LEADER 05921nam 22008535 450 001 9910438157603321 005 20200701045428.0 010 $a0-8176-8385-2 024 7 $a10.1007/978-0-8176-8385-6 035 $a(CKB)2670000000298237 035 $a(EBL)1030323 035 $a(OCoLC)821030893 035 $a(SSID)ssj0000799845 035 $a(PQKBManifestationID)11518627 035 $a(PQKBTitleCode)TC0000799845 035 $a(PQKBWorkID)10765062 035 $a(PQKB)10482876 035 $a(DE-He213)978-0-8176-8385-6 035 $a(MiAaPQ)EBC1030323 035 $a(MiAaPQ)EBC6314365 035 $a(PPN)168288699 035 $a(EXLCZ)992670000000298237 100 $a20121026d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNew Foundations in Mathematics $eThe Geometric Concept of Number /$fby Garret Sobczyk 205 $a1st ed. 2013. 210 1$aBoston, MA :$cBirkhäuser Boston :$cImprint: Birkhäuser,$d2013. 215 $a1 online resource (372 p.) 300 $aDescription based upon print version of record. 311 $a0-8176-8384-4 320 $aIncludes bibliographical references and index. 327 $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. 330 $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. 606 $aMatrix theory 606 $aAlgebra 606 $aTopological groups 606 $aLie groups 606 $aGroup theory 606 $aPhysics 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 615 0$aMatrix theory. 615 0$aAlgebra. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aGroup theory. 615 0$aPhysics. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aLinear and Multilinear Algebras, Matrix Theory. 615 24$aTopological Groups, Lie Groups. 615 24$aGroup Theory and Generalizations. 615 24$aMathematical Methods in Physics. 615 24$aMathematical and Computational Engineering. 615 24$aAlgebra. 676 $a512 700 $aSobczyk$b Garret$4aut$4http://id.loc.gov/vocabulary/relators/aut$031979 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438157603321 996 $aNew Foundations in Mathematics$92518599 997 $aUNINA