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1. Mathematical Logic by Stephen Cole Kleene | |
Paperback: 416
Pages
(2002-12-18)
list price: US$24.95 -- used & new: US$14.02 (price subject to change: see help) Asin: 0486425339 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (4)
Still very usefull
Excellent Excellent Book
Excellent introduction
Not for the autodidact If one were to read this book under the guidance of a teacher, I think it might be worthwhile.It may not be fair for me to blame the author for my inability to understand his writing.If you're smarter than I am, you might breeze right through it. I cannot recommend this book, though, good though it may be, for anyone who wishes to teach him/herself logic, nor for anyone who wishes to brush up on the subject.There are exercises for the reader to test his/her understanding of the material, but no answer key is provided.This is heavy-duty stuff, and not well-suited to the self-teacher. ... Read more |
2. My Best Mathematical and Logic Puzzles (Math & Logic Puzzles) by Martin Gardner | |
Paperback: 96
Pages
(1994-11-01)
list price: US$4.95 -- used & new: US$1.65 (price subject to change: see help) Asin: 0486281523 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (13)
Fun book to bring on vacation
Very good puzzles book
Don't waste your money
Great bathroom reading!
Good for warming up your brain. |
3. A Mathematical Introduction to Logic, Second Edition by Herbert Enderton, Herbert B. Enderton | |
Hardcover: 317
Pages
(2001-01-05)
list price: US$113.00 -- used & new: US$64.88 (price subject to change: see help) Asin: 0122384520 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (13)
Best Intro. Logic Book Ever!
NOT A GOOD CHOICE FOR THE BUKKAKE LOVER
Fascinating material, poor proofs
From the point of a CS student
John Wilson |
4. A Course on Mathematical Logic (Universitext) by Shashi Mohan Srivastava | |
Paperback: 150
Pages
(2008-03-12)
list price: US$54.95 -- used & new: US$34.99 (price subject to change: see help) Asin: 0387762752 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This is a short, distinctive, modern, and motivated introduction to mathematical logic for senior undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in knowing what logic is concerned with and who would like to learn Gödel’s incompleteness theorems should find this book particularly convenient. The treatment is thoroughly mathematical, and the entire subject has been approached like a branch of mathematics. Serious efforts have been made to make the book suitable for the classroom as well as for self-reading. The book does not strive to be a comprehensive encyclopedia of logic. Still, it gives essentially all the basic concepts and results in mathematical logic. The book prepares students to branch out in several areas of mathematics related to foundations and computability such as logic, axiomatic set theory, model theory, recursion theory, and computability. The main prerequisite for this book is the willingness to work at a reasonable level of mathematical rigor and generality. |
5. Introduction to Logic by Alfred Tarski | |
Paperback: 239
Pages
(1995-03-27)
list price: US$12.95 -- used & new: US$7.78 (price subject to change: see help) Asin: 048628462X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout. Customer Reviews (4)
An Important Work in Logic History
Perhaps the best written written elementary book of logic
TIMELESS CORE HOLDING IN ANY LOGIC LIBRARY
I will always keep it as a reference |
6. Introduction to Mathematical Logic, Fifth Edition (Discrete Mathematics and Its Applications) by Elliott Mendelson | |
Hardcover: 469
Pages
(2009-08-11)
list price: US$89.95 -- used & new: US$42.98 (price subject to change: see help) Asin: 1584888768 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing. New to the Fifth Edition
This long-established text continues to expose students to natural proofs and set-theoretic methods. Only requiring some experience in abstract mathematical thinking, it offers enough material for either a one- or two-semester course on mathematical logic. |
7. Proofs and Refutations: The Logic of Mathematical Discovery | |
Paperback: 188
Pages
(1976-01-01)
list price: US$43.00 -- used & new: US$25.79 (price subject to change: see help) Asin: 0521290384 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (11)
Largely trivial
the heuristic of mathematical discovery
nice reading for the general public It discusses polyhedra in 3 (or more) dimensions and Euler's formula that describes their numbers of vertices, edges, faces, e.t.c. The challenge is to determine what specific kinds of polyhedra satisfy the formula and conversely, how one could generalize the formula so as to describe more (if not all) polyhedra. Lots of historical references illustrate the fact that the discussion is not naive and that reflects the actual history of the subject. One can realize through this book that math people are not Gods and do not produce theories out of nowhere, but they experiment with their objects like any other scientist, and then try to summarize in an elegant/rigorous way.
