This textbook is written for advanced undegraduates or first year graduate students of mathematics and computer science. It is also intended for the working mathematician who wants to gain an appreciation of Mathematical Logic. There are no prerequisites for this book; however, some mathematical maturity is required. The book is written in a totally mathematical style, and any mathematician should feel at home reading this. The book starts with the definition of first order languages, proceeds through propositional logic, completeness theorems, and finally the two Incompleteness Theorems of Godel. In the process, the reader is also introduced to model theory and recursion Theory. After reading this book, the reader will be ready to branch into model Theory, recursion Theory, axiomatic set theory or even theoretical computer science.
Logic is a very profound subject, Godel's work being one the most remarkable discoveries in 20th-Century mathematics, having made an enormous impact on set theory, model theory as well as computer science. In spite of this impact, there exists a dearth of modern books which allow an aspiring mathematician to read and develop an appreciation for the subject. This book attempts to fill that gap by providing a short, distinctive, modern, and well-motivated introduction to mathematical logic. Read more... Categories
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Posted: February 19th, 2008, 2:06pm CET
Tags: A Course On Mathematical Logic [edit]
This textbook is written for advanced undegraduates or first year graduate students of mathematics and computer science. It is also intended for the working mathematician who wants to gain an appreciation of Mathematical Logic. There are no prerequisites for this book; however, some mathematical maturity is required. The book is written in a totally mathematical style, and any mathematician should feel at home reading this. The book starts with the definition of first order languages, proceeds through propositional logic, completeness theorems, and finally the two Incompleteness Theorems of Godel. In the process, the reader is also introduced to model theory and recursion Theory. After reading this book, the reader will be ready to branch into model Theory, recursion Theory, axiomatic set theory or even theoretical computer science.
Logic is a very profound subject, Godel's work being one the most remarkable discoveries in 20th-Century mathematics, having made an enormous impact on set theory, model theory as well as computer science. In spite of this impact, there exists a dearth of modern books which allow an aspiring mathematician to read and develop an appreciation for the subject. This book attempts to fill that gap by providing a short, distinctive, modern, and well-motivated introduction to mathematical logic. Read more... Full download
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Posted: February 18th, 2008, 8:27pm CET by RufatZ
Tags: A Short Course in Discrete [edit]
Edward A. Bender, S. Gill Williamson “A Short Course in Discrete Mathematics"
Dover Publications | 2004-12-13 | ISBN:0486439461 | PDF | 256 pages | 1,6 Mb
What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 ed. Notation Index. Subject Index.
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