# krainaksiazek a friendly introduction to mathematical logic 20044846

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### An Algebraic Introduction to Mathematical Logic Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a sub stantial course on abstract algebra. Consequently, our treatment ofthe sub ject is algebraic. Although we assurne a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of . the exercises. We also assurne a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model oflogic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based-rather, any conclusions to be drawn about the foundations of mathematics co me only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory.

Sklep: Libristo.pl

### Introduction to Mathematical Logic Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence.

Sklep: Libristo.pl

### Introduction to Mathematical Logic Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence.

Sklep: Libristo.pl

### Introduction To Mathematical Logic

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Mathematical foundations>Mathematical logic**

This Is A Systematic And Well-paced Introduction To Mathematical Logic. Excellent As A Course Text, The Book Presupposes Only Elementary Background And Can Be Used Also For Self-study By More Ambitious Students.

Sklep: Gigant.pl

### Introduction To Mathematical Logic

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Mathematical foundations>Mathematical logic**

This Is A Systematic And Well-paced Introduction To Mathematical Logic. Excellent As A Course Text, The Book Presupposes Only Elementary Background And Can Be Used Also For Self-study By More Ambitious Students.

Sklep: Gigant.pl

### Friendly Introduction to Number Theory PEARSON

**Książki / Literatura obcojęzyczna**

For one-semester undergraduate courses in Elementary Number Theory. A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet-number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.

Sklep: Libristo.pl

### Mathematical Logic Dover Publications

**Książki / Literatura obcojęzyczna**

PART I. ELEMENTARY MATHEMATICAL LOGIC CHAPTER I. THE PROPOSITIONAL CALCULUS 1. Linguistic considerations: formulas 2. "Model theory: truth tables,validity " 3. "Model theory: the substitution rule, a collection of valid formulas" 4. Model theory: implication and equivalence 5. Model theory: chains of equivalences 6. Model theory: duality 7. Model theory: valid consequence 8. Model theory: condensed truth tables 9. Proof theory: provability and deducibility 10. Proof theory: the deduction theorem 11. "Proof theory: consistency, introduction and elimination rules" 12. Proof theory: completeness 13. Proof theory: use of derived rules 14. Applications to ordinary language: analysis of arguments 15. Applications to ordinary language: incompletely stated arguments CHAPTER II. THE PREDICATE CALCULUS 16. "Linguistic considerations: formulas, free and bound occurrences of variables" 17. "Model theory: domains, validity" 18. Model theory: basic results on validity 19. Model theory: further results on validity 20. Model theory: valid consequence 21. Proof theory: provability and deducibility 22. Proof theory: the deduction theorem 23. "Proof theory: consistency, introduction and elimination rules" 24. "Proof theory: replacement, chains of equivalences" 25. "Proof theory: alterations of quantifiers, prenex form" 26. "Applications to ordinary language: sets, Aristotelian categorical forms" 27. Applications to ordinary language: more on translating words into symbols CHAPTER III. THE PREDICATE CALCULUS WITH EQUALITY 28. "Functions, terms" 29. Equality 30. "Equality vs. equivalence, extensionality" 31. Descriptions PART II. MATHEMATICAL LOGIC AND THE FOUNDATIONS OF MATHEMATICS CHAPTER IV. THE FOUNDATIONS OF MATHEMATICS 32. Countable sets 33. Cantor's diagonal method 34. Abstract sets 35. The paradoxes 36. Axiomatic thinking vs. intuitive thinking in mathematics 37. "Formal systems, metamathematics" 38. Formal number theory 39. Some other formal systems CHAPTER V. COMPUTABILITY AND DECIDABILITY 40. Decision and computation procedures 41. "Turing machines, Church's thesis" 42. Church's theorem (via Turing machines) 43. Applications to formal number theory: undecidability (Church) and incompleteness (Gödel's theorem) 44. Applications to formal number theory: consistency proofs (Gödel's second theorem) 45. "Application to the predicate calculus (Church, Turing)" 46. "Degrees of unsolvability (Post), hierarchies (Kleene, Mostowski)." 47. Undecidability and incompleteness using only simple consistency (Rosser) CHAPTER VI. THE PREDICATE CALCULUS (ADDITIONAL TOPICS) 48. Gödel's completeness theorem: introduction 49. Gödel's completeness theorem: the basic discovery 50. "Gödel's completeness theorem with a Gentzen-type formal system, the Löwenheim-Skolem theorem" 51. Gödel's completeness theorem (with a Hilbert-type formal system) 52. "Gödel's completeness theorem, and the Löwenheim-Skolem theorem, in the predicate calculus with equality" 53. Skolen's paradox and nonstandard models of arithmetic 54. Gentzen's theorem 55. "Permutability, Herbrand's theorem" 56. Craig's interpolation theorem 57. "Beth's theorem on definability, Robinson's consistency theorem" BIBLIOGRAPHY THEOREM AND LEMMA NUMBERS: PAGES LIST OF POSTULATES SYMBOLS AND NOTATIONS INDEX

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### Introduction to Logic and to the Methodology of Deductive Sciences Oxford University Press Inc

**Książki / Literatura obcojęzyczna**

Now in it's fourth edition, this classic work on logic presents the student with a clear, concise introduction to the subject of logic and its apllications. The first part of the book introduces the concepts and principles which make up the elements of logic, demonstrating that the concepts of logic are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The book goes on to show the applications of logic in mathematical theory building using concrete examples, drawing upon the concepts and principles presented in the first section. An introduction to the theory of real numbers is also presented. Exercises are included, designed to assist in the assimilation of the concepts and principles. Throughout the conceptual side or logic is stressed. Thoroughly revised by the author's son, the book remains a fundametal guide to modern mathematica logic and is a very important addition to this highly successful series.

