Exercises in algebra: a collection of exercises in algebra, linear algebra and geometry
Saved in:
| Format: | Book |
|---|---|
| Language: | English Russian |
| Published: |
Luxembourg
Gordon and Breach
1996
|
| Edition: | Expanded English ed. |
| Series: | Algebra, logic and applications
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XII, 464 S. |
| ISBN: | 2884490299 2884490302 |
Staff View
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| 245 | 1 | 0 | |a Exercises in algebra |b a collection of exercises in algebra, linear algebra and geometry |c ed. by Alexei I. Kostrikin |
| 250 | |a Expanded English ed. | ||
| 264 | 1 | |a Luxembourg |b Gordon and Breach |c 1996 | |
| 300 | |a XII, 464 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algebra, logic and applications |v 6 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 7 | |a Algebra |2 gtt | |
| 650 | 7 | |a Meetkunde |2 gtt | |
| 650 | 4 | |a Algebra |v Problems, exercises, etc | |
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Record in the Search Index
| _version_ | 1804125431048175616 |
|---|---|
| adam_text | EXERCISES IN ALGEBRA A COLLECTION OF EXERCISES IN ALGEBRA, LINEAR
ALGEBRA AND GEOMETRY EXPANDED ENGLISH EDITION EDITED BY ALEXEI I.
KOSTRIKIN MOSCOW STATE UNIVERSITY, RUSSIA TRANSLATED BY V. A. ARTAMONOV
GORDON AND BREACH PUBLISHERS AUSTRALIA * CHINA * FRANCE * GERMANY *
INDIA * JAPAN * LUXEMBOURG * MALAYSIA THE NETHERLANDS * RUSSIA *
SINGAPORE * SWITZERLAND * THAILAND * UNITED KINGDOM * UNITED STATES
CONTENTS PREFACE TO THE RUSSIAN EDITION IX FOREWORD TO THE ENGLISH
EDITION XI PART ONE: FOUNDATIONS OF ALGEBRA 1 1 SETS AND MAPS 3 1.
OPERATIONS ON SUBSETS. CALCULATION OF THE NUMBER OF ELEMENTS 3 2.
CALCULATION OF THE NUMBER OF MAPS AND OF THE NUMBER OF SUBSETS. BINOMIAL
COEFFICIENTS 4 3. PERMUTATIONS 6 4. RECURRENCE RELATIONS. INDUCTION 11
5. SUMMATIONS 13 2 ARITHMETIC SPACES AND LINEAR EQUATIONS 15 6.
ARITHMETIC SPACES 15 7. RANK OF A MATRIX 19 8. SYSTEMS OF LINEAR
EQUATIONS 22 3 DETERMINANTS 31 9. DETERMINANTS OF SIZES TWO AND THREE 31
10. EXPANDING A DETERMINANT. INDUCTIVE DEFINITION 32 11. BASIC
PROPERTIES OF A DETERMINANT 33 12. EXPANDING A DETERMINANT ACCORDING TO
THE ELEMENTS OF A ROW OR A COLUMN 35 13. CALCULATING A DETERMINANT WITH
THE HELP OF ELEMENTARY OPERATIONS 37 14. CALCULATING SPECIAL
DETERMINANTS 40 15. DETERMINANT OFAPRODUCTOF MATRICES 42 16. ADDITIONAL
EXERCISES * 43 4 MATRICES - 49 17. OPERATIONS ON MATRICES 49 18. MATRIX
EQUATIONS. INVERSE MATRIX 53 19. SPECIAL MATRICES 57 VI CONTENTS 5
COMPLEX NUMBERS 61 20. COMPLEX NUMBERS IN ALGEBRAIC FORM 61 21. COMPLEX
NUMBERS IN TRIGONOMETRIC FORM 63 22. ROOTS OF COMPLEX NUMBERS.
