Algebraic approach to geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Jaipur
Oxford Book Company
2018
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | viii, 296 pages illustrations (black and white) 24 cm |
| ISBN: | 9789350303344 9350303345 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804177833149333504 |
|---|---|
| adam_text | Contents
Preface (vii)
1. Vector Algebra 1
2. The Sphere and The Paraboloids 58
3. The Conic Section 81
4. Eigenvalues and Eigenvectors 120
5. Matrices 157
6. Orientation on Manifolds 184
7. Rotation 195
8. Bipolar Coordinates 201
9. Surface Area of a Sphere 209
10. Lie Theory 217
11. Triangle 229
Bibliography 293
Index 295
Algebraic Approach to Geometry
Algebraic geometry is the study of geometries that come from algebra, in
particular, from rings. In classical algebraic geometry, the algebra is the ring of
polynomials, and the geometry is the set of zeros of polynomials, called an
algebraic variety. In the twentieth century, it was discovered that the basic ideas
of classical algebraic geometry can be applied to any commutative ring with a
unit, such as the integers. The geometry of such a ring is determined by its
algebraic structure, in particular its prime ideals. Grothendieck defined schemes
as the basic geometric objects, which have the same relationship to the
geometry of a ring as a manifold to a coordinate chart. The language of category
theory evolved at around the same time, largely in response to the needs of the
increasing abstraction in algebraic geometry. The study of algebraic curves in
the complex projective plane is the natural link between linear geometry at an
undergraduate level and algebraic geometry at a graduate level, and it is also an
important topic in geometric applications, such as cryptography. This book will
be of interest for students and teachers of linear geometry at graduate level.
Contents: Vector Algebra • The Sphere and The Paraboloids • The Conic
Section • Eigenvalues and Eigenvectors • Matrices • Orientation on
Manifolds • Rotation • Bipolar Coordinates • Surface Area of a Sphere • Lie
Theory • Triangle
Naseer Khan has received a doctoral degree in civil engineering from MIT,
Bareilly followed by degree in civil engineering and mathematics from the same
institute. His research interests are in random vibration, stochastic calculus,
numerical methods for solving stochastic problems, probabilistic models for
microstructures, wind/earthquake engineering, climate models, and Monte
Carlo simulation. His teaching interests focus on engineering applications
starting from fundamental concepts of mechanics, probability theory, statistics,
and mathematics.
ISBN : 1701350303344
Oxford Book Company
Publishers «Distributors* Exporters
Email: oxfordhookjpr@gmaiL com
Website: www.oxfordbookconipany.com
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| isbn | 9789350303344 9350303345 |
| language | English |
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| physical | viii, 296 pages illustrations (black and white) 24 cm |
| publishDate | 2018 |
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| spelling | Khan, Naseer Verfasser aut Algebraic approach to geometry Naseer Khan Jaipur Oxford Book Company 2018 viii, 296 pages illustrations (black and white) 24 cm txt rdacontent n rdamedia nc rdacarrier Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029889382&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029889382&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Khan, Naseer Algebraic approach to geometry Algebraische Geometrie (DE-588)4001161-6 gnd |
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| title | Algebraic approach to geometry |
| title_auth | Algebraic approach to geometry |
| title_exact_search | Algebraic approach to geometry |
| title_full | Algebraic approach to geometry Naseer Khan |
| title_fullStr | Algebraic approach to geometry Naseer Khan |
| title_full_unstemmed | Algebraic approach to geometry Naseer Khan |
| title_short | Algebraic approach to geometry |
| title_sort | algebraic approach to geometry |
| topic | Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algebraische Geometrie |
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