New Foundations In Mathematics

Author : Garret Sobczyk
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 46,9 Mb
Release : 2012-10-26
Category : Mathematics
ISBN : 9780817683856

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New Foundations in Mathematics by Garret Sobczyk Pdf

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 : Tim Maudlin
Publisher : Oxford University Press
Page : 374 pages
File Size : 47,8 Mb
Release : 2014-02
Category : Mathematics
ISBN : 9780198701309

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New Foundations for Physical Geometry by Tim Maudlin Pdf

Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.

Author : Joseph Kouneiher
Publisher : Springer
Page : 441 pages
File Size : 55,9 Mb
Release : 2018-05-26
Category : Science
ISBN : 9783319648132

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Foundations of Mathematics and Physics One Century After Hilbert by Joseph Kouneiher Pdf

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

Author : McGraw-Hill Ryerson, Limited
Publisher : Unknown
Page : 460 pages
File Size : 40,9 Mb
Release : 2013-04-23
Category : Mathematics
ISBN : 1259077411

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Foundations of Mathematics 9 S Tudent Edition by McGraw-Hill Ryerson, Limited Pdf

"A new resource written specifically for the Foundations of Mathematics 9 (MFM 1P) course. The McGraw-Hill Ryerson Foundations of Mathematics 9 program is a carefully blended mix of print and digital resources designed to meet all teaching and learning needs."--Publ. website.

Author : D. Hestenes
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400948020

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New Foundations for Classical Mechanics by D. Hestenes Pdf

This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

Author : Anonim
Publisher : Univalent Foundations
Page : 484 pages
File Size : 49,5 Mb
Release : 2024-05-13
Category : Electronic
ISBN : 8210379456XXX

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Homotopy Type Theory: Univalent Foundations of Mathematics by Anonim Pdf

Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 42,8 Mb
Release : 2020-01-23
Category : History
ISBN : 9781108497824

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Conceptions of Set and the Foundations of Mathematics by Luca Incurvati Pdf

Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Author : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 40,6 Mb
Release : 2018-12-13
Category : History
ISBN : 9781107152502

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Quine, New Foundations, and the Philosophy of Set Theory by Sean Morris Pdf

Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.

Author : D. Hestenes
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 44,8 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306471223

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New Foundations for Classical Mechanics by D. Hestenes Pdf

(revised) This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

Author : William S. Hatcher
Publisher : Elsevier
Page : 330 pages
File Size : 49,8 Mb
Release : 2014-05-09
Category : Mathematics
ISBN : 9781483189635

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The Logical Foundations of Mathematics by William S. Hatcher Pdf

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 : Richard A. Lesh,Eric Hamilton,James J. Kaput
Publisher : Routledge
Page : 437 pages
File Size : 55,6 Mb
Release : 2020-10-07
Category : Education
ISBN : 9781000149500

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Foundations for the Future in Mathematics Education by Richard A. Lesh,Eric Hamilton,James J. Kaput Pdf

The central question addressed in Foundations for the Future in Mathematics Education is this: What kind of understandings and abilities should be emphasized to decrease mismatches between the narrow band of mathematical understandings and abilities that are emphasized in mathematics classrooms and tests, and those that are needed for success beyond school in the 21st century? This is an urgent question. In fields ranging from aeronautical engineering to agriculture, and from biotechnologies to business administration, outside advisors to future-oriented university programs increasingly emphasize the fact that, beyond school, the nature of problem-solving activities has changed dramatically during the past twenty years, as powerful tools for computation, conceptualization, and communication have led to fundamental changes in the levels and types of mathematical understandings and abilities that are needed for success in such fields. For K-12 students and teachers, questions about the changing nature of mathematics (and mathematical thinking beyond school) might be rephrased to ask: If the goal is to create a mathematics curriculum that will be adequate to prepare students for informed citizenship—as well as preparing them for career opportunities in learning organizations, in knowledge economies, in an age of increasing globalization—how should traditional conceptions of the 3Rs be extended or reconceived? Overall, this book suggests that it is not enough to simply make incremental changes in the existing curriculum whose traditions developed out of the needs of industrial societies. The authors, beyond simply stating conclusions from their research, use results from it to describe promising directions for a research agenda related to this question. The volume is organized in three sections: *Part I focuses on naturalistic observations aimed at clarifying what kind of “mathematical thinking” people really do when they are engaged in “real life” problem solving or decision making situations beyond school. *Part II shifts attention toward changes that have occurred in kinds of elementary-but-powerful mathematical concepts, topics, and tools that have evolved recently—and that could replace past notions of “basics” by providing new foundations for the future. This section also initiates discussions about what it means to “understand” the preceding ideas and abilities. *Part III extends these discussions about meaning and understanding—and emphasizes teaching experiments aimed at investigating how instructional activities can be designed to facilitate the development of the preceding ideas and abilities. Foundations for the Future in Mathematics Education is an essential reference for researchers, curriculum developers, assessment experts, and teacher educators across the fields of mathematics and science education.

Author : Cathy Canavan-McGrath,Serge Desrochers,Hugh MacDonald,Carolyn Matrin,Hank Reinbold,Michael Pruner,Carol Shaw,Darin Trufyn,Rupi Samra-Gynane,Roger Teshima,Joanne Landry,Darlene Olson-St. Pierre,Sarah Wade,Karen Iversen,Gerry Varty
Publisher : Unknown
Page : 595 pages
File Size : 45,9 Mb
Release : 2011-05-26
Category : Algebra
ISBN : 017650270X

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Foundations of Mathematics 11 WNCP by Cathy Canavan-McGrath,Serge Desrochers,Hugh MacDonald,Carolyn Matrin,Hank Reinbold,Michael Pruner,Carol Shaw,Darin Trufyn,Rupi Samra-Gynane,Roger Teshima,Joanne Landry,Darlene Olson-St. Pierre,Sarah Wade,Karen Iversen,Gerry Varty Pdf

This educational resource has been developed by many writers and consultants to bring the very best of mathematics to you.

Author : Philip Brown
Publisher : Mercury Learning and Information
Page : 382 pages
File Size : 48,8 Mb
Release : 2016-03-14
Category : Mathematics
ISBN : 9781944534417

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Foundations of Mathematics by Philip Brown Pdf

Foundations of Mathematics offers the university student or interested reader a unique reference book by covering the basics of algebra, trigonometry, geometry, and calculus. There are many instances in the book to demonstrate the interplay and interconnectedness of these topics. The book presents definitions and examples throughout for clear, easy learning. Numerous exercises are included at the ends of the chapters, and readers are encouraged to complete all of them as an essential part of working through the book. It offers a unique experience for readers to understand different areas of mathematics in one clear, concise text. Instructors’ resources are available upon adoption. Features: •Covers the basics of algebra, trigonometry, geometry, and calculus •Includes all of the mathematics needed to learn calculus •Demonstrates the interplay and interconnectedness of these topics •Uses numerous examples and exercises to reinforce concepts

Author : Raymond L. Wilder
Publisher : Courier Corporation
Page : 352 pages
File Size : 51,8 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486276205

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Introduction to the Foundations of Mathematics by Raymond L. Wilder Pdf

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 : Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher : Courier Corporation
Page : 450 pages
File Size : 40,5 Mb
Release : 2012-09-11
Category : Mathematics
ISBN : 9780486134772

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Foundations of Mathematical Analysis by Richard Johnsonbaugh,W.E. Pfaffenberger Pdf

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.