CYCLOTOMIC POLYNOMIALS 65 23. CALCULATION OF SUMS AND PRODUCTS WITH THE
HELP OF COMPLEX NUMBERS 69 24. COMPLEX NUMBERS AND GEOMETRY OF A PLANE
72 6 POLYNOMIALS 77 25. DIVISION WITH A REMAINDER. EUCLIDEAN ALGORITHM
77 26. SIMPLE AND MULTIPLE ROOTS OVER FIELDS OF CHARACTERISTIC ZERO 79
27. PRIME DECOMPOSITION OVER M AND C 81 28. POLYNOMIALS OVER THE FIELD
OF RATIONALS AND OVER FINITE FIELDS 83 29. RATIONAL FRACTIONS 86 30.
INTERPOLATION 87 31. SYMMETRIC POLYNOMIALS. VIETA FORMULAS 89 32.
RESULTANT AND DISCRIMINANT 94 33. ISOLATION OF ROOTS 96 PART TWO: LINEAR
ALGEBRA AND GEOMETRY 99 7 VECTOR SPACES 101 34. CONCEPT OF A VECTOR
SPACE. BASES 101 35. SUBSPACES 104 36. LINEAR FUNCTIONS AND MAPPINGS 110
8 BILINEAR AND QUADRATIC FUNCTIONS 115 37. GENERAL BILINEAR AND
SESQUILINEAR FUNCTIONS 115 38. SYMMETRIC BILINEAR, HERMITIAN AND
QUADRATIC FUNCTIONS 124 9 LINEAR OPERATORS 131 39. DEFINITION OF A
LINEAR OPERATOR. THE IMAGE, THE KERNEL, THE MATRIX OF A LINEAR OPERATOR
131 40. EIGENVECTORS, INVARIANT SUBSPACES, ROOT SUBSPACES 135 41. JORDAN
CANONICAL FORM AND ITS APPLICATIONS. MINIMAL POLYNOMIAL 140 42. NORMED
VECTOR SPACES AND ALGEBRAS. NON-NEGATIVE MATRICES 146 10 METRIC VECTOR
SPACES 151 43. GEOMETRY OF METRIC SPACES 151 44. ADJOINT AND NORMAL
OPERATORS 158 45. SELFADJOINT OPERATORS. REDUCTION OF QUADRATIC
FUNCTIONS TO PRINCIPAL AXES 163 46. ORTHOGONAL AND UNITARY OPERATORS.
POLAR FACTORIZATION 166 CONTENTS VII 11 TENSORS 171 47. BASIC CONCEPTS
171 48. SYMMETRIC AND SKEW-SYMMETRIC TENSORS 174 12 AFFINE, EUCLIDEAN,
AND PROJECTIVE GEOMETRY 177 49. AFFINE SPACES 177 50. CONVEX SETS 183
51. EUCLIDEAN SPACES * 188 52. HYPERSURFACES OF SECOND DEGREE 194 53.
PROJECTIVE SPACES 201 PART THREE: BASIC ALGEBRAIC STRUCTURES 205 13
GROUPS 20 7 54. ALGEBRAIC OPERATIONS. SEMIGROUPS 207 55. CONCEPT OF A
GROUP. ISOMORPHISMS OF GROUPS 208 56. SUBGROUPS. ORDERS OF ELEMENTS OF
GROUPS. COSETS 213 57. ACTION OF A GROUP ON A SET. RELATION OF CONJUGACY
219 58. HOMOMORPHISMS AND NORMAL SUBGROUPS. FACTORGROUPS AND CENTERS 225
59. SYLOW SUBGROUPS. GROUPS OF SMALL ORDERS 230 60. DIRECT PRODUCTS AND
DIRECT SUMS. ABELIAN GROUPS 233 61. GENERATORS AND DEFINING RELATIONS
239 62. SOLVABLE GROUPS 243 14 RINGS 247 63. RINGS AND ALGEBRAS 247 64.
IDEALS, HOMOMORPHISMS, FACTOR-RINGS 254 65. SPECIAL CLASSES OF ALGEBRAS
264 66. FIELDS 269 67. EXTENSIONS OF FIELDS. GALOIS THEORY 274 68.
