01107nam0-22003731i-450-99000799496040332120050728134046.00-521-83920-3000799496FED01000799496(Aleph)000799496FED0100079949620050129d2004----km-y0itay50------baengUSa---a---001yy<<The >>covering property axiom, CPAa combinatorial core of the iterated perfect set modelK. Ciesielski, J. PawlikowskiCambridgeCambridge University Pressc2004xxi,174 p.24 cmCambridge tracts in mathematics164Teoria degli insiemiAssiomatica511.322itaCiesielski,Krzysztof287859Pawlikowski,Janusz287860ITUNINARICAUNIMARCBK990007994960403321C-34-(16420724MA1MA103E3003EXXCovering property axiom, CPA750288UNINA04130nam 22006615 450 991036084860332120200705012411.09783030017569303001756710.1007/978-3-030-01756-9(CKB)4100000009939771(MiAaPQ)EBC5983809(DE-He213)978-3-030-01756-9(PPN)269145311(MiAaPQ)EBC31886955(Au-PeEL)EBL31886955(OCoLC)1499722089(EXLCZ)99410000000993977120191122d2019 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGeometric Multiplication of Vectors An Introduction to Geometric Algebra in Physics /by Miroslav Josipović1st ed. 2019.Cham :Springer International Publishing :Imprint: Birkhäuser,2019.1 online resource (258 pages) illustrationsCompact Textbooks in Mathematics,2296-45689783030017552 3030017559 Includes bibliographical references.Basic Concepts -- Euclidean 3D Geometric Algebra -- Applications -- Geometric Algebra and Matrices -- Appendix -- Solutions for Some Problems -- Problems -- Why Geometric Algebra? -- Formulae -- Literature -- References.This book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it, and undergraduate students can master it. The universality, the clear geometric interpretation, the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth.Compact Textbooks in Mathematics,2296-4568Matrix theoryAlgebraQuantum theoryComputer science—MathematicsLinear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Quantum Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19080Math Applications in Computer Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/I17044Matrix theory.Algebra.Quantum theory.Computer science—Mathematics.Linear and Multilinear Algebras, Matrix Theory.Quantum Physics.Math Applications in Computer Science.512.57Josipović Miroslavauthttp://id.loc.gov/vocabulary/relators/aut781338MiAaPQMiAaPQMiAaPQBOOK9910360848603321Geometric Multiplication of Vectors1732487UNINA