In modern mathematics, both the theory of proof and the derivation of theorems from axioms bear an unquestioned importance. The necessary skills behind these methods, however, are frequently underdeveloped. This book counters that neglect with a rigorous introduction that is simple enough in presenta... read more
The Elements of Mathematical Logic by Paul C. Rosenbloom This excellent introduction to mathematical logic provides a sound knowledge of the most important approaches, stressing the use of logical methods. "Reliable." — The Mathematical Gazette. 1950 edition.
A Profile of Mathematical Logic by Howard DeLong This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.
Foundations of Mathematical Logic by Haskell B. Curry Comprehensive graduate-level account of constructive theory of first-order predicate calculus covers formal methods: algorithms and epitheory, brief treatment of Markov's approach to algorithms, elementary facts about lattices, logical connectives, more. 1963 edition.
Introduction to Elementary Mathematical Logic by A. A. Stolyar Lucid, accessible exploration of propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. 1970 edition.
What Is Mathematical Logic? by J. N. Crossley, C.J. Ash, C.J. Brickhill, J.C. Stillwell A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.
Undecidable Theories: Studies in Logic and the Foundation of Mathematics by Alfred Tarski, Andrzej Mostowski, Raphael M. Robinson This well-known book by the famed logician consists of three treatises: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups." 1953 edition.
Recursive Analysis by R. L. Goodstein This text by a master in the field covers recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.
Satan, Cantor and Infinity: Mind-Boggling Puzzles by Raymond M. Smullyan A renowned mathematician tells stories of knights and knaves in an entertaining look at the logical precepts behind infinity, probability, time, and change. Complete solutions appear within the narrative of the text.
The Philosophy of Mathematics: An Introductory Essay by Stephan Körner A distinguished philosopher surveys the mathematical views and influence of Plato, Aristotle, Leibniz, and Kant. He also examines the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.
Logic for Mathematicians by J. Barkley Rosser Examination of essential topics and theorems assumes no background in logic. "Undoubtedly a major addition to the literature of mathematical logic." — Bulletin of the American Mathematical Society. 1978 edition.
Set Theory and the Continuum Hypothesis by Paul J. Cohen This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The award-winning author employs intuitive explanations and detailed proofs in this self-contained treatment. 1966 edition. Copyright renewed 1994.
Mathematical Logic: A First Course by Joel W. Robbin This self-contained text will appeal to readers from diverse fields and varying backgrounds. Topics include 1st-order recursive arithmetic, 1st- and 2nd-order logic, and the arithmetization of syntax. Numerous exercises; some solutions. 1969 edition.
Basic Concepts of Mathematics and Logic by Michael C. Gemignani Intended as a first look at mathematics at the college level, this text emphasizes logic and set theory — counting, numbers, functions, ordering, probabilities, and other components of higher mathematics.
Mathematical Logic by Stephen Cole Kleene Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
Introduction to Logic by Patrick Suppes Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.
First-Order Logic by Raymond M. Smullyan This self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus is on the tableau point of view. Includes 144 illustrations.
Mathematics and Logic by Mark Kac, Stanislaw M. Ulam Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, more. Includes 34 illustrations. 1968 edition.
First Order Mathematical Logic by Angelo Margaris Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. Also covers first-order theories, completeness theorem, Godel's incompleteness theorem, much more. Exercises. Bibliography.
Set Theory and Logic by Robert R. Stoll Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Symbolic Logic and the Game of Logic by Lewis Carroll Over 350 ingenious problems involving classical logic: logic expressed in symbols; syllogisms and the sorites diagrammed; logic as a game played with 2 diagrams and a set of counters.
101 Puzzles in Thought and Logic by C. R. Wylie, Jr. Solve murder problems and robberies, see which fishermen are liars and how a blind man can identify color — purely by reasoning! Hours of mind-strengthening entertainment.
In modern mathematics, both the theory of proof and the derivation of theorems from axioms bear an unquestioned importance. The necessary skills behind these methods, however, are frequently underdeveloped. This book counters that neglect with a rigorous introduction that is simple enough in presentation and context to permit relatively easy comprehension. It comprises the sentential theory of inference, inference with universal quantifiers, and applications of the theory of inference developed to the elementary theory of commutative groups. Throughout the book, the authors emphasize the pervasive and important problem of translating English sentences into logical or mathematical symbolism. Their clear and coherent style of writing ensures that this work may be used by students in a wide range of ages and abilities.
Reprint of the Blaisdell Publishing Company, Waltham, MA, 1964 edition.
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