Foundations Of Mathematics

Author : Garret Sobczyk
Publisher : Springer Science & Business Media
ISBN 13 : 0817683852
Total Pages : 370 pages
Book Rating : 4.56/5 ( download)

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Download or read book New Foundations in Mathematics written by Garret Sobczyk and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.

Author : William S. Hatcher
Publisher : Elsevier
ISBN 13 : 1483189635
Total Pages : 330 pages
Book Rating : 4.35/5 ( download)

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Download or read book The Logical Foundations of Mathematics written by William S. Hatcher and published by Elsevier. This book was released on 2014-05-09 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a "natural deduction" style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.

Author : Paul Taylor
Publisher : Cambridge University Press
ISBN 13 : 9780521631075
Total Pages : 590 pages
Book Rating : 4.76/5 ( download)

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Download or read book Practical Foundations of Mathematics written by Paul Taylor and published by Cambridge University Press. This book was released on 1999-05-13 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programs). It contains original material and original developments of standard material, so it is also for professional researchers, but as it deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics, the reader is expected to be open minded about these things.

Author : Raymond L. Wilder
Publisher : Courier Corporation
ISBN 13 : 0486276201
Total Pages : 352 pages
Book Rating : 4.05/5 ( download)

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Download or read book Introduction to the Foundations of Mathematics written by Raymond L. Wilder and published by Courier Corporation. This book was released on 2013-09-26 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

Author : Denny Burzynski
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.74/5 ( download)

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Download or read book Fundamentals of Mathematics written by Denny Burzynski and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who: have had previous courses in prealgebra wish to meet the prerequisites of higher level courses such as elementary algebra need to review fundamental mathematical concenpts and techniques This text will help the student devlop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives: to provide the student with an understandable and usable source of information to provide the student with the maximum oppurtinity to see that arithmetic concepts and techniques are logically based to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material cources and nonclassroom situations to give the students the ability to correctly interpret arithmetically obtained results We have tried to meet these objects by presenting material dynamically much the way an instructure might present the material visually in a classroom. (See the development of the concept of addition and subtraction of fractions in section 5.3 for examples) Intuition and understanding are some of the keys to creative thinking, we belive that the material presented in this text will help students realize that mathematics is a creative subject.

Author : John P. Mayberry
Publisher : Cambridge University Press
ISBN 13 : 9780521770347
Total Pages : 454 pages
Book Rating : 4.43/5 ( download)

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Download or read book The Foundations of Mathematics in the Theory of Sets written by John P. Mayberry and published by Cambridge University Press. This book was released on 2000 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.

Author : Yves Nievergelt
Publisher : Springer Science & Business Media
ISBN 13 : 146120125X
Total Pages : 425 pages
Book Rating : 4.50/5 ( download)

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Download or read book Foundations of Logic and Mathematics written by Yves Nievergelt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.

Author : Matthias Baaz
Publisher : Cambridge University Press
ISBN 13 : 1139498436
Total Pages : 541 pages
Book Rating : 4.32/5 ( download)

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Download or read book Kurt Gödel and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

Author : Stefania Centrone
Publisher : Springer Nature
ISBN 13 : 3030156559
Total Pages : 511 pages
Book Rating : 4.58/5 ( download)

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Download or read book Reflections on the Foundations of Mathematics written by Stefania Centrone and published by Springer Nature. This book was released on 2019-11-11 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.

Author : Luca Incurvati
Publisher : Cambridge University Press
ISBN 13 : 1108497829
Total Pages : 255 pages
Book Rating : 4.24/5 ( download)

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Download or read book Conceptions of Set and the Foundations of Mathematics written by Luca Incurvati and published by Cambridge University Press. This book was released on 2020-01-23 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.