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Author: Michael L. O'Leary Publisher: John Wiley & Sons ISBN: 1118548019 Category : Mathematics Languages : en Pages : 464
Book Description
A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Author: Michael L. O'Leary Publisher: John Wiley & Sons ISBN: 1118548019 Category : Mathematics Languages : en Pages : 464
Book Description
A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Author: Patrick Suppes Publisher: Courier Corporation ISBN: 0486138054 Category : Mathematics Languages : en Pages : 340
Book Description
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.
Author: R. E. Houser Publisher: Catholic University of America Press ISBN: 0813232341 Category : Philosophy Languages : en Pages : 481
Book Description
In the twenty-first century there are two ways to study logic. The more recent approach is symbolic logic. The history of teaching logic since World War II, however, casts doubt on the idea that symbolic logic is best for a first logic course. Logic as a Liberal Art is designed as part of a minority approach, teaching logic in the "verbal" way, in the student's "natural" language, the approach invented by Aristotle. On utilitarian grounds alone, this "verbal" approach is superior for a first course in logic, for the whole range of students. For millennia, this "verbal" approach to logic was taught in conjunction with grammar and rhetoric, christened the trivium. The decline in teaching grammar and rhetoric in American secondary schools has led Dr. Rollen Edward Houser to develop this book. The first part treats grammar, rhetoric, and the essential nature of logic. Those teachers who look down upon rhetoric are free, of course, to skip those lessons. The treatment of logic itself follows Aristotle's division of the three acts of the mind (Prior Analytics 1.1). Formal logic is then taken up in Aristotle's order, with Parts on the logic of Terms, Propositions, and Arguments. The emphasis in Logic as a Liberal Art is on learning logic through doing problems. Consequently, there are more problems in each lesson than would be found, for example, in many textbooks. In addition, a special effort has been made to have easy, medium, and difficult problems in each Problem Set. In this way the problem sets are designed to offer a challenge to all students, from those most in need of a logic course to the very best students.
Author: Warren Goldfarb Publisher: Hackett Publishing ISBN: 1603845852 Category : Philosophy Languages : en Pages : 309
Book Description
This text provides a straightforward, lively but rigorous, introduction to truth-functional and predicate logic, complete with lucid examples and incisive exercises, for which Warren Goldfarb is renowned.
Author: Denise Eide Publisher: Logic of English, Inc ISBN: 1936706075 Category : Education Languages : en Pages : 204
Book Description
"English is so illogical!" It is generally believed that English is a language of exceptions. For many, learning to spell and read is frustrating. For some, it is impossible... especially for the 29% of Americans who are functionally illiterate. But what if the problem is not the language itself, but the rules we were taught? What if we could see the complexity of English as a powerful tool rather than a hindrance? --Denise Eide Uncovering the Logic of English challenges the notion that English is illogical by systematically explaining English spelling and answering questions like "Why is there a silent final E in have, large, and house?" and "Why is discussion spelled with -sion rather than -tion?" With easy-to-read examples and anecdotes, this book describes: - the phonograms and spelling rules which explain 98% of English words - how English words are formed and how this knowledge can revolutionize vocabulary development - how understanding the reasons behind English spelling prevents students from needing to guess The author's inspiring commentary makes a compelling case that understanding the logic of English could transform literacy education and help solve America's literacy crisis. Thorough and filled with the latest linguistic and reading research, Uncovering the Logic of English demonstrates why this systematic approach should be as foundational to our education as 1+1=2.
Author: P. T. Geach Publisher: Univ of California Press ISBN: 9780520038479 Category : Philosophy Languages : en Pages : 356
Book Description
"This is a significant and ofren rather demanding collection of essays. It is an anthology purring together the uncollected works of an important twentieth-century philosopher. Many of the articles treat one or another of the more important issues considered by analytic philosophers during the last quarter-century. Of significant importance to philosophers interested in researching the many topics contained in Logic Matters is the inclusion in this anthology of a rather extensive eight-page name-topic index."--Thomist "The papers are arranged by topic: Historical Essays, Traditional Logic, Theory of Reference and Syntax, Intentionality, Quotation and Semantics, Set Theory, Identity Theory, Assertion, Imperatives and Practical Reasoning, Logic in Metaphysics and Theology. The broad range of issues that have engaged Geach's complex and systematic reasoning is impressive. In addition to classical logic, topics in ethics, ontology, and even the logic of religious dogmas are tackled .... the work in this collection is more brilliant and ingenious than it is difficult and demanding."--Philosophy of Science "Geach displays his mastery of applying logical techniques and concepts to philosophical questions. Compared with most works in philosophical logic this book is remarkable for its range of topics. Plato, Aristotle, Aquinas, Russell, Wittgenstein, and Quine all figure prominently. Geach's style is remarkably lively considering the rightly argued matter. Although some of the articles treat rather technical questions in mathematical logic, most are accessible to philosophers with modest backgrounds in logic." --Choice
Author: Michael L. O'Leary
Author: Michael L. O'Leary
Author: Lewis Carroll
Author: Sharon Berry
Author: Craig DeLancey
Author: Patrick Suppes
Author: R. E. Houser
Author: Warren Goldfarb
Author: Denise Eide
Author: P. T. Geach
Author: Irving M. Copi