000			04715nam a22005657a 4500
001			sulb-eb0021068
003			BD-SySUS
005			20160413122129.0
007			cr nn 008mamaa
008			121026s2013 xxu| s |||| 0|eng d
020			_a9780817683856 _9978-0-8176-8385-6
024	7		_a10.1007/978-0-8176-8385-6 _2doi
050		4	_aQA184-205
072		7	_aPBF _2bicssc
072		7	_aMAT002050 _2bisacsh
082	0	4	_a512.5 _223
100	1		_aSobczyk, Garret. _eauthor.
245	1	0	_aNew Foundations in Mathematics _h[electronic resource] : _bThe Geometric Concept of Number / _cby Garret Sobczyk.
264		1	_aBoston : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2013.
300			_aXIV, 370 p. 55 illus., 32 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_a1 Modular Number Systems -- 2 Complex and Hyperbolic Numbers -- 3 Geometric Algebra -- 4 Vector Spaces and Matrices -- 5 Outer Product and Determinants -- 6 Systems of Linear Equations -- 7 Linear Transformations on R^n -- 8 Structure of a Linear Operator -- 9 Linear and Bilinear Forms -- 10 Hermitian Inner Product Spaces -- 11 Geometry of Moving Planes -- 12 Representations of the Symmetric Group -- 13 Calculus on m-Surfaces -- 14 Differential Geometry of Curves -- 15 Differential Geometry of k-Surfaces -- 16 Mappings Between Surfaces -- 17 Non-Euclidean and Projective Geometries -- 18 Lie Groups and Lie Algebras -- References -- Symbols.
520			_aThe 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. 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.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aGroup theory.
650		0	_aMatrix theory.
650		0	_aTopological groups.
650		0	_aLie groups.
650		0	_aPhysics.
650		0	_aApplied mathematics.
650		0	_aEngineering mathematics.
650	1	4	_aMathematics.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
650	2	4	_aTopological Groups, Lie Groups.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aMathematical Methods in Physics.
650	2	4	_aAppl.Mathematics/Computational Methods of Engineering.
650	2	4	_aAlgebra.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817683849
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-8385-6
912			_aZDB-2-SMA
942			_2Dewey Decimal Classification _ceBooks
999			_c43160 _d43160