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41. Mathematical Reasoning: Writing and Proof (2nd Edition) by Ted Sundstrom | |
Hardcover: 544
Pages
(2006-03-23)
list price: US$114.67 -- used & new: US$65.00 (price subject to change: see help) Asin: 0131877186 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout. For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Theodore Sundstrom Customer Reviews (3)
Terrible book on proofs.Avoid.
I expected better
Very Helpful |
42. Mathematical Logic Hierarchies: Arithmetical Hierarchy | |
Paperback: 44
Pages
(2010-09-15)
list price: US$14.14 -- used & new: US$12.73 (price subject to change: see help) Asin: 1156528224 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
43. Mathematical Logic Introduction: Primitive Notion, Truth Value, Lcf, Infinite Set, Shelah Cardinal, Singular Cardinals Hypothesis | |
Paperback: 388
Pages
(2010-09-15)
list price: US$45.84 -- used & new: US$34.84 (price subject to change: see help) Asin: 1157069118 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
44. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Applied Logic Series) by Peter B. Andrews | |
Paperback: 408
Pages
(2010-11-02)
list price: US$169.00 -- used & new: US$140.09 (price subject to change: see help) Asin: 9048160790 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. Customer Reviews (1)
used early draft as grad text |
45. Logic, Induction and Sets (London Mathematical Society Student Texts) by Thomas Forster | |
Paperback: 244
Pages
(2003-07-21)
list price: US$39.99 -- used & new: US$30.57 (price subject to change: see help) Asin: 0521533619 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Unusual reliance on text rather than equations |
46. First-Order Logic by Raymond M. Smullyan | |
Paperback: 158
Pages
(1995-01-30)
list price: US$9.95 -- used & new: US$6.39 (price subject to change: see help) Asin: 0486683702 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
Great stuff. It's not a general mathematical logic text- there is no model theory (beyond basic Skolem-Lowenheim), incompleteness, recursion theory, or set theory. It covers tableaux (this alone is worth the price of the book), Hilbert-style axiomatic systems (briefly), sequent systems, Gentzen's Hauptsatz and Extended Hauptsatz, Craig's and Beth's theorems, and more. But the heart of the book is completeness theorems, their proofs, and closely related material such as compactness and Herbrand-like theorems. Smullyan shows there are two main approaches to completeness (analytic vs. synthetic), breaks each into stages, provides nice abstracted formulations, and usually gives several different proofs of each result. The centerpiece is his "Fundamental Theorem of Quantification Theory", a theorem associating a truth-table tautology with every valid first-order sentence (check out the amazingly slick proof of completeness for the the Hilbert-style system that this provides). Similar constructions such as magic sets are also discussed. All this forms a much more extensive and illuminating look at completeness proofs than I've seen elsewhere. The first-order logic used in the book has no equality and no function signs. There are few exercises, most of them simple. Smullyan writes clearly and with an appropriate amount of rigor (but its not as polished as his later books). Makes a great supplement to more general-purpose introductory mathematical logic books. If you haven't seen the tableau method yet buy this book immediately. Experienced readers will appreciate the sophisticated coverage of completeness proofs.
An Oddity But a Good-ity. Wait, that's terrible.
a classic
Great as a Reference, Probably Not for True Beginners However, I doubt it would be appropriate for someone that has not previously been introduced to the material.If a truly introductory text is required, I would look elsewhere.
