Please use this identifier to cite or link to this item: http://localhost/handle/Hannan/1224
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dc.contributor.authorVince, John. ;en_US
dc.date.accessioned2013en_US
dc.date.accessioned2020-05-17T08:26:39Z-
dc.date.available2020-05-17T08:26:39Z-
dc.date.issued2018en_US
dc.identifier.isbn9783319946375 ;en_US
dc.identifier.isbn9783319946368 (print) ;en_US
dc.identifier.isbn9783319946382 (print) ;en_US
dc.identifier.urihttp://localhost/handle/Hannan/1224-
dc.descriptionSpringerLink (Online service) ;en_US
dc.descriptionen_US
dc.descriptionen_US
dc.descriptionPrinted edition: ; 9783319946368. ;en_US
dc.descriptionen_US
dc.descriptionen_US
dc.descriptionPrinted edition: ; 9783319946382. ;en_US
dc.descriptionen_US
dc.descriptionen_US
dc.description.abstractThe imaginary unit i = ee-1 has been used by mathematicians for nearly five-hundred years, during which time its physical meaning has been a constant challenge. Unfortunately, Rene Descartes referred to it as eeimaginaryee, and the use of the term eecomplex numberee compounded the unnecessary mystery associated with this amazing object. Today, i = ee-1 has found its way into virtually every branch of mathematics, and is widely employed in physics and science, from solving problems in electrical engineering to quantum field theory. John Vince describes the evolution of the imaginary unit from the roots of quadratic and cubic equations, Hamiltonees quaternions, Cayleyees octonions, to Grassmannees geometric algebra. In spite of the aura of mystery that surrounds the subject, John Vince makes the subject accessible and very readable. The first two chapters cover the imaginary unit and its integration with real numbers. Chapter 3 describes how complex numbers work with matrices, and shows how to compute complex eigenvalues and eigenvectors. Chapters 4 and 5 cover Hamiltonees invention of quaternions, and Cayleyees development of octonions, respectively. Chapter 6 provides a brief introduction to geometric algebra, which possesses many of the imaginary qualities of quaternions, but works in space of any dimension. The second half of the book is devoted to applications of complex numbers, quaternions and geometric algebra. John Vince explains how complex numbers simplify trigonometric identities, wave combinations and phase differences in circuit analysis, and how geometric algebra resolves geometric problems, and quaternions rotate 3D vectors. There are two short chapters on the Riemann hypothesis and the Mandelbrot set, both of which use complex numbers. The last chapter references the role of complex numbers in quantum mechanics, and ends with Schredingerees famous wave equation. Filled with lots of clear examples and useful illustrations, this compact book provides an excellent introduction to imaginary mathematics for computer science. ;en_US
dc.description.statementofresponsibilityby John Vince.en_US
dc.description.tableofcontentsIntroduction -- Complex Numbers -- Matrix Algebra -- Quaternions -- Octonions -- Geometric Algebra -- Trigonometric Identities using Complex Numbers -- Combining Waves using Complex Numbers -- Circuit Analysis using Complex Numbers -- Geometry Using Geometric Algebra -- Rotating Vectors using Quaternions -- Complex Numbers and the Riemann Hypothesis -- The Mandelbrot Set -- Conclusion -- Index. ;en_US
dc.format.extentXVII, 301 p. 99 illus. in color. ; online resource. ;en_US
dc.publisherSpringer International Publishing :en_US
dc.publisherImprint: Springer,en_US
dc.relation.haspart9783319946368.pdfen_US
dc.subjectComputer Scienceen_US
dc.subjectMath Applications in Computer Science. ; http://scigraph.springernature.com/things/product-market-codes/I17044. ;en_US
dc.subject.ddc004.0151 ; 23 ;en_US
dc.subject.lccQA76.9.M35 ;en_US
dc.titleImaginary Mathematics for Computer Scienceen_US
dc.typeBooken_US
dc.publisher.placeCham :en_US
Appears in Collections:مدیریت فناوری اطلاعات

Files in This Item:
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9783319946368.pdf10.49 MBAdobe PDFThumbnail
