# krainaksiazek a friendly introduction to mathematical logic 20044846

- znaleziono 68 produktów w 2 sklepach

### A Mathematical Introduction To Logic

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

Presents Material On Computer Science Issues Such As Computational Complexity And Database Queries, With Coverage Of Introductory Material Such As Sets. This Book Helps Instructors With Choices In How They Use The Textbook In Courses, And Reduced Mathematical Rigour To Fit The Needs Of Undergraduate Students.

Sklep: Gigant.pl

### 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

### 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

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.

Sklep: Libristo.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

### Mathematical Modeling and Scale-Up of Liquid Chromatography Springer, Berlin

**Książki / Literatura obcojęzyczna**

Tingyue Gu's second edition provides a comprehensive set of nonlinear multicomponent liquid chromatography (LC) models for various forms of LC, such as adsorption, size exclusion, ion-exchange, reversed-phase, affinity, isocratic/gradient elution and axial/radial flow LC. Much has advanced since the first edition of this book and the author's software, described here, is now used for teaching and research in 32 different countries. This book comes together with a complete software package with graphical user interface for personal computers, offered free for academic applications. Additionally, this book provides detailed methods for parameter estimation of mass transfer coefficients, bed voidage, particle porosity and isotherms. The author gives examples of how to use the software for predicitons and scale-up. In contrast to the first edition, authors do not need to deal with complicated math. Instead, they focus on how to obtain a few parameters for simulation and how to compare simulation results with experimental data. After reading the detailed descriptions in the book, a reader is able to use the simulation software to investigate chromatographic behavior without doing actual experiments. This book is aimed at readers who are interested in learning about LC behaviors and at those who want to scale up LC for preparative- and large-scale applications. Both academic personnel and industrial practitioners can benefit from the use of the book. This new edition includes:- New models and software for pellicular (cored) beads in liquid chromatography§- Introduction of user-friendly software (with graphical user interface)§- Detailed descriptions on how to use the software§- Step-by-step instructions on parameter estimation for the models§- New mass-transfer correlations for parameter estimation§- Experimental methods for parameter estimation§- Several actual examples using the model for product development and scale-up§- Updated literature review

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

### Introduction to College Mathematics with A Programming Language Springer, Berlin

**Książki / Literatura obcojęzyczna**

The topics covered in this text are those usually covered in a full year's course in finite mathematics or mathematics for liberal arts students. They correspond very closely to the topics I have taught at Western New England College to freshmen business and liberal arts students. They include set theory, logic, matrices and determinants, functions and graph ing, basic differential and integral calculus, probability and statistics, and trigonometry. Because this is an introductory text, none of these topics is dealt with in great depth. The idea is to introduce the student to some of the basic concepts in mathematics along with some of their applications. I believe that this text is self-contained and can be used successfully by any college student who has completed at least two years of high school mathematics including one year of algebra. In addition, no previous knowledge of any programming language is necessary. The distinguishing feature of this text is that the student is given the opportunity to learn the mathematical concepts via A Programming Lan guage (APL). APL was developed by Kenneth E. Iverson while he was at Harvard University and was presented in a book by Dr. Iverson entitled A i Programming Language in 1962. He invented APL for educational purpo ses. That is, APL was designed to be a consistent, unambiguous, and powerful notation for communicating mathematical ideas. In 1966, APL became available on a time-sharing system at IBM.

Sklep: Libristo.pl

### Logical Introduction to Proof Springer

**Książki / Literatura obcojęzyczna**

A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or bridge course between calculus and advanced mathematics courses. The author s approach prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may also be beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs. Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument for analyzing the structure of mathematical assertions and is a tool for composing mathematical proofs. Exercises are given at the end of each section within a chapter.§Chapter 1 focuses on propositional logic while Chapter 2 is devoted to the logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs; each presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theorems concerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamental theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts that appear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finally, Chapter 9 presents proof strategies that explicitly show students how to deal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies. The appendix provides a useful summary of strategies for dealing with proofs.

Sklep: Libristo.pl

### Logic for Applications Springer, Berlin

**Książki / Literatura obcojęzyczna**

§This book is a rigorous introduction to classical and nonclassical logics which emphasizes deduction as a form of computation. It can be used to teach classical, modal, and intuitistic predicate logic. It also presents the logical and mathematical foundations for resolution theorem proving and Logic Programming. A distinctive feature of this book is its uniform mathematical treatment of logic, based on the tableau method of classical logic, which includes soundness, completeness, compactness, incompleteness, and the theorems of Herb Rand and Skolem-L Wenheim. The same uniform treatment is used for important areas of application in computer science and artificial intelligence. These include resolution theorem proving, Logic Programming and Prolog, Predicate Intuitionistic Logic, and Predicate Modal Logic. §There is also an historical appendix and an extensive list of selected references so that both the background and more advanced developments of these subjects can be understood and pursued. This text is appropriate for upper level undergraduate and beginning graduate students.

Sklep: Libristo.pl

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