A Stripped-Down Exposition of a Bare-bones Subject Smullyan procedes rapidly because he makes some assumptions about the reader's knowledge. The reader must understand the difference between mathematics and meta-mathematics-that is, should be able to separate out the talking about the sentences of the system, which may contain (among other signs) the conjunction, disjunction, and negation, from the more-or-less informal arguments that prove assertions about these sentences using natural language, with its "and", "or", and "not". Moreover, the concept of "proof" is used at two levels: the particular tableau that constitutes a proof of a sentence, and the "proofs" about tableaux and other concepts of the "system". Besides this, the reader should have a good feel for recursive definitions, which are used everywhere. Finally, this model reader should know the difference between countably-infinite sets and uncountably-infinite sets. I knew all that, but still found the text slow going, maybe because I have been away from mathematics for decades. But there is another reason, too. Smullyan has divorced logic from its roots: logics are simply recursively-defined sets of sentences and mappings, and that is that. No discussions, ala WvO Quine, on the history or linguistic difficulties of a concept, just definition and proof. This is an abstraction of a subject which is already an abstraction. So I usually found myself trying to understand what it all meant, in other than these stark set-and-mapping terms. On the other hand, many difficulties caused by the details of historical development of the subject vanish, and the results stand-... simple, directly derived. This is a slender Dover volume, of high quality and low cost. I would have given the book 5 stars, but for two things. The exercises are too hard, sometimes, and without answers, and the index is very poor. Still, I think the treatment is the best around for those who want to use logic as a basis for studying incompleteness or proof theory. It is not to be confused with a more full-blown treatment that also treats logic as a branch of the humanities. ... Read more |
47. Mathematical Logic and the Foundations of Mathematics: An Introductory Survey by G. T. Kneebone | |
Paperback: 452
Pages
(2001-04-25)
list price: US$16.95 -- used & new: US$9.99 (price subject to change: see help) Asin: 0486417123 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Nothing Great. |
48. Advances in Linear Logic (London Mathematical Society Lecture Note Series) | |
Paperback: 400
Pages
(1995-06-30)
list price: US$85.00 -- used & new: US$70.63 (price subject to change: see help) Asin: 0521559618 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
49. Mathematical Logic Applications and Theory (Saunders Series) by Jean E. Rubin | |
Hardcover: 417
Pages
(1990-01)
list price: US$81.95 Isbn: 0030128080 Canada | United Kingdom | Germany | France | Japan | |
50. Mathematical Logic : A course with exercises -- Part I -- Propositional Calculus, Boolean Algebras, Predicate Calculus, Completeness Theorems by Rene Cori, Daniel Lascar | |
Paperback: 360
Pages
(2000-11-09)
list price: US$85.00 -- used & new: US$72.56 (price subject to change: see help) Asin: 0198500483 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
OK but Hard Interesting topic covered: the resolution so dear to the AI crowd. Unlike most mathematicians, Cori and Lascar have time for Haven't seen Part II, so cannot comment on the treatment of set theory. This is something Mendelson and Machover already do well. ... Read more |
51. Mathematical Methods in Linguistics (Studies in Linguistics and Philosophy) (Volume 0) by Alice ter Meulen | |
Paperback: 692
Pages
(1990-04-30)
list price: US$42.95 -- used & new: US$34.10 (price subject to change: see help) Asin: 9027722455 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Extremely good.
Comprehensive
Not Just for Linguists Instead it covers such mathematical topics as sets (including infinite sets), relations, a good deal of mathematical logic, This would be an excellent book for an advanced undergraduate or graduate student in either mathematics or computer science to use |
52. Mathematical Fallacies and Paradoxes by Bryan Bunch | |
Paperback: 224
Pages
(1997-07-01)
list price: US$10.95 -- used & new: US$3.00 (price subject to change: see help) Asin: 0486296644 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
An adequate introduction
A great introduction to the limits of math
Informal and engaging
This is a Great Book for Math Fans This book may also be of interest to neuroscientists, cognitive scientists, and psychologists who are interested in how human beings learn and apply mathematics. On a somewhat related note, I have noticed that (for some strange reason) this book has attracted a set of rather bizarre reviewers (see below). Please ignore them and buy this inexpensive and insightful book on math.
Zeno and set theory |
53. The Moscow Puzzles: 359 Mathematical Recreations (Math & Logic Puzzles) by Boris A. Kordemsky | |
Paperback: 320
Pages
(1992-04-10)
list price: US$12.95 -- used & new: US$5.53 (price subject to change: see help) Asin: 0486270785 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (13)
Jewel of math history!
