Projective geometry and modern algebra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 199 - 202 |
| Beschreibung: | XVI, 208 S. Ill., graph. Darst. |
| ISBN: | 3764339004 0817639004 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV010621164 | ||
| 003 | DE-604 | ||
| 005 | 20090728 | ||
| 007 | t | ||
| 008 | 960212s1996 gw ad|| |||| 00||| eng d | ||
| 016 | 7 | |a 946659648 |2 DE-101 | |
| 020 | |a 3764339004 |c (Basel ...) Pp. : sfr 68.00 |9 3-7643-3900-4 | ||
| 020 | |a 0817639004 |c (Boston) Pp. |9 0-8176-3900-4 | ||
| 035 | |a (OCoLC)33818158 | ||
| 035 | |a (DE-599)BVBBV010621164 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-29T |a DE-20 |a DE-739 |a DE-703 |a DE-824 |a DE-91 |a DE-19 |a DE-634 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA471 | |
| 082 | 0 | |a 516/.5 |2 20 | |
| 084 | |a SK 380 |0 (DE-625)143235: |2 rvk | ||
| 084 | |a MAT 110f |2 stub | ||
| 100 | 1 | |a Kadison, Lars |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Projective geometry and modern algebra |c Lars Kadison ; Matthias T. Kromann |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a XVI, 208 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 199 - 202 | ||
| 650 | 7 | |a Projectieve meetkunde |2 gtt | |
| 650 | 4 | |a Geometry, Projective | |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Projektive Geometrie |0 (DE-588)4047436-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Projektive Geometrie |0 (DE-588)4047436-7 |D s |
| 689 | 0 | 1 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kromann, Matthias T. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007085719&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007085719 | ||
Datensatz im Suchindex
| _version_ | 1804125096031289344 |
|---|---|
| adam_text | Contents 1
Preface ix
Historical Foreword xiii
1 Affine Geometry 1
1.1 Affine Planes 2
1.2 Transformations of the Affine Plane 5
2 Projective Planes 13
2.1 Completion of the Affine Plane 14
2.2 Homogeneous Coordinates for the Real Projective Plane 16
3 Desargues Theorem and the Principle of Duality 23
3.1 The Axiom P5 of Desargues 23
3.2 Moulton s Example 26
3.3 Axioms for Projective Space 27
3.4 Principle of Duality 29
4 A Brief Introduction to Groups 35
4.1 Elements of Group Theory 35
4.2 Automorphisms of the Projective Plane of 7 Points 39
5 Elementary Synthetic Projective Geometry 45
5.1 Fano s Axiom P6 45
5.2 Harmonic Points 47
5.3 Perspectivities and Projectivities 52
6 The Fundamental Theorem for Projectivities on a Line 61
6.1 The Fundamental Theorem: Axiom P7 61
6.2 Geometry of Complex Numbers 64
6.3 Pappus Theorem 67
v
vi CONTENTS
7 A Brief Introduction to Division Rings 75
7.1 Division Rings 75
7.2 The Quaternions H 78
7.3 A Noncommutative Division Ring with Characteristic p 81
8 Projective Planes over Division Rings 87
8.1 V2{R) 87
8.2 The Automorphism Group of P2{R) 89
8.3 The Algebraic Meaning of Axioms P6 and P7 101
8.4 Independence of Axioms 102
9 Introduction of Coordinates in a Projective Plane 105
9.1 The Major and Minor Desargues Axioms 106
9.2 Division Ring Number Lines 113
9.3 Introducing Coordinates in A 116
10 Mobius Transformations and Cross Ratio 123
10.1 Assessment 123
10.2 Mobius Transformations of the Extended Field 124
10.3 PJ(^) = PGL(1,F) 126
10.4 Cross Ratio: a Projective Invariant 129
11 Projective Collineations 135
11.1 Projective Collineations 135
11.2 Elations and Homologies 136
11.3 The Fundamental Theorem of Projective Collineation 139
11.4 PC(ji)=*PGL(2,F) 141
11.5 Ceva s Theorem 143
A Conies 151
A.I Conies 151
B Algebraic Curves and Bezout s Theorem 159
B.I Algebraic Curves 159
B.2 Intersection Theory of Algebraic Curves 162
C Elliptic Geometry 167
C.I The Laws of Sines and of Cosines 167
C.2 The Incidence Geometry of the Hyperbolic Plane 171
CONTENTS vii
D Ternary Rings 175
D.I Coordinatization 176
D.2 Addition 179
D.3 Multiplication 179
E The Lattice of Subspaces 183
E. 1 Posets and Lattices 184
E.2 Axioms for General Projective Geometry 187
E.3 The Fundamental Theorem of Projective Geometry 190
Solutions to Selected Exercises 195
Annotated Bibliography 198
Index of Notation 202
Index 205
|
| any_adam_object | 1 |
| author | Kadison, Lars Kromann, Matthias T. |
| author_facet | Kadison, Lars Kromann, Matthias T. |
| author_role | aut aut |
| author_sort | Kadison, Lars |
| author_variant | l k lk m t k mt mtk |
| building | Verbundindex |
| bvnumber | BV010621164 |
| callnumber-first | Q - Science |
| callnumber-label | QA471 |
| callnumber-raw | QA471 |
| callnumber-search | QA471 |
| callnumber-sort | QA 3471 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 380 |
