introduction to a subtle and deep field 
12. How to Solve It : A New Aspect of Mathematical Method (Princeton Science Library) by G. Polya  
list price: $16.95
our price: $11.53 (price subject to change: see help) Asin: 069111966X Catlog: Book (20040405) Publisher: Princeton University Press Sales Rank: 46582 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" outfrom building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deftindeed, brilliantinstructions on stripping away irrelevancies and going straight to the heart of the problem. ... Read more Reviews (19)
Resolute favorite: How to Solve It Polya's consideration of the Various Approaches to problem solving hangs on several key structural bands that take the forms of a teacher's questions: Do you know any related problem? Do you know an analogous problem? [Parallelograms are considered.] Here is a problem related to yours and solved before. Can you use it? Should you introduce some auxiliary element in order to make its use possible? These ring true to this recently mustered parental pedantic. Polya's actual treatise is just 30 pages; the associated 'dictionary' definitions section is quite extended, actually, making up some 200 pages. He describes going back to first principles in problem solving. January 1, 2003 is a day perhaps to remember such back tracking is sometimes in order.
Getting to Eureka Polya's consideration of the Various Approaches to problem solving hangs on several key structural bands that take the forms of a teacher's questions: Do you know any related problem? Do you know an analogous problem? [Parallelograms are considered.] Here is a problem related to yours and solved before. Can you use it? Should you introduce some auxiliary element in order to make its use possible? These ring true to this recently mustered parental pedantic. Polya's actual treatise is just 30 pages; the associated 'dictionary' definitions section is quite extended, actually, making up some 200 pages. He describes going back to first principles in problem solving. January 1, 2003 is a day perhaps to remember such back tracking is sometimes in order.
Buy it! This book beautifully explains the process of problemsolving. It starts from simple problems, lays down the fundamentals and leads to more complex problems. One of the gems is the simple formula: It is also a good reference to teach kids how to approach problems. Buy it and it will be a very handy reference.
Very helpful to my programming work I'm glad I have discovered an excellent book on problem solving which would prove indispensable in my programming career. Other programming books mainly demonstrate features of an OS or a computer language but this book goes into the heart of the computer science which is problem solving.
For math thinkers maybe 
13. An Introduction to Mathematical Reasoning : Numbers, Sets and Functions by Peter J. Eccles  
list price: $31.99
our price: $31.99 (price subject to change: see help) Asin: 0521597188 Catlog: Book (19971211) Publisher: Cambridge University Press Sales Rank: 134173 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (5)
Now I know how beautiful proofs can be
Just buy this With this book, I was able to truly learn and understand the major concepts behind mathematical logic and proof. This text brings a whole new meaning to teaching the reader about being precise; and I mean the author does an extremely terrific job of doing just that. Wow! Seriously, the focus here is on content so you won't find any sexy graphs or anything. The content is so good that I often felt that just by reading it I was propelled into a quasi pseudolecture meeting. After following this text, I can say that I now appreciate the act of being precise to the point that is required for mathematical proof. If you want to extend the knowledge of your 'white board' then just buy this thing. I am so glad I did. BTW, I only needed the content from the first five chapters, I can't say much about the rest of the text. However, taking an inductive approach, I must assume that the other chapters are also very excellent. Yess, see it worked!
Fabulous So Far. An excellent supplement for a typical college text.
It's a Jewel
UserFriendly! Almost makes learning analysis fun! 
14. Greek, Indian and Arabic Logic (Handbook of the History of Logic Series) by Dov Gabbay, John Hayden Woods  
list price: $145.00
(price subject to change: see help) Asin: 0444504664 Catlog: Book (20040206) Publisher: North Holland Sales Rank: 468861 US  Canada  United Kingdom  Germany  France  Japan  
Book Description

15. Elements of the Theory of Computation (2nd Edition) by Harry R. Lewis, Christos H. Papadimitriou  
list price: $92.00
our price: $92.00 (price subject to change: see help) Asin: 0132624788 Catlog: Book (19970807) Publisher: Prentice Hall Sales Rank: 198504 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (28)
A classic text on the theory of computation. The book begins with a brief introduction to the relevant discrete mathematics (such as set theory and cardinality) and proof techniques, then introduces the concepts of finite automata, regular expressions, and regular languages, describing their interrelationships. It proceeds to contextfree languages, pushdown automata, parse trees, pumping lemmas, Turing machines, undecidability, computational complexity, and the theory of NPcompleteness. (These are all standard topics.) Along the way, Lewis and Papadimitriou also introduce random access Turing machines and recursive functions, and do a nice job of explaining the halting problem and how this translates into undecidable problems involving grammars, various questions about Turing machines, and even twodimensional tiling problems. All of these topics are covered with an appropriate mix of formalism and intuition. Perhaps the feature I like best is the discussion of composing simple Turing machines to obtain more complex and interesting machines. The authors even introduce a convenient graphical notation for combining Turing machines and spell out specific rules for composition. While most authors are forced to immediately employ heuristics in reasoning about complex Turing machines (lest the notation become overwhelming), Lewis and Papadimitriou are able to keep the discussion more formal and structured by virtue of their Turing machine "schema". I believe this makes their arguments more rigorous and even easier to follow. This is clearly one of the best books on the theory of computation. However, be aware that there have been very significant changes from the first edition, which was lengthier and more thorough. I confess that I actually prefer the first edition, as it contains nice sections on logic and predicate calculus (which have been removed from the 2nd edition), and is a bit more formal (albeit with some fairly awful notation). The 2nd edition is definitely crisper, with much cleaner notation; it is clearly more studentfriendly, which was presumably the aim of the new edition. If you wish to teach an introduction to theoretical computer science, or wish to learn it on your own, this would be a fine book to use. It's hard to go wrong with this classic.
