George Tourlakis's Books

Theory of Computation

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Learn the skills and acquire the intuition to assess the theoretical limitations of computer programming Offering an accessible approach to the topic, Theory of Computation focuses on the metatheory of computing and the theoretical boundaries between what various computational models can do and not do—from the most general model, the URM (Unbounded Register Machines), to the finite automaton. A wealth of programming-like examples and easy-to-follow explanations build the general theory gradually, which guides readers through the modeling and mathematical analysis of computational phenomena and provides insights on what makes things tick and also what restrains the ability of computational processes. Recognizing the importance of acquired practical experience, the book begins with the metatheory of general purpose computer programs, using URMs as a straightforward, technology-independent model of modern high-level programming languages while also exploring the restrictions of the URM language. Once readers gain an understanding of computability theory—including the primitive recursive functions—the author presents automata and languages, covering the regular and context-free languages as well as the machines that recognize these languages. Several advanced topics such as reducibilities, the recursion theorem, complexity theory, and Cook's theorem are also discussed. Features of the book include: A review of basic discrete mathematics, covering logic and induction while omitting specialized combinatorial topics A thorough development of the modeling and mathematical analysis of computational phenomena, providing a solid foundation of un-computability The connection between un-computability and un-provability: Gödel's first incompleteness theorem The book provides numerous examples of specific URMs as well as other programming languages including Loop Programs, FA (Deterministic Finite Automata), NFA (Nondeterministic Finite Automata), and PDA (Pushdown Automata). Exercises at the end of each chapter allow readers to test their comprehension of the presented material, and an extensive bibliography suggests resources for further study. Assuming only a basic understanding of general computer programming and discrete mathematics, Theory of Computation serves as a valuable book for courses on theory of computation at the upper-undergraduate level. The book also serves as an excellent resource for programmers and computing professionals wishing to understand the theoretical limitations of their craft.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

410

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118315359

ISBN 13

9781118315354

Computability

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Computability

By: George Tourlakis

This survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of “mechanical process” using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs. Advanced chapters cover the Ackerman function, Tarski’s theorem on the non-representability of truth, Goedel’s incompleteness and Rosser’s incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church’s thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oracle computations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum’s complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

652

Publisher

Springer Nature

Published Date

ISBN 10

3030832023

ISBN 13

9783030832025

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

By: George Tourlakis

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

344

Publisher

Cambridge University Press

Published Date

ISBN 10

1139439421

ISBN 13

9781139439428

Lectures in Logic and Set Theory: Volume 2, Set Theory

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures in Logic and Set Theory: Volume 2, Set Theory

By: George Tourlakis

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

596

Publisher

Cambridge University Press

Published Date

ISBN 10

113943943X

ISBN 13

9781139439435

Discrete Mathematics

A Concise Introduction

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Discrete Mathematics

A Concise Introduction

By: George Tourlakis

This book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. “Safe” – that is, paradox-free – informal set theory is introduced following on the heels of Russell’s Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor’s diagonalisation technique. Predicate logic “for the user” is introduced along with axioms and rules and extensive examples. Partial orders and the minimal condition are studied in detail with the latter shown to be equivalent to the induction principle. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of functions and sets. Techniques for solving recurrence relations including generating functions, the O- and o-notations, and trees are provided. Over 200 end of chapter exercises are included to further aid in the understanding and applications of discrete mathematics.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

266

Publisher

Springer Nature

Published Date

ISBN 10

3031304888

ISBN 13

9783031304880

Mathematical Logic

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Mathematical Logic

By: George Tourlakis

A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

314

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118030699

ISBN 13

9781118030691

Computability

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Computability

By: George Tourlakis

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

652

Publisher

Springer Nature

Published Date

ISBN 10

3030832023

ISBN 13

9783030832025

The Mathematical Heritage of C F Gauss

By: George M. Rassias

Write a review Read reviews Take a Quiz Solve Book Puzzle

The Mathematical Heritage of C F Gauss

By: George M. Rassias

This volume is a collection of original and expository papers in the fields of Mathematics in which Gauss had made many fundamental discoveries. The contributors are all outstanding in their fields and the volume will be of great interest to all research mathematicians, research workers in the history of science, and graduate students in Mathematics and Mathematical Physics.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

930

Publisher

World Scientific

Published Date

ISBN 10

9810237979

ISBN 13

9789810237974

Discrete Mathematics

A Concise Introduction

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Discrete Mathematics

A Concise Introduction

By: George Tourlakis

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

266

Publisher

Springer Nature

Published Date

ISBN 10

3031304888

ISBN 13

9783031304880

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

By: George Tourlakis

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

344

Publisher

Cambridge University Press

Published Date

ISBN 10

1139439421

ISBN 13

9781139439428

Lectures in Logic and Set Theory: Volume 2, Set Theory

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures in Logic and Set Theory: Volume 2, Set Theory

By: George Tourlakis

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

596

Publisher

Cambridge University Press

Published Date

ISBN 10

113943943X

ISBN 13

9781139439435

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

By: George Tourlakis

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

By: George Tourlakis

This two-volume work bridges the gap between introductory expositions of logic (or set theory) and the research literature. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly lecture style that makes them equally effective for self-study or class use. Volume I includes formal proof techniques, applications of compactness (including nonstandard analysis), computability and its relation to the completeness phenonmenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

342

Publisher

Cambridge University Press

Published Date

ISBN 10

0521753732

ISBN 13

9780521753739

Book's by George Tourlakis

Theory of Computation

Theory of Computation

Computability

Computability

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

Lectures in Logic and Set Theory: Volume 2, Set Theory

Lectures in Logic and Set Theory: Volume 2, Set Theory

Discrete Mathematics

Discrete Mathematics

Mathematical Logic

Mathematical Logic

Computability

Computability

The Mathematical Heritage of C F Gauss

The Mathematical Heritage of C F Gauss

Discrete Mathematics

Discrete Mathematics

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

Lectures in Logic and Set Theory: Volume 2, Set Theory

Lectures in Logic and Set Theory: Volume 2, Set Theory

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

Username

Password

Username

Password

Password again

Birthday

Email