| classification_tum | MAT 110f |
| ctrlnum | (OCoLC)33818158 (DE-599)BVBBV010621164 |
| dewey-full | 516/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.5 |
| dewey-search | 516/.5 |
| dewey-sort | 3516 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01750nam a2200457 c 4500</leader><controlfield tag="001">BV010621164</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090728 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960212s1996 gw ad|| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">946659648</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764339004</subfield><subfield code="c">(Basel ...) Pp. : sfr 68.00</subfield><subfield code="9">3-7643-3900-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817639004</subfield><subfield code="c">(Boston) Pp.</subfield><subfield code="9">0-8176-3900-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)33818158</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010621164</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA471</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516/.5</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 380</subfield><subfield code="0">(DE-625)143235:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 110f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kadison, Lars</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Projective geometry and modern algebra</subfield><subfield code="c">Lars Kadison ; Matthias T. Kromann</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 208 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 199 - 202</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Projectieve meetkunde</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Projective</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Projektive Geometrie</subfield><subfield code="0">(DE-588)4047436-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Projektive Geometrie</subfield><subfield code="0">(DE-588)4047436-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kromann, Matthias T.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007085719&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-007085719</subfield></datafield></record></collection> |
| id | DE-604.BV010621164 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:56:07Z |
| institution | BVB |
| isbn | 3764339004 0817639004 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007085719 |
| oclc_num | 33818158 |
| open_access_boolean | |
| owner | DE-29T DE-20 DE-739 DE-703 DE-824 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-11 DE-188 |
| owner_facet | DE-29T DE-20 DE-739 DE-703 DE-824 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-11 DE-188 |
| physical | XVI, 208 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Kadison, Lars Verfasser aut Projective geometry and modern algebra Lars Kadison ; Matthias T. Kromann Boston [u.a.] Birkhäuser 1996 XVI, 208 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 199 - 202 Projectieve meetkunde gtt Geometry, Projective Algebra (DE-588)4001156-2 gnd rswk-swf Projektive Geometrie (DE-588)4047436-7 gnd rswk-swf Projektive Geometrie (DE-588)4047436-7 s Algebra (DE-588)4001156-2 s DE-604 Kromann, Matthias T. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007085719&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kadison, Lars Kromann, Matthias T. Projective geometry and modern algebra Projectieve meetkunde gtt Geometry, Projective Algebra (DE-588)4001156-2 gnd Projektive Geometrie (DE-588)4047436-7 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4047436-7 |
| title | Projective geometry and modern algebra |
| title_auth | Projective geometry and modern algebra |
| title_exact_search | Projective geometry and modern algebra |
| title_full | Projective geometry and modern algebra Lars Kadison ; Matthias T. Kromann |
| title_fullStr | Projective geometry and modern algebra Lars Kadison ; Matthias T. Kromann |
| title_full_unstemmed | Projective geometry and modern algebra Lars Kadison ; Matthias T. Kromann |
| title_short | Projective geometry and modern algebra |
| title_sort | projective geometry and modern algebra |
| topic | Projectieve meetkunde gtt Geometry, Projective Algebra (DE-588)4001156-2 gnd Projektive Geometrie (DE-588)4047436-7 gnd |
| topic_facet | Projectieve meetkunde Geometry, Projective Algebra Projektive Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007085719&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kadisonlars projectivegeometryandmodernalgebra AT kromannmatthiast projectivegeometryandmodernalgebra |