Practical Foundations of Mathematics
by Paul Taylor
Publisher: Cambridge University Press 1999
Number of pages: 588
Practical Foundations of Mathematics explains the basis of mathematical reasoning both in pure mathematics itself (algebra and topology in particular) and in computer science. In addition to the formal logic, this volume examines the relationship between computer languages and "plain English" mathematical proofs. The book introduces the reader to discrete mathematics, reasoning, and categorical logic.
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by W.B.V. Kandasamy, F. Smarandache, K.Ilanthenral - arXiv
Basic properties of codes and super matrices are given. New type of super special vector space is constructed. Three new classes of super special codes namely, super special row code, super special column code and super special codes are introduced.
by John Wesley Young - Macmillan and co.
The following lectures contain an elementary account of the logical foundations of algebra and geometry. Except in a very few instances, no knowledge of mathematics beyond the most elementary portions of algebra and geometry has been assumed.
by Stephen G. Simpson - Pennsylvania State University
These are lecture notes for an introductory graduate-level course in foundations of mathematics. The topics covered are: computability, unsolvable problems, undecidability of the natural number system, decidability of the real number system, etc.
by Claus Tondering
This text will provide the readers with a free and accessible introduction to a very fascinating subject. The author is not a mathematician by profession, the book shows that pure mathematics is not that complicated once you get down to the rules.