You'll love it or hate it.
A reference at best, a textbook from hell
Recommended for some... Overall a great book, but you should supplement it with other inexpensive computation theory and logic books. After you've mastered this, check out Papadimitriou's "Computational Complexity" and Hartley Rogers' "Theory of Recursive Functions and Effective Computability", two fantastic intermediatelevel books.
Just plain boring. 
16. Foundations and Fundamental Concepts of Mathematics by Howard Whitley Eves, Howard Eves  
list price: $16.95
our price: $11.87 (price subject to change: see help) Asin: 048669609X Catlog: Book (19970501) Publisher: Dover Publications Sales Rank: 21372 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (3)
'Swiss Army Knife' of Upper Level Mathematics
Excellent Overview. Belongs on Your Bookshelf. My few semesters of calculus, differential equations, and other applied math failed to formally introduce me to abstract algebras, nonEuclidian geometries, projective geometry, symbolic logic, and mathematical philosophy. I generally considered algebra and geometry to be singular nouns. Howard Eves corrected my grammar. "Foundations and Fundamental Concepts" is not a traditional history of mathematics, but an investigation of the philosophical context in which new developments emerged. Eves paints a clear picture of the critical ideas and turning points in mathematics and he does so without requiring substantial mathematics by the reader. Calculus is not required. The first two chapters, titled "Mathematics Before Euclid" and "Euclid's Elements", consider the origin of mathematics and the remarkable development of the Greek axiomatic method that dominated mathematics for nearly 2000 years. In chapter three Eves introduces nonEuclidian geometry. Mathematics is transformed from an empirical method focused on describing our real, threedimensional world to a creative endeavor that manufactures new, abstract geometries. This discussion of geometries, as opposed to geometry, continues in chapter four. The key topics include Hilbert's highly influential work that placed Euclidian geometry on a firm (but more abstract) postulational basis, Poincaire's model and the consistency of Lobachevskian geometry, the principle of duality in projective geometry, and Decartes development of analytic geometry. For the noninitiated these topics may seem daunting, but Eves' approach is clear and quite fascinating. Chapter five, which might have been titled "The Liberation of Algebra", may at first be a bit overwhelming to those unaware of algebraic structures like groups, rings, and fields. But take solace as even mathematicians in the early nineteenth century still considered algera to be little more than symbolized arithmetic. As Eves says, nonEuclidian geometry released the "invisible shackles of Euclidian geometry". Likewise, abstract algebra created a parallel revolution. (Again, don't be intimidated by the terminology. Eves is quite good.) The remaining four chapters look at the axiomatic foundation of modern mathematics, the real number system, set theory, and finally mathematical logic and philosophy. Eves concludes with the surprising discovery of contradictions within Cantor's set theory as well as Hilbert's unsuccessful effort to define procedures to avoid inconsistencies or contradictions within an axiomatic system. Eves mentions Godel's fundamental contribution to mathematical logic, but stops short of delving into Godel's Proof. For additional reading I highly recommend "Godel's Proof" by Ernest Nagel and James R. Newman. I also highly recommend Richard Courant's and Herbert Robbins' classic, "What is Mathematics?", a more detailed examination of the development of fundamental ideas and methods underlying mathematics. I would suggest that most readers, particularly nonmath majors, first read Eves and later tackle Courant and Robbins. I have read "Foundations and Fundamentals of Mathematics" at least twice. I gave my son a copy for Christmas. He says that the book is great and he even claims to be reading it as he walks across his campus between classes. The price is great. It belongs in your book collection.
Ecellent description of the history of mathematical thinking The book goes on with chapters on Hilbert's Grundlagen, Algebraic Structure etc, always showing not only the substance of these periods but also the shift in the way of thinking and the development towards rigor. The last chapter is titled Logic and Philosophy. Eves divides "contemporary" philosophies of mathematics into three schools: logistic (Russel/Whitehead), intuitionist (Brouwer) and the formalist (Hilbert). The book ends with some interesting appendices on specific problems like the first propositions of Euclid, nonstandard analysis and even Gödel's incompleteness theorem. Bibliography, solutions to selected problems and an index are carefully prepared to round up an excellent book. Should you buy this book ? Yes. What kind of mistake can you make in spending US$ 12.95 on a book that has withstood the test of time through three editions (each with a different publisher). I havent completed reading the book yet, but I dont regret having bought it. ... Read more 
17. Attacking Faulty Reasoning: A Practical Guide to FallacyFree Arguments by T. Edward Damer  
list price: $47.95
our price: $47.95 (price subject to change: see help) Asin: 0534551335 Catlog: Book (20000614) Publisher: Wadsworth Publishing Sales Rank: 212823 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (10)
The antidote for contradiction and controversy.