As usual, Gardner rocks
In Soviet Russia, the puzzle solves you
Funny, challenging, and well written!
very good |
54. The Principles of Inductive Logic (AMS Chelsea Publishing) by John Venn | |
Hardcover: 604
Pages
(1973-01-01)
list price: US$55.00 -- used & new: US$44.00 (price subject to change: see help) Asin: 0828402655 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
55. Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition) by Gary Chartrand, Albert D. Polimeni, Ping Zhang | |
Hardcover: 384
Pages
(2007-10-13)
list price: US$114.67 -- used & new: US$91.99 (price subject to change: see help) Asin: 0321390539 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (17)
Appropriate for beginning the trek into advanced math.
A must read for the major!
A very solid introduction to mathematical thinking
Superb
Gripping and Suspenseful |
56. Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers by Bernd S. W. Schr?der | |
Hardcover: 338
Pages
(2010-08-16)
list price: US$79.95 -- used & new: US$57.89 (price subject to change: see help) Asin: 0470551380 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Addressing the importance of constructing and understanding mathematical proofs, Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet. The book begins with a focus on the elements of logic used in everyday mathematical language, exposing readers to standard proof methods and Russell's Paradox. Once this foundation is established, subsequent chapters explore more rigorous mathematical exposition that outlines the requisite elements of Zermelo-Fraenkel set theory and constructs the natural numbers and integers as well as rational, real, and complex numbers in a rigorous, yet accessible manner. Abstraction is introduced as a tool, and special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas. The book concludes with a self-contained proof of Abel's Theorem and an investigation of deeper set theory by introducing the Axiom of Choice, ordinal numbers, and cardinal numbers. Throughout each chapter, proofs are written in much detail with explicit indications that emphasize the main ideas and techniques of proof writing. Exercises at varied levels of mathematical development allow readers to test their understanding of the material, and a related Web site features video presentations for each topic, which can be used along with the book or independently for self-study. Classroom-tested to ensure a fluid and accessible presentation, Fundamentals of Mathematics is an excellent book for mathematics courses on proofs, logic, and set theory at the upper-undergraduate level as well as a supplement for transition courses that prepare students for the rigorous mathematical reasoning of advanced calculus, real analysis, and modern algebra. The book is also a suitable reference for professionals in all areas of mathematics education who are interested in mathematical proofs and the foundation upon which all mathematics is built. |
57. Stat Labs:Mathematical Statistics Through Applications by Deborah Nolan, Terry P. Speed | |
Paperback: 282
Pages
(2000-05-31)
list price: US$49.95 -- used & new: US$28.99 (price subject to change: see help) Asin: 0387989749 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
interesting approach to teaching statistics
An Excellent Book I recommend the software MiniTAB to accompany this book. I especially liked the chapter on HIV and mortality (very interesting results)! ... Read more |
58. Sweet Reason: A Field Guide to Modern Logic (Textbooks in Mathematical Sciences) by Tom Tymoczko, Jim Henle | |
Paperback: 644
Pages
(1999-12-10)
list price: US$54.95 -- used & new: US$48.95 (price subject to change: see help) Asin: 0387989307 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Do not take a class that requires this book.
the best logic book ever
logic textbook |
59. Lectures in Logic and Set Theory: Volume 2, Set Theory (Cambridge Studies in Advanced Mathematics) by George Tourlakis | |
Paperback: 591
Pages
(2010-09-09)
list price: US$70.00 -- used & new: US$70.00 (price subject to change: see help) Asin: 0521168481 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Excellent book as an advanced introduction. |
60. Understanding Symbolic Logic (5th Edition) by Virginia Klenk | |
Paperback: 480
Pages
(2007-04-29)
list price: US$111.40 -- used & new: US$84.99 (price subject to change: see help) Asin: 0132051524 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This comprehensive introduction presents the fundamentals of symbolic logic clearly, systematically, and in a straightforward style accessible to readers. Each chapter, or unit, is divided into easily comprehended small “bites” that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics. For individuals interested in the formal study of logic. Customer Reviews (11)
Oh Logic...
Excellent textbook
Has its ups and downs...
Excellent Start in Logical Studies
Better than most logic books out there! |
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