a study in mathematical thought However, for those readers (including beginning mathematicians) who are interested in the broader picture, who are interested in the nature of mathematical proof, then Lakatos is essential reading. The examples chosen are vivid, and there is a rich sense of historical context. The dramatised setting (with Teacher and students Alpha, Beta, Gamma, etc) is handled skilfully. Now and then, a foolish-seeming comment from one of the students has a footnote tagged to it; more often than not, that student is standing in for Euler, Cauchy, Poincare or some other great mathematician from a past era, closely paraphrasing actual remarks made by them. That in some ways is the most important lesson I learned from this book; "obvious" now doesn't mean obvious then, even to the greatest intellects of the time. Although "Proofs and Refuatations" is an easy book to begin reading, it is not an easy book per se. I have returned to it repeatedly over the last ten years, and I always learn something new. The text matures with the reader.
Excellent Critical Reasoning Framework Displaying solid content with artful execution, this book interested me in both the math of the thing and the acompanying thought processes. Content:This book has near-poetic density and elegance in arguing a non-linear approach to mathematical development and, for me, to just plain thinking.Our tendency (as born worshippers of linearity and causality) is to discover a brick for the building then immediately look for the next to stack on top.Lakatos contends that PERHAPS you have discovered a brick worthy of the building, now let's see what truly objective tests we will put to this brick and before giving it a final stamp of approval.It seems obvious to say "always question", but the exercise in this book will take you through the process and show you what you may take for granted in this simple concept.For example, do you observe HOW you question? See his discussion throughout on global vs. local counterexamples, just as a start. Execution of the text:This is the beautiful part.Mr. Lakatos has written this book as theater: characters with definite identities, plot, drama. The narrative flows in the voices of students and a professor who proves to be a sound moderator, intervening at timely points, i.e. those where questions may be crystallized or thoughts prodded to that point.This is where learning takes place, in a heated, moderated debate over Euler's formula.What was most interesting to me about this method was that it lent itself easily to isolating a particular thread of discussion. I literally chose certain characters to research from beginning to end in order to follow the evolution or confirmation of their thinking. You emerge with a good framework that makes this book excellent reference material for problem-solving. One last, but important note.This book will have you praising the lowly footnote.I would buy it for that alone.You will read along with the discussion, then get off and examine a footnote, and then pick the dialogue back up not having lost a step.On the contrary, Mr. Lakatos deepens your context with on-point explanations and math history. ... Read more |
8. Fundamentals of Mathematical Logic by Peter G. Hinman | |
Hardcover: 896
Pages
(2005-11-15)
list price: US$99.00 -- used & new: US$98.01 (price subject to change: see help) Asin: 1568812620 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Based on the author’s more than 35 years of teaching experience, the book develops students’ intuition by presenting complex ideas in the simplest context for which they make sense. He also provides extensive introductions to set theory, model theory and recursion (computability) theory, which allows this book to be used as a classroom text, for self-study, and as a reference on the state ofmodern logic. Customer Reviews (2)
Where's the proof?
A Comprehensive Graduate Text |
9. Yes--No, Stop--Go: Some Patterns in Mathematical Logic (Young Math Books) by Judith L. Gersting, Joseph E. Kuczkowski, Don Madden | |
Library Binding: 34
Pages
(1977-10)
list price: US$12.89 Isbn: 069001130X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Logic for children
Why this book is great |
10. Logic For Dummies by Mark Zegarelli | |
Paperback: 384
Pages
(2006-11-29)
list price: US$19.99 -- used & new: US$9.53 (price subject to change: see help) Asin: 0471799416 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description
Logic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you’ve learned. Customer Reviews (8)
The most readable introductory-level book on logic I've read
Easy to understand logic!