FINITE FIELDS 285 15 ELEMENTS OF REPRESENTATION THEORY 289 69.
REPRESENTATIONS OF GROUPS. BASIC CONCEPTS 289 70. REPRESENTATIONS OF
FINITE GROUPS . 294 71. GROUP ALGEBRAS AND THEIR MODULES 299 72.
CHARACTERS OF REPRESENTATIONS 304 73. INITIAL INFORMATION ON
REPRESENTATIONS OF CONTINUOUS GROUPS 309 ANSWERS AND HINTS 313 VIII
CONTENTS THEORETICAL MATERIAL 439 1. AFFINE AND EUCLIDEAN GEOMETRY 439
2. HYPERSURFACES OF THE SECOND ORDER 441 3. PROJECTIVE SPACE 443 4.
TENSORS 444 5. ELEMENTS OF REPRESENTATION THEORY 445 LIST OF DEFINITIONS
449 LIST OF SYMBOLS 457 INDEX 461
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| ctrlnum | (OCoLC)35158866 (DE-599)BVBBV010944240 |
| dewey-full | 512/.0076 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.0076 |
| dewey-search | 512/.0076 |
| dewey-sort | 3512 276 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Expanded English ed. |
| format | Book |
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| genre_facet | Aufgabensammlung |
| id | DE-604.BV010944240 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:01:27Z |
| institution | BVB |
| isbn | 2884490299 2884490302 |
| language | English Russian |
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| physical | XII, 464 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Gordon and Breach |
| record_format | marc |
| series | Algebra, logic and applications |
| series2 | Algebra, logic and applications |
| spelling | Exercises in algebra a collection of exercises in algebra, linear algebra and geometry ed. by Alexei I. Kostrikin Expanded English ed. Luxembourg Gordon and Breach 1996 XII, 464 S. txt rdacontent n rdamedia nc rdacarrier Algebra, logic and applications 6 Aus dem Russ. übers. Algebra gtt Meetkunde gtt Algebra Problems, exercises, etc Algebras, Linear Problems, exercises, etc Geometry, Algebraic Problems, exercises, etc Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Algebra (DE-588)4001156-2 s DE-604 Kostrikin, Aleksej I. Sonstige oth Algebra, logic and applications 6 (DE-604)BV002639285 6 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007319236&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Exercises in algebra a collection of exercises in algebra, linear algebra and geometry Algebra, logic and applications Algebra gtt Meetkunde gtt Algebra Problems, exercises, etc Algebras, Linear Problems, exercises, etc Geometry, Algebraic Problems, exercises, etc Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4143389-0 |
| title | Exercises in algebra a collection of exercises in algebra, linear algebra and geometry |
| title_auth | Exercises in algebra a collection of exercises in algebra, linear algebra and geometry |
| title_exact_search | Exercises in algebra a collection of exercises in algebra, linear algebra and geometry |
| title_full | Exercises in algebra a collection of exercises in algebra, linear algebra and geometry ed. by Alexei I. Kostrikin |
| title_fullStr | Exercises in algebra a collection of exercises in algebra, linear algebra and geometry ed. by Alexei I. Kostrikin |
| title_full_unstemmed | Exercises in algebra a collection of exercises in algebra, linear algebra and geometry ed. by Alexei I. Kostrikin |
| title_short | Exercises in algebra |
| title_sort | exercises in algebra a collection of exercises in algebra linear algebra and geometry |
| title_sub | a collection of exercises in algebra, linear algebra and geometry |
| topic | Algebra gtt Meetkunde gtt Algebra Problems, exercises, etc Algebras, Linear Problems, exercises, etc Geometry, Algebraic Problems, exercises, etc Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra Meetkunde Algebra Problems, exercises, etc Algebras, Linear Problems, exercises, etc Geometry, Algebraic Problems, exercises, etc Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007319236&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002639285 |
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