Автор: Garret Sobczyk Название: New Foundations in Mathematics: The Geometric Concept of Number Издательство: Birkh?user Год: 2013 ISBN: 9780817683849 Язык: English Формат: pdf Размер: 12,6 mb Страниц: 370
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.
The book begins with a discussion of modular numbers (clock arithmetic) and modular polynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light, including:
- vector spaces and matrices; - structure of linear operators and quadratic forms; - Hermitian inner product spaces; - geometry of moving planes; - spacetime of special relativity; - classical integration theorems; - differential geometry of curves and smooth surfaces; - projective geometry; - Lie groups and Lie algebras.
Exercises with selected solutions are provided, and chapter summaries are included to reinforce concepts as they are covered. Links to relevant websites are often given, and supplementary material is available on the author’s website.
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.
Уважаемый посетитель, Вы зашли на сайт как незарегистрированный пользователь.
С этой публикацией часто скачивают:
Pure Mathematics for Beginners Название: Pure Mathematics for Beginners Автор: Steve Warner Издательство: Get 800 Год: 2018 Формат: PDF Размер: 10 Мб Язык: английский / English ...
Imaginary Mathematics for Computer Science Название: Imaginary Mathematics for Computer Science Автор: John Vince Издательство: Springer Год: 2018 Страниц: 301 Формат: PDF, EPUB Размер: 25 Mb...
Fundamentals of Mathematics: 3 Vols. Set Название: Fundamentals of Mathematics: 3 Vols. Set Автор: H. Behnke, F. Bachmann, K. Fladt Издательство: MIT Press Год: 1987 ISBN: 0262520931...
Geometric Algebra Название: Geometric Algebra Автор: Emil Artin Издательство: Dover Publications Год: 2016 ISBN: 9780486801551 Серия: Dover Books on Mathematics...
Numerical Linear Algebra: Theory and Applications Название: Numerical Linear Algebra: Theory and Applications Автор: Larisa Beilina, Evgenii Karchevskii, Mikhail Karchevskii Издательство: Springer...
Навигация
Вход на сайт
Реклама
New Foundations in Mathematics: The Geometric Concept of Number 