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Full metadata record
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dc.contributor.authorVince, John. ;en_US
dc.date.accessioned2013en_US
dc.date.accessioned2020-05-17T08:26:39Z-
dc.date.available2020-05-17T08:26:39Z-
dc.date.issued2018en_US
dc.identifier.isbn9783319946375 ;en_US
dc.identifier.isbn9783319946368 (print) ;en_US
dc.identifier.isbn9783319946382 (print) ;en_US
dc.identifier.urihttp://localhost/handle/Hannan/1224-
dc.descriptionSpringerLink (Online service) ;en_US
dc.descriptionen_US
dc.descriptionen_US
dc.descriptionPrinted edition: ; 9783319946368. ;en_US
dc.descriptionen_US
dc.descriptionen_US
dc.descriptionPrinted edition: ; 9783319946382. ;en_US
dc.descriptionen_US
dc.descriptionen_US
dc.description.abstractThe imaginary unit i = ee-1 has been used by mathematicians for nearly five-hundred years, during which time its physical meaning has been a constant challenge. Unfortunately, Rene Descartes referred to it as eeimaginaryee, and the use of the term eecomplex numberee compounded the unnecessary mystery associated with this amazing object. Today, i = ee-1 has found its way into virtually every branch of mathematics, and is widely employed in physics and science, from solving problems in electrical engineering to quantum field theory. John Vince describes the evolution of the imaginary unit from the roots of quadratic and cubic equations, Hamiltonees quaternions, Cayleyees octonions, to Grassmannees geometric algebra. In spite of the aura of mystery that surrounds the subject, John Vince makes the subject accessible and very readable. The first two chapters cover the imaginary unit and its integration with real numbers. Chapter 3 describes how complex numbers work with matrices, and shows how to compute complex eigenvalues and eigenvectors. Chapters 4 and 5 cover Hamiltonees invention of quaternions, and Cayleyees development of octonions, respectively. Chapter 6 provides a brief introduction to geometric algebra, which possesses many of the imaginary qualities of quaternions, but works in space of any dimension. The second half of the book is devoted to applications of complex numbers, quaternions and geometric algebra. John Vince explains how complex numbers simplify trigonometric identities, wave combinations and phase differences in circuit analysis, and how geometric algebra resolves geometric problems, and quaternions rotate 3D vectors. There are two short chapters on the Riemann hypothesis and the Mandelbrot set, both of which use complex numbers. The last chapter references the role of complex numbers in quantum mechanics, and ends with Schredingerees famous wave equation. Filled with lots of clear examples and useful illustrations, this compact book provides an excellent introduction to imaginary mathematics for computer science. ;en_US
dc.description.statementofresponsibilityby John Vince.en_US
dc.description.tableofcontentsIntroduction -- Complex Numbers -- Matrix Algebra -- Quaternions -- Octonions -- Geometric Algebra -- Trigonometric Identities using Complex Numbers -- Combining Waves using Complex Numbers -- Circuit Analysis using Complex Numbers -- Geometry Using Geometric Algebra -- Rotating Vectors using Quaternions -- Complex Numbers and the Riemann Hypothesis -- The Mandelbrot Set -- Conclusion -- Index. ;en_US
dc.format.extentXVII, 301 p. 99 illus. in color. ; online resource. ;en_US
dc.publisherSpringer International Publishing :en_US
dc.publisherImprint: Springer,en_US
dc.relation.haspart9783319946368.pdfen_US
dc.subjectComputer Scienceen_US
dc.subjectMath Applications in Computer Science. ; http://scigraph.springernature.com/things/product-market-codes/I17044. ;en_US
dc.subject.ddc004.0151 ; 23 ;en_US
dc.subject.lccQA76.9.M35 ;en_US
dc.titleImaginary Mathematics for Computer Scienceen_US
dc.typeBooken_US
dc.publisher.placeCham :en_US
Appears in Collections:مدیریت فناوری اطلاعات

Files in This Item:
File Description SizeFormat 