Sklep: Libristo.pl

### An Introduction to Fuzzy Logic for Practical Applications Springer, Berlin

**Książki / Literatura obcojęzyczna**

Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of human knowledge and experience to behave in a manner similar to a human controller. Throughout, the level of mathematical knowledge required is kept basic and the concepts are illustrated with numerous diagrams to aid in comprehension. As a result, all those curious to know more about fuzzy concepts and their real-world application will find this a good place to start.

Sklep: Libristo.pl

### Introduction to Languages, Machines, and Logic Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book provides an accessible introduction to three key topics within computer science: formal languages, abstract machines and formal logic. It is written in an easy-to-read, informal style and assumes only a basic knowledge of programming on the part of the reader. The approach is deliberately non-mathematical and features: - Clear explanations of formal notation and jargon - Extensive use of examples to illustrate algorithms and proofs - Pictorial representations of key concepts - Lots of end-of-chapter exercises Introduction to Languages, Machines and Logic is suitable for use on courses covering formal languages, formal logic, computability and automata theory. It will also make an excellent supplementary text for courses on algorithm complexity and compilers.

Sklep: Libristo.pl

### A Concise Introduction to Languages and Machines Springer, Berlin

**Książki / Literatura obcojęzyczna**

A Concise Introduction to Languages, Machines and Logic provides an accessible introduction to three key topics within computer science: formal languages, abstract machines and formal logic. Written in an easy-to-read, informal style, this textbook assumes only a basic knowledge of programming on the part of the reader.§The approach is deliberately non-mathematical, and features: - Clear explanations of formal notation and jargon, - Extensive use of examples to illustrate algorithms and proofs, - Pictorial representations of key concepts, - Chapter opening overviews providing an introduction and guidance to each topic, - End-of-chapter exercises and solutions, - Offers an intuitive approach to the topics.§This reader-friendly textbook has been written with undergraduates in mind and will be suitable for use on course covering formal languages, formal logic, computability and automata theory. It will also make an excellent supplementary text for courses on algorithm complexity and compilers.

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### A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics Springer Verlag GmbH

**Książki / Literatura obcojęzyczna**

This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it demonstrates how these theories are used to solve modeling problems in biomathematics, and presents existing derivatives and integrals applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented. The book has been developed on the basis of the authors' lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical consultants and modelers, and for researchers alike, as it may provide both groups with new ideas and inspirations for projects in the fields of fuzzy logic and biomathematics.

Sklep: Libristo.pl

### Mathematical Methods In Linguistics

**Książki Obcojęzyczne>Angielskie>Language>linguistics**

Including The Standard Constructions Of Relations, Functions, And Orderings, And Leading To A Discussion Of The Various Orders Of Infinity, This Work Covers The Standard Statement Logic And First-order Predicate Logic, And Includes An Introduction To Formal Systems, Axiomatization, And Model Theory.

Sklep: Gigant.pl

### Mathematical Proofs Pearson Education (US)

**Książki / Literatura obcojęzyczna**

"Mathematical Proofs: A Transition to Advanced Mathematics, 2/e, " prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. KEY TOPICS Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory. MARKET For all readers interested in advanced mathematics and logic.

Sklep: Libristo.pl

### Handbook of Logic and Proof Techniques for Computer Science Birkhäuser

**Książki / Literatura obcojęzyczna**

Logic plays a central conceptual role in modern mathematics. However, mathematical logic has grown into one of the most recondite areas of mathematics. As a result, most of modern logic is inaccessible to all but the specialist. This new book is a resource that provides a quick introduction and review of the key topics in logic for the computer scientist, engineer, or mathematician.§Handbook of Logic and Proof Techniques for Computer Science presents the elements of modern logic, including many current topics, to the reader having only basic mathematical literacy. Computer scientists will find specific examples and important ideas such as axiomatics, recursion theory, decidability, independence, completeness, consistency, model theory, and P/NP completeness. The book contains definitions, examples and discussion of all of the key ideas in basic logic, but also makes a special effort to cut through the mathematical formalism, difficult notation, and esoteric terminology that is typical of modern mathematical logic. T§This handbook delivers cogent and self-contained introductions to critical advanced topics, including:§Godel`s completeness and incompleteness theorems§Methods of proof, cardinal and ordinal numbers, the continuum hypothesis, the axiom of choice, model theory, and number systems and their construction§Extensive treatment of complexity theory and programming applications§ Applications to algorithms in Boolean algebra§Discussion of set theory and applications of logic§The book is an excellent resource for the working mathematical scientist. The graduate student or professional in computer science and engineering or the systems scientist who needs to have a quick sketch of a key idea from logic will find it here in this self-contained, accessible, and easy-to-use reference.§

Sklep: Libristo.pl

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