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)

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
Creator
Contributor
Author
Provider
Subject
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
QA184-205
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)
Instantiates
Publication
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 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
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
10.1007/978-0-8176-8385-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-0-8176-8385-6
Label
New Foundations in Mathematics : The Geometric Concept of Number, by Garret Sobczyk, (electronic resource)
Publication
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 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
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
10.1007/978-0-8176-8385-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-0-8176-8385-6

Library Locations

  • African Studies LibraryBorrow it
    771 Commonwealth Avenue, 6th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Alumni Medical LibraryBorrow it
    72 East Concord Street, Boston, MA, 02118, US
    42.336388 -71.072393
  • Astronomy LibraryBorrow it
    725 Commonwealth Avenue, 6th Floor, Boston, MA, 02445, US
    42.350259 -71.105717
  • Fineman and Pappas Law LibrariesBorrow it
    765 Commonwealth Avenue, Boston, MA, 02215, US
    42.350979 -71.107023
  • Frederick S. Pardee Management LibraryBorrow it
    595 Commonwealth Avenue, Boston, MA, 02215, US
    42.349626 -71.099547
  • Howard Gotlieb Archival Research CenterBorrow it
    771 Commonwealth Avenue, 5th Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Mugar Memorial LibraryBorrow it
    771 Commonwealth Avenue, Boston, MA, 02215, US
    42.350723 -71.108227
  • Music LibraryBorrow it
    771 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350723 -71.108227
  • Pikering Educational Resources LibraryBorrow it
    2 Silber Way, Boston, MA, 02215, US
    42.349804 -71.101425
  • School of Theology LibraryBorrow it
    745 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US
    42.350494 -71.107235
  • Science & Engineering LibraryBorrow it
    38 Cummington Mall, Boston, MA, 02215, US
    42.348472 -71.102257
  • Stone Science LibraryBorrow it
    675 Commonwealth Avenue, Boston, MA, 02445, US
    42.350103 -71.103784
Processing Feedback ...