Simple Logic
Good for leisure reading
Beware of typos and errors |
11. A Profile of Mathematical Logic (Dover Books on Mathematics) by Howard DeLong | |
Paperback: 320
Pages
(2004-06-17)
list price: US$19.95 -- used & new: US$11.77 (price subject to change: see help) Asin: 0486434753 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This text explores the historical reasons for the formation of Aristotelian logic, the rise of mathematical logic, the nature of the formal axiomatic method and its use, and the main results of metatheory and their import. 1971 edition. Includes 22 figures and 19 tables. Appendixes. Bibliography. Indexes. Customer Reviews (1)
Oldie But Goodie |
12. A Concise Introduction to Mathematical Logic (Universitext) by Wolfgang Rautenberg | |
Paperback: 319
Pages
(2009-12-17)
list price: US$69.95 -- used & new: US$48.54 (price subject to change: see help) Asin: 1441912207 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Traditional logic as a part of philosophy is one of the oldest scientific disciplines and can be traced back to the Stoics and to Aristotle. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, and others to create a logistic foundation for mathematics. It steadily developed during the twentieth century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. This book treats the most important material in a concise and streamlined fashion. The third edition is a thorough and expanded revision of the former. Although the book is intended for use as a graduate text, the first three chapters can easily be read by undergraduates interested in mathematical logic. These initial chapters cover the material for an introductory course on mathematical logic, combined with applications of formalization techniques to set theory. Chapter 3 is partly of descriptive nature, providing a view towards algorithmic decision problems, automated theorem proving, non-standard models including non-standard analysis, and related topics. The remaining chapters contain basic material on logic programming for logicians and computer scientists, model theory, recursion theory, Gödel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. Each section of the seven chapters ends with exercises some of which of importance for the text itself. There are hints to most of the exercises in a separate file Solution Hints to the Exercises which is not part of the book but is available from the author’s website. Customer Reviews (2)
Complete and demanding
The best intro to logic to-date |
13. Mathematical Logic by Joseph R. Shoenfield | |
Paperback: 356
Pages
(2001-01-15)
list price: US$35.00 -- used & new: US$35.00 (price subject to change: see help) Asin: 1568811357 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Standard by default
Rock-solid introduction to Mathematical Logic Usually, of course, most work in mathematics doesn't require a deep knowledge of rigorous mathematical logic, but it's always a good thing to a serious mathematician to have some acquaintance with it, even if it's just to avoid boobytraps. Then, it's hard to find a better choice than Shoenfield's book. After a long absence from the book market, A K Peters made the wise decision of reprint this masterpiece. Although most of its contents are fairly standard for a book on mathematical logic (unlike the equally marvellous out-of-print book of Yu.I. Manin, which has a more philosophical slant and concerns itself with issues such as quantum logic, literature, etc.), it provides proofs for many propositions that in most of the literature are only stated. It has, of course, some extras not generally found in other books, as for example issues concerning constructibility of sets. But the most important characteristic of this book is its clarity and precision. Itdoesn't waste time in unnecessary stuff, and shows why we need mathamaticallogic at all. Although it lacks some topics (for example, it doesn't discuss otheraxiomatic set theories besides Zermelo-Fraenkel. This is not so nice, because itlacks the distinction between classes and sets, one of the tenets of the Goedel- -Bernays-von Neumann set theory, although it is conceptually easier than thislast one. But maybe it's a pedagogical choice, because the set theory we allintuitively know is more or less based in Zermelo-Fraenkel), its main concern ispedagogy, so this limitation has a sound reason: this book exposes mainly the logic present in the math most mathematicians and alike scientists (mathematicalphysicists, etc.) use. Its solidity and razor-sharp precision is great to instruct thesepeople to be more careful with the math they use. Besides that, some of the missing topics can be complemented by Mendelsson's "Introduction to Mathematical Logic", which is a bit more "merciful" book, which, by the other side, welcomes the thoroughness of Shoenfield. ... Read more |
14. Mathematical Logic: A First Course (Dover Books on Mathematics) by Joel W. Robbin | |
Paperback: 224
Pages
(2006-07-07)
list price: US$13.95 -- used & new: US$8.85 (price subject to change: see help) Asin: 048645018X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Suitable for advanced undergraduates and graduate students, this self-contained text will appeal to readers from diverse fields and varying backgrounds — including mathematics, philosophy, linguistics, computer science, and engineering. Topics include 1st-order recursive arithmetic, 1st- and 2nd-order logic, and the arithmetization of syntax. Numerous exercises; some solutions. 1969 edition. Customer Reviews (2)
