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Author: Jaakko Hintikka
Publisher: Cambridge University Press
ISBN: 9780521624985
Category : Mathematics
Languages : en
Pages : 308
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Book Description
This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.
Author: Jaakko Hintikka
Publisher: Cambridge University Press
ISBN: 9780521624985
Category : Mathematics
Languages : en
Pages : 308
Get Book Here
Book Description
This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.
Author: Vladimir Lepetic
Publisher: John Wiley & Sons
ISBN: 1119131650
Category : Mathematics
Languages : en
Pages : 672
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Book Description
Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra. The author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, Principles of Mathematics: A Primer features: Detailed explanations of important theorems and their applications Hundreds of completely solved problems throughout each chapter Numerous exercises at the end of each chapter to encourage further exploration Discussions of interesting and provocative issues that spark readers’ curiosity and facilitate a better understanding and appreciation of the field of mathematics Principles of Mathematics: A Primer is an ideal textbook for upper-undergraduate courses in the foundations of mathematics and mathematical logic as well as for graduate-level courses related to physics, engineering, and computer science. The book is also a useful reference for readers interested in pursuing careers in mathematics and the sciences.
Author: Katherine (Loop) Hannon
Publisher: Master Books
ISBN: 9780890519073
Category : Juvenile Nonfiction
Languages : en
Pages : 0
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Book Description
Teacher Guide for use with Principles of Mathematics Book 2. Katherine Loop's Principles of Mathematics Book 2 guides students through the core principles of algebra-equipping your student for High School success! Teacher Guide includes daily schedule, student worksheets, quizzes, tests, and answer key.
Author: Gareth E. Roberts
Publisher: JHU Press
ISBN: 1421419181
Category : Mathematics
Languages : en
Pages : 320
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Book Description
A guided tour of the mathematical principles inherent in music. Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic. The mathematics advances in level of difficulty from calculating with fractions, to manipulating trigonometric formulas, to constructing group multiplication tables and proving a number is irrational. Topics discussed in the book include • Rhythm • Introductory music theory • The science of sound • Tuning and temperament • Symmetry in music • The Bartók controversy • Change ringing • Twelve-tone music • Mathematical modern music • The Hemachandra–Fibonacci numbers and the golden ratio • Magic squares • Phase shifting Featuring numerous musical excerpts, including several from jazz and popular music, each topic is presented in a clear and in-depth fashion. Sample problems are included as part of the exposition, with carefully written solutions provided to assist the reader. The book also contains more than 200 exercises designed to help develop students' analytical skills and reinforce the material in the text. From the first chapter through the last, readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity.
Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3662223430
Category : Mathematics
Languages : en
Pages : 194
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Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author: Yoshitsugu Oono
Publisher: Springer Science & Business Media
ISBN: 4431540296
Category : Science
Languages : en
Pages : 307
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Book Description
The most important characteristic of the “world filled with nonlinearity” is the existence of scale interference: disparate space–time scales interfere with each other. Thus, the effects of unknowable scales invade the world that we can observe directly. This leads to various peculiar phenomena such as chaos, critical phenomena, and complex biological phenomena, among others. Conceptual analysis and phenomenology are the keys to describe and understand phenomena that are subject to scale interference, because precise description of unfamiliar phenomena requires precise concepts and their phenomenological description. The book starts with an illustration of conceptual analysis in terms of chaos and randomness, and goes on to explain renormalization group philosophy as an approach to phenomenology. Then, abduction is outlined as a way to express what we have understood about the world. The book concludes with discussions on how we can approach genuinely complex phenomena, including biological phenomena. The main target of this volume is young people who have just started to appreciate the world seriously. The author also wishes the book to be helpful to those who have been observing the world, but who wish to appreciate it afresh from a different angle.
Author: Richard Mason
Publisher: SUNY Press
ISBN: 9780791445310
Category : Philosophy
Languages : en
Pages : 166
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Book Description
Argues that there is an undeniable and essentially historical dimension to logic.
Author:
Publisher: BRILL
ISBN: 900445750X
Category : Philosophy
Languages : en
Pages : 386
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Book Description
ISBN 9042000694 (paperback) NLG 50.00 Main headings: I. Historical perspectives.- II. Formal tools: induction, observation and identifiability.- III. Questions in inquiry: the interrogative model.- IV. Growth of knowledge: explanation and discovery.- V. Jaakko Hintikka: replies.- VI. Abstracts. skills in writing.
Author: Thomas Bonk
Publisher: Springer Science & Business Media
ISBN: 9401701512
Category : Philosophy
Languages : en
Pages : 210
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Book Description
This collection will prove a valuable resource for our understanding of the historic Carnap and the living philosophical issues with which he grappled. It arose out of a symposium on Carnap's work (Vienna, 2001). With essays by Graham H. Bird, Jaakko Hintikka, Ilkka Niiniluoto, Jan Wolenski, this volume will interest graduate students of the philosophy of language and logic, as well as professional philosophers, historians of analytic philosophy, and philosophically inclined logicians.
Author: Catarina Dutilh Novaes
Publisher: Cambridge University Press
ISBN: 110847988X
Category : Computers
Languages : en
Pages : 287
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Book Description
The first comprehensive account of the concept and practices of deduction covering philosophy, history, cognition and mathematical practice.
