A first course in abstract algebra: with applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Upper Saddle River, NJ
Pearson Prentice Hall
2006
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | Getr. Zählung Ill. |
| ISBN: | 0131862677 9780131862678 |
Staff View
MARC
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| 245 | 1 | 0 | |a A first course in abstract algebra |b with applications |c Joseph J. Rotman |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Upper Saddle River, NJ |b Pearson Prentice Hall |c 2006 | |
| 300 | |a Getr. Zählung |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Álgebra abstrata |2 larpcal | |
| 650 | 7 | |a Álgebra |2 larpcal | |
| 650 | 4 | |a Algebra, Abstract | |
| 650 | 4 | |a Commutative rings | |
| 650 | 4 | |a Group rings | |
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Universelle Algebra |0 (DE-588)4061777-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804136521180119040 |
|---|---|
| adam_text | Contents
Preface
to the Third Edition
........................ ix
Suggested Syllabi
............................... xiii
To the Reader
................................. xvii
Chapter
1
Number Theory
........................ 1
Section
1.1
Induction
............................. 1
Section
1.2
Binomial Theorem and Complex Numbers
........... 18
Section
1.3
Greatest Common Divisors
................... 37
Section
1.4
The Fundamental Theorem of Arithmetic
............ 55
Section
1.5
Congruences
........................... 59
Section
1.6
Dates and Days
......................... 76
Chapter
2
Groups I
............................. 84
Section
2.1
Some Set Theory
......................... 84
Functions
................................. 87
Equivalence Relations
........................... 99
Section
2.2
Permutations
........................... 106
Section
2.3
Groups
.............................. 125
Symmetry
................................. 137
Section
2.4
Subgroups and Lagrange s Theorem
.............. 147
Section
2.5
Homomorphisms
......................... 159
Section
2.6
Quotient Groups
......................... 171
Section
2.7
Group Actions
.......................... 192
Section
2.8
Counting with Groups
...................... 208
vi
Contents
Chapters Commutative Rings I
.................... 217
Section
3.1
First Properties
.......................... 217
Section
3.2
Fields
............................... 230
Section
3.3
Polynomials
........................... 235
Section
3.4
Homomorphisms
......................... 243
Section
3.5
From Numbers to Polynomials
................. 252
Euclidean Rings
.............................. 267
Section
3.6
Unique Factorization
....................... 275
Section
3.7
Irreducibility
........................... 281
Section
3.8
Quotient Rings and Finite Fields
................ 290
Section
3.9
A Mathematical Odyssey
.................... 305
Latin Squares
............................... 305
Magic Squares
............................... 310
Design of Experiments
.......................... 314
Projective
Planes
............................. 316
Chapter
4
Linear Algebra
........................ 320
Section
4.1
Vector Spaces
.......................... 320
Gaussian Elimination
........................... 344
Section
4.2
Euclidean Constructions
..................... 354
Section
4.3
Linear Transformations
..................... 366
Section
4.4
Eigenvalues
........................... 383
Section
4.5
Codes
.............................. 399
Block Codes
................................ 399
Linear Codes
............................... 406
Decoding
................................. 423
Chapter
5
Fields
............................... 432
Section
5.1
Classical Formulas
........................ 432
Viète s
Cubic Formula
.......................... 444
Section
5.2
Insolvability of the General Quintic
............... 449
Formulas and Solvability by Radicals
.................. 459
Quadratics
................................. 460
Cubics
................................... 461
Quartics
.................................. 461
Translation into Group Theory
...................... 462
Section
5.3
Epilog
.............................. 471
Chapter
6
Groups II
............................ 475
Section
6.1
Finite Abelian Groups
...................... 475
Section
6.2
The Sylow Theorems
...................... 489
Section
6.3
Ornamental Symmetry
...................... 501
Contents
vii
Chapter
7
Commutative Rings II
.................... 518
Section
7.1
Prime Ideals and Maximal Ideals
................ 518
Section
7.2
Unique Factorization
....................... 525
Section
7.3
Noetherian Rings
........................ 535
Section
7.4
Varieties
............................. 540
Section
7.5
Generalized Divison Algorithm
................. 558
Monomial Orders
............................. 559
Division Algorithm
............................ 565
Section
7.6 Gröbner
Bases
.......................... 570
Appendix A Inequalities
..........................
A-l
Appendix
В
Pseudocodes
.........................
