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The Resource New Foundations in Mathematics : The Geometric Concept of Number, by Garret Sobczyk, (electronic resource)
New Foundations in Mathematics : The Geometric Concept of Number, by Garret Sobczyk, (electronic resource)
Resource Information
The item New Foundations in Mathematics : The Geometric Concept of Number, by Garret Sobczyk, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item New Foundations in Mathematics : The Geometric Concept of Number, by Garret Sobczyk, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 The 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
 Language
 eng
 Extent
 XIV, 370 p. 55 illus., 32 illus. in color.
 Contents

 1 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 mSurfaces
 14 Differential Geometry of Curves
 15 Differential Geometry of kSurfaces
 16 Mappings Between Surfaces
 17 NonEuclidean and Projective Geometries
 18 Lie Groups and Lie Algebras
 References
 Symbols
 Isbn
 9780817683856
 Label
 New Foundations in Mathematics : The Geometric Concept of Number
 Title
 New Foundations in Mathematics
 Title remainder
 The Geometric Concept of Number
 Statement of responsibility
 by Garret Sobczyk
 Subject

 Algebra
 Topological Groups
 Algebra
 Group Theory and Generalizations
 Topological Groups
 Mathematical physics
 Mathematics
 Appl.Mathematics/Computational Methods of Engineering
 Mathematics
 Algebra
 Topological Groups
 Group theory
 Electronic resources
 Topological Groups, Lie Groups
 Engineering mathematics
 Mathematics
 Linear and Multilinear Algebras, Matrix Theory
 Engineering mathematics
 Mathematical physics
 Mathematical physics
 Mathematical Methods in Physics
 Engineering mathematics
 Group theory
 Group theory
 Matrix theory
 Language
 eng
 Summary
 The 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
 http://library.link/vocab/creatorName
 Sobczyk, Garret
 Image bit depth
 0
 LC call number
 QA184205
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Group theory
 Matrix theory
 Topological Groups
 Mathematical physics
 Engineering mathematics
 Mathematics
 Linear and Multilinear Algebras, Matrix Theory
 Topological Groups, Lie Groups
 Group Theory and Generalizations
 Mathematical Methods in Physics
 Appl.Mathematics/Computational Methods of Engineering
 Algebra
 Label
 New Foundations in Mathematics : The Geometric Concept of Number, by Garret Sobczyk, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1 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 mSurfaces  14 Differential Geometry of Curves  15 Differential Geometry of kSurfaces  16 Mappings Between Surfaces  17 NonEuclidean and Projective Geometries  18 Lie Groups and Lie Algebras  References  Symbols
 Dimensions
 unknown
 Extent
 XIV, 370 p. 55 illus., 32 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9780817683856
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9780817683856
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9780817683856
 Label
 New Foundations in Mathematics : The Geometric Concept of Number, by Garret Sobczyk, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1 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 mSurfaces  14 Differential Geometry of Curves  15 Differential Geometry of kSurfaces  16 Mappings Between Surfaces  17 NonEuclidean and Projective Geometries  18 Lie Groups and Lie Algebras  References  Symbols
 Dimensions
 unknown
 Extent
 XIV, 370 p. 55 illus., 32 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9780817683856
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9780817683856
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9780817683856
Subject
 Algebra
 Algebra
 Algebra
 Appl.Mathematics/Computational Methods of Engineering
 Electronic resources
 Engineering mathematics
 Engineering mathematics
 Engineering mathematics
 Group Theory and Generalizations
 Group theory
 Group theory
 Group theory
 Linear and Multilinear Algebras, Matrix Theory
 Mathematical Methods in Physics
 Mathematical physics
 Mathematical physics
 Mathematical physics
 Mathematics
 Mathematics
 Mathematics
 Matrix theory
 Topological Groups
 Topological Groups
 Topological Groups
 Topological Groups, Lie Groups
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