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Author: Michael C. Gemignani Publisher: Courier Corporation ISBN: 0486435067 Category : Mathematics Languages : en Pages : 290
Book Description
This text emphasizes logic and the theory of sets. Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics. Others will discover the foundations for future studies — set theory, logic, counting, numbers, functions, and more. 1968 edition. 43 figures. 25 tables.
Author: Michael C. Gemignani Publisher: Courier Corporation ISBN: 0486435067 Category : Mathematics Languages : en Pages : 290
Book Description
This text emphasizes logic and the theory of sets. Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics. Others will discover the foundations for future studies — set theory, logic, counting, numbers, functions, and more. 1968 edition. 43 figures. 25 tables.
Author: Mark Kac Publisher: Courier Corporation ISBN: 0486670856 Category : Philosophy Languages : en Pages : 189
Book Description
Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."
Author: Richard E. Hodel Publisher: Courier Corporation ISBN: 0486497852 Category : Mathematics Languages : en Pages : 514
Book Description
This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
Author: Robert L. Rogers Publisher: Elsevier ISBN: 1483257975 Category : Mathematics Languages : en Pages : 248
Book Description
Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.
Author: Elliot Mendelsohn Publisher: Springer Science & Business Media ISBN: 1461572886 Category : Science Languages : en Pages : 351
Book Description
This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.
Author: Peter G. Hinman Publisher: CRC Press ISBN: 1439864276 Category : Mathematics Languages : en Pages : 894
Book Description
This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.
Author: Keith J. Devlin Publisher: Springer ISBN: 1489929673 Category : Mathematics Languages : en Pages : 99
Book Description
The purpose of this book is to provide the student beginning undergraduate mathematics with a solid foundation in the basic logical concepts necessary for most of the subjects encountered in a university mathematics course. The main distinction between most school mathematics and university mathematics lies in the degree of rigour demanded at university level. In general, the new student has no experience of wholly rigorous definitions and proofs, with the result that, although competent to handle quite difficult problems in, say, the differential calculus, he/she is totally lost when presented with a rigorous definition oflimits and derivatives. In effect, this means that in the first few weeks at university the student needs to master what is virtually an entire new language {'the language of mathematics'} and to adopt an entirely new mode ofthinking. Needless to say, only the very ablest students come through this process without a great deal of difficulty.
Author: Michael C. Gemignani
Author: Michael C. Gemignani
Author: Mark Kac
Author: Serge Lang
Author: Alonzo Church
Author: Richard E. Hodel
Author: Robert L. Rogers
Author: Elliot Mendelsohn
Author: Peter G. Hinman
Author: Elias Zakon
Author: Keith J. Devlin