It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, and other subjects. 1960 edition.

    Impressed by the simplicity and mathematical elegance of the tableau point of view, the author focuses on it here.After preliminary material on tress (necessary for the tableau method), Part I deals with propositional logic from the viewpoint of analytic tableaux, covering such topics as formulas or propositional logic, Boolean valuations and truth sets, the method of tableaux and compactness.Part II covers first-order logic, offering detailed treatment of such matters as first-order analytic tableaux, analytic consistency, quantification theory, magic sets, and analytic versus synthetic consistency properties.Part III continues coverage of first-order logic. Among the topics discussed are Gentzen systems, elimination theorems, prenex tableaux, symmetric completeness theorems, and system linear reasoning.Raymond M. Smullyan is a well-known logician and inventor of mathematical and logical puzzles. In this book he has written a stimulating and challenging exposition of first-order logic that will be welcomed by logicians, mathematicians, and anyone interested in the field.

    Traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers created by Hamilton and Grassmann to the final acceptance around 1910 of the modern system of vector analysis. Concentrates on vector addition and subtraction, the forms of vector multiplication, vector division (in those systems where it occurs), and the specification of vector types. 1985 corrected edition of 1967 original.

    Arthur N. Prior (1914-1969) was the founding father of temporal logic, and his book offers an excellent introduction to the fundamental questions in the field. Several important papers have been added to the original selection, as well as a comprehensive bibliography of Prior's work and an illuminating interview with his widow, Mary Prior. In addition, the Polish logic which made Prior's writings difficult for many readers has been replaced by standard logical notation. This new edition will secure the classic status of the book.

    Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms. One of the most complex and essential of modern mathematical innovations, the theory of sets (crucial to quantum mechanics and other sciences), is introduced in a most careful concept manner, aiming for the maximum in clarity and stimulation for further study in set logic. Contents include: Sets and Relations — Cantor's concept of a set, etc.Natural Number Sequence — Zorn's Lemma, etc.Extension of Natural Numbers to Real NumbersLogic — the Statement and Predicate Calculus, etc.Informal Axiomatic MathematicsBoolean AlgebraInformal Axiomatic Set TheorySeveral Algebraic Theories — Rings, Integral Domains, Fields, etc.First-Order Theories — Metamathematics, etc.Symbolic logic does not figure significantly until the final chapter. The main theme of the book is mathematics as a system seen through the elaboration of real numbers; set theory and logic are seen s efficient tools in constructing axioms necessary to the system. Mathematics students at the undergraduate level, and those who seek a rigorous but not unnecessarily technical introduction to mathematical concepts, will welcome the return to print of this most lucid work."Professor Stoll . . . has given us one of the best introductory texts we have seen." — Cosmos."In the reviewer's opinion, this is an excellent book, and in addition to its use as a textbook (it contains a wealth of exercises and examples) can be recommended to all who wish an introduction to mathematical logic less technical than standard treatises (to which it can also serve as preliminary reading)." — Mathematical Reviews.

    The authors show how mathematicians came to consider groups of general transformations and then, looking upon the sets of such subjects as spaces, how they attempted to build theories of structures in general. Also considered here are the relations between mathematics and the empirical disciplines, the profound effect of high-speed computers on the scope of mathematical experimentation, and the question of how much mathematical progress depends on "invention" and how much on "discovery." For mathematicians, physicists, or any student of the evolution of mathematical thought, this highly regarded study offers a stimulating investigation of the essential nature of mathematics.