9783319946368.pdf10.49 MBAdobe PDFThumbnail
Preview File
Full metadata record
DC FieldValueLanguage
dc.contributor.authorVince, John. ;en_US
dc.date.accessioned2013en_US
dc.date.accessioned2020-05-17T08:26:39Z-
dc.date.available2020-05-17T08:26:39Z-
dc.date.issued2018en_US
dc.identifier.isbn9783319946375 ;en_US
dc.identifier.isbn9783319946368 (print) ;en_US
dc.identifier.isbn9783319946382 (print) ;en_US
dc.identifier.urihttp://localhost/handle/Hannan/1224-
dc.descriptionSpringerLink (Online service) ;en_US
dc.descriptionen_US
dc.descriptionen_US
dc.descriptionPrinted edition: ; 9783319946368. ;en_US
dc.descriptionen_US
dc.descriptionen_US
dc.descriptionPrinted edition: ; 9783319946382. ;en_US
dc.descriptionen_US
dc.descriptionen_US
dc.description.abstractThe imaginary unit i = ee-1 has been used by mathematicians for nearly five-hundred years, during which time its physical meaning has been a constant challenge. Unfortunately, Rene Descartes referred to it as eeimaginaryee, and the use of the term eecomplex numberee compounded the unnecessary mystery associated with this amazing object. Today, i = ee-1 has found its way into virtually every branch of mathematics, and is widely employed in physics and science, from solving problems in electrical engineering to quantum field theory. John Vince describes the evolution of the imaginary unit from the roots of quadratic and cubic equations, Hamiltonees quaternions, Cayleyees octonions, to Grassmannees geometric algebra. In spite of the aura of mystery that surrounds the subject, John Vince makes the subject accessible and very readable. The first two chapters cover the imaginary unit and its integration with real numbers. Chapter 3 describes how complex numbers work with matrices, and shows how to compute complex eigenvalues and eigenvectors. Chapters 4 and 5 cover Hamiltonees invention of quaternions, and Cayleyees development of octonions, respectively. Chapter 6 provides a brief introduction to geometric algebra, which possesses many of the imaginary qualities of quaternions, but works in space of any dimension. The second half of the book is devoted to applications of complex numbers, quaternions and geometric algebra. John Vince explains how complex numbers simplify trigonometric identities, wave combinations and phase differences in circuit analysis, and how geometric algebra resolves geometric problems, and quaternions rotate 3D vectors. There are two short chapters on the Riemann hypothesis and the Mandelbrot set, both of which use complex numbers. The last chapter references the role of complex numbers in quantum mechanics, and ends with Schredingerees famous wave equation. Filled with lots of clear examples and useful illustrations, this compact book provides an excellent introduction to imaginary mathematics for computer science. ;en_US
dc.description.statementofresponsibilityby John Vince.en_US
dc.description.tableofcontentsIntroduction -- Complex Numbers -- Matrix Algebra -- Quaternions -- Octonions -- Geometric Algebra -- Trigonometric Identities using Complex Numbers -- Combining Waves using Complex Numbers -- Circuit Analysis using Complex Numbers -- Geometry Using Geometric Algebra -- Rotating Vectors using Quaternions -- Complex Numbers and the Riemann Hypothesis -- The Mandelbrot Set -- Conclusion -- Index. ;en_US
dc.format.extentXVII, 301 p. 99 illus. in color. ; online resource. ;en_US
dc.publisherSpringer International Publishing :en_US
dc.publisherImprint: Springer,en_US
dc.relation.haspart9783319946368.pdfen_US
dc.subjectComputer Scienceen_US
dc.subjectMath Applications in Computer Science. ; http://scigraph.springernature.com/things/product-market-codes/I17044. ;en_US
dc.subject.ddc004.0151 ; 23 ;en_US
dc.subject.lccQA76.9.M35 ;en_US
dc.titleImaginary Mathematics for Computer Scienceen_US
dc.typeBooken_US
dc.publisher.placeCham :en_US
Appears in Collections:مدیریت فناوری اطلاعات

Files in This Item:
File Description SizeFormat 
9783319946368.pdf10.49 MBAdobe PDFThumbnail
Preview File