AGood Mathematical Logic Text
I've worked throught the first two chapters |
15. Introduction to Elementary Mathematical Logic by Abram Aronovich Stolyar | |
Paperback: 209
Pages
(2010-10-18)
list price: US$10.95 -- used & new: US$7.55 (price subject to change: see help) Asin: 0486645614 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Awesome
Not for beginners |
16. The Mathematical Analysis of Logic: Being an Essay Towards a Calculus of Deductive Reasoning (Classic Reprint) by George Boole | |
Paperback: 90
Pages
(2010-03-18)
list price: US$7.08 -- used & new: US$7.08 (price subject to change: see help) Asin: 1440066426 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
What sould I do? |
17. Mathematical Logic, Revised Edition by W. V. Quine | |
Paperback: 358
Pages
(1981-04-15)
list price: US$30.50 -- used & new: US$27.44 (price subject to change: see help) Asin: 0674554515 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (3)
Good book
Very good but be aware of omissions I like the set theory of this book, but I warn you that it is very nonstandard. Even ardent lovers of Quine's NF theory hate The weakness of this book is its treatment of metatheory: I respect the historical remarks a lot. Just one big omission: Quine, like nearly everyone of his generation, missed that
In Depth Look at Logic |
18. A Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics) by Yu. I. Manin | |
Hardcover: 384
Pages
(2009-10-30)
list price: US$69.95 -- used & new: US$55.69 (price subject to change: see help) Asin: 1441906142 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The book starts with an elementary introduction to formal languages appealing to the intuition of working mathematicians and unencumbered by philosophical or normative prejudices such as those of constructivism or intuitionism. It proceeds to the Proof Theory and presents several highlights of Mathematical Logic of 20th century: Gödel's and Tarski's Theorems, Cohen's Theorem on the independence of Continuum Hypothesis. Unusual for books on logic is a section dedicated to quantum logic. Then the exposition moves to the Computability Theory, based on the notion of recursive functions and stressing number{theoretic connections. A complete proof of Davis{Putnam{Robinson{Matiyasevich theorem is given, as well as a proof of Higman's theorem on recursive groups. Kolmogorov complexity is treated. The third Part of the book establishes essential equivalence of proof theory and computation theory and gives applications such as Gödel's theorem on the length of proofs. The new Chapter IX, written for the second edition, treats, among other things, categorical approach to the theory of computation, quantum computation, and P/NP problem. The new Chapter X, written for the second edition by Boris Zilber, contains basic results of Model Theory and its applications to mainstream mathematics. This theory found deep applications in algebraic and Diophantine geometry. Yuri Ivanovich Manin is Professor Emeritus at Max-Planck-Institute for Mathematics in Bonn, Germany, Board of Trustees Professor at the Northwestern University, Evanston, USA, and Principal Researcher at the Steklov Institute of Mathematics, Moscow, Russia. Boris Zilber, Professor of Mathematics at the University of Oxford, has been added to the second edition. |
19. Principles of Mathematical Logic by David Hilbert, W. Ackermann | |
Hardcover: 172
Pages
(1999-07-01)
list price: US$30.00 -- used & new: US$24.00 (price subject to change: see help) Asin: 0821820249 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Good old book
classic |
20. Mathematical Logic (Undergraduate Texts in Mathematics) by H.-D. Ebbinghaus, J. Flum, W. Thomas | |
Hardcover: 308
Pages
(1994-06-10)
list price: US$79.95 -- used & new: US$47.96 (price subject to change: see help) Asin: 0387942580 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (12)
Will not suggest to anyone.
Excellent Choice for Teaching Mathematical Logic
The steepest on-ramp to the fast lane of logic
Should be the standard undergrad introduction
Reads like Mathematical Poetry The question this book addresses is not "why logic?", or "what is a formal logic?", but more specifically, "why is first-order predicate calculus with equality such a good foundation for mathematics?" The formal mathematics is organized and presented so clearly and precisely that I felt I was admiring a fine crystal structure. The book explores second-order predicate logic and makes explicit some of the difficulties, such as incompleteness and even the problem of how closely the truth of a formula in second order logic depends on what we take as true in set theory: different axiomatizations of set theory lead to different semantics for second-order predicate logic! There is a great chapter on the incompleteness theorems, and in addition to Goedel's theorems, there is a section on Register Machines (a version of Turing Machines) and a proof of the undecidability of arithmetic using the halting problem, as well as a more general theorem about the undecidability of any theory that can encode the workings of a Register Machine. The next section is a reasonable presentation of the mathematical underpinnings of logic programming. The book concludes with an algebraic characterization of elementary equivalence followed by two deep theorems by Lindstrom that demonstrate the uniqueness of first order predicate calculus among formal languages with set theoretic semantics. ... Read more |
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