Best critical thinking book out there I particularly liked the author's focus on WHY fallacies are bad instead of just rattling them off. This is a book I can recommend to anyone, even the old veterans of argumentation.
Argument Karate
Liberal bias?
Excellent overall, but some examples are weak With such a large number of fallacies demanding multiple examples, the author must be forgiven if some of them seem a little off the mark, even while being technically correct. For example, the proposition (I'm paraphrasing) "Our baseball team was 1 and 11 this year, but with a new coach we'll do better next year." is in fact false. However, if the proposition were that "we'll probably do better" it would be true, because the probability is that we would get an average coach and an average coach has a record of 0.500, while assuming that coaching has a positive effect. Another example has former Predident Bush answering the question, "Did Dan Quayle's parents help him get into the national guard?" with words to the effect that "At least he served patrioticly and didn't run to Canada or burn the flag." The answer while technically irrelevant is a politician's way of saying, "Whether his parents helped or not is unimportant, at least ...blah, blah." Such an answer invites a rejoinder along the lines of "It really is important, because ..." The fault of the example is that it implies it is OK to rest on the technicalities even when you have a very good idea of what your opponent is really saying. So if some of the example are a little offbase, perhaps that is all to the good as a learning experience. The small bits of uneasiness are left to the student as an exercise to resolve. The author provides the tools for doing so. ... Read more 
18. Languages and Machines: An Introduction to the Theory of Computer Science (2nd Edition) by Thomas A. Sudkamp  
list price: $110.40
our price: $110.40 (price subject to change: see help) Asin: 0201821362 Catlog: Book (19961104) Publisher: Addison Wesley Sales Rank: 142658 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Amazon.com Reviews (7)
Good Book for those who have had discrete math
Great Read (For those of us with IQs higher than 180)
Difficult stuff, but not in the way you might think That said, this isn't too bad a textbook. It does a pretty decent job explaining the subject matter, which isn't very hard to pick up... IF you can stay awake! I get the feeling Dr. Sudkamp was falling asleep as he finished off each paragraph, and he sure managed to do the same to me when reading it. Though the chapters seem short, you'll find it takes you up to an hour to read through them. Why? Because you'll read the first part, go on to the next... realize you've forgotten everything in the first part, and have to reread it. Repeat as necessary, ad infinitum. The exercises have no solutions whatsoever, which can be a pain for this sort of material. Examples don't really help you do them because only the very general solving method is similar, and each problem really is a completely new thing. The bottom line is, if you have to learn this material, then you're probably going to have to read it. But I wouldn't advise getting this book for some light reading at night.
Excellent Book, A Must have. My only complaint: It would have helped if the author could have gave answers to some of the problems at the end of the chapters.
A good introduction, bent towards formal languages The book stresses formal languages and parsing, and is therefore best suited for persons interested in creating languages, compiler technology and parsing. However, it covers also Turing machines, computability and complexity issues, among others, and is therefore reasonably comprehensive. Exercises range from easy to moderate, and many of them are stimulating. Another reviewer complained about the lack of drill exercises (see below). I can understand the anguish of students; some of the exercises, as well as parts of the text, may be difficult if one doesn't have much experience in formal reasoning and abstract problem solving. However, all exercises I have taken a look at are solvable with the knowledge provided in the text, and are therefore suitable for readers with at least a fair mathematical background. My main complaint is the small number of applications. In chapter 3, there is a nice example: the arithmetic expressions of Pascal; in chapter 15, good examples of NPcomplete problems. However, these are exceptions. In my opinion the text would greatly benefit from e.g. endofchapter exercises related to programming minilanguages which could be defined on the spot. Also examples of finite state machines (copier machines, services in a mobile phone etc.) would add flesh to exercises. All in all, this is a good entry point to theoretical computer science for a person trained in mathematics or a related field, but may partly be too challenging to a firstyear student. ... Read more 
19. Friendly Introduction to Mathematical Logic, A by Christopher C. Leary  
list price: $68.00
our price: $68.00 (price subject to change: see help) Asin: 0130107050 Catlog: Book (19991208) Publisher: Prentice Hall Sales Rank: 726793 US  Canada  United Kingdom  Germany  France  Japan  
Book Description 
20. Basic Category Theory for Computer Scientists (Foundations of Computing) by Benjamin C. Pierce  
list price: $25.00
our price: $25.00 (price subject to change: see help) Asin: 0262660717 Catlog: Book (19910807) Publisher: The MIT Press Sales Rank: 232540 Average Customer Review: US  Canada  United Kingdom  Germany  France  Japan  
Book Description Reviews (4)
Too terse
the best understaning of categories you can get
Clear and concise Read this book before you tackle Mac Lane.
This book is a CCC. 
120 of 200 1 2 3 4 5 6 7 8 9 10 Next 20 