Foundations of Logic and Theory of Computation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Logic and Theory of Computation write by A. Sernadas. This book was released on 2008. Foundations of Logic and Theory of Computation available in PDF, EPUB and Kindle. The book provides a self-contained introduction to mathematical logic and computability theory for students of mathematics or computer science. It is organized around the failures and successes of Hilbert's programme for the formalization of Mathematics. It is widely known that the programme failed with Gödel's incompleteness theorems and related negative results about arithmetic. Unfortunately, the positive outcomes of the programme are less well known, even among mathematicians. The book covers key successes, like Gödel's proof of the completeness of first-order logic, Gentzen's proof of its consistency by purely symbolic means, and the decidability of a couple of useful theories. The book also tries to convey the message that Hilbert's programme made a significant contribution to the advent of the computer as it is nowadays understood and, thus, to the latest industrial revolution. Part I of the book addresses Hilbert's programme and computability. Part II presents first-order logic, including Gödel's completeness theorem and Gentzen's consistency theorem. Part III is focused on arithmetic, representability of computable maps, Gödel's incompleteness theorems and decidability of Presburger arithmetic. Part IV provides detailed answers to selected exercises. The book can be used at late undergraduate level or early graduate level. An undergraduate course would concentrate on Parts I and II, leaving out the Gentzen calculus, and sketching the way to the 1st incompleteness theorem. A more advanced course might skip early material already known to the students and concentrate on the positive and negative results of Hilbert's programme, thus covering Gentzen's proof of consistency and Part III in full.
Foundations of Computation
Foundations of Computation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Computation write by Carol Critchlow. This book was released on 2011. Foundations of Computation available in PDF, EPUB and Kindle. Foundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages and grammar that would ordinarily be encountered in an upper level course in theoretical computer science.
Foundations of Logic and Mathematics
Foundations of Logic and Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Logic and Mathematics write by Yves Nievergelt. This book was released on 2012-12-06. Foundations of Logic and Mathematics available in PDF, EPUB and Kindle. This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.
Foundations of Computing
Foundations of Computing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Computing write by Thierry Scheurer. This book was released on 1994. Foundations of Computing available in PDF, EPUB and Kindle. Written for professionals learning the field of discrete mathematics, this book provides the necessary foundations of computer science without requiring excessive mathematical prerequisites. Using a balanced approach of theory and examples, software engineers will find it a refreshing treatment of applications in programming.
Logic for Computer Science
Logic for Computer Science - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Logic for Computer Science write by Jean H. Gallier. This book was released on 2015-06-18. Logic for Computer Science available in PDF, EPUB and Kindle. This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.