A-3
Hints for Selected Exercises
........................
H-l
Bibliography
..................................
R-l
Index
....................................... 1-1
|
| adam_txt |
Contents
Preface
to the Third Edition
. ix
Suggested Syllabi
. xiii
To the Reader
. xvii
Chapter
1
Number Theory
. 1
Section
1.1
Induction
. 1
Section
1.2
Binomial Theorem and Complex Numbers
. 18
Section
1.3
Greatest Common Divisors
. 37
Section
1.4
The Fundamental Theorem of Arithmetic
. 55
Section
1.5
Congruences
. 59
Section
1.6
Dates and Days
. 76
Chapter
2
Groups I
. 84
Section
2.1
Some Set Theory
. 84
Functions
. 87
Equivalence Relations
. 99
Section
2.2
Permutations
. 106
Section
2.3
Groups
. 125
Symmetry
. 137
Section
2.4
Subgroups and Lagrange's Theorem
. 147
Section
2.5
Homomorphisms
. 159
Section
2.6
Quotient Groups
. 171
Section
2.7
Group Actions
. 192
Section
2.8
Counting with Groups
. 208
vi
Contents
Chapters Commutative Rings I
. 217
Section
3.1
First Properties
. 217
Section
3.2
Fields
. 230
Section
3.3
Polynomials
. 235
Section
3.4
Homomorphisms
. 243
Section
3.5
From Numbers to Polynomials
. 252
Euclidean Rings
. 267
Section
3.6
Unique Factorization
. 275
Section
3.7
Irreducibility
. 281
Section
3.8
Quotient Rings and Finite Fields
. 290
Section
3.9
A Mathematical Odyssey
. 305
Latin Squares
. 305
Magic Squares
. 310
Design of Experiments
. 314
Projective
Planes
. 316
Chapter
4
Linear Algebra
. 320
Section
4.1
Vector Spaces
. 320
Gaussian Elimination
. 344
Section
4.2
Euclidean Constructions
. 354
Section
4.3
Linear Transformations
. 366
Section
4.4
Eigenvalues
. 383
Section
4.5
Codes
. 399
Block Codes
. 399
Linear Codes
. 406
Decoding
. 423
Chapter
5
Fields
. 432
Section
5.1
Classical Formulas
. 432
Viète's
Cubic Formula
. 444
Section
5.2
Insolvability of the General Quintic
. 449
Formulas and Solvability by Radicals
. 459
Quadratics
. 460
Cubics
. 461
Quartics
. 461
Translation into Group Theory
. 462
Section
5.3
Epilog
. 471
Chapter
6
Groups II
. 475
Section
6.1
Finite Abelian Groups
. 475
Section
6.2
The Sylow Theorems
. 489
Section
6.3
Ornamental Symmetry
. 501
Contents
vii
Chapter
7
Commutative Rings II
. 518
Section
7.1
Prime Ideals and Maximal Ideals
. 518
Section
7.2
Unique Factorization
. 525
Section
7.3
Noetherian Rings
. 535
Section
7.4
Varieties
. 540
Section
7.5
Generalized Divison Algorithm
. 558
Monomial Orders
. 559
Division Algorithm
. 565
Section
7.6 Gröbner
Bases
. 570
Appendix A Inequalities
.
A-l
Appendix
В
Pseudocodes
.
A-3
Hints for Selected Exercises
.
H-l
Bibliography
.
R-l
Index
. 1-1 |
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| discipline | Mathematik |
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| id | DE-604.BV022444039 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:33:44Z |
| indexdate | 2024-07-09T20:57:43Z |
| institution | BVB |
| isbn | 0131862677 9780131862678 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015652041 |
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| physical | Getr. Zählung Ill. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Pearson Prentice Hall |
| record_format | marc |
| spelling | Rotman, Joseph J. 1934- Verfasser (DE-588)120676826 aut A first course in abstract algebra with applications Joseph J. Rotman 3. ed. Upper Saddle River, NJ Pearson Prentice Hall 2006 Getr. Zählung Ill. txt rdacontent n rdamedia nc rdacarrier Álgebra abstrata larpcal Álgebra larpcal Algebra, Abstract Commutative rings Group rings Number theory Universelle Algebra (DE-588)4061777-4 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s DE-604 Universelle Algebra (DE-588)4061777-4 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015652041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rotman, Joseph J. 1934- A first course in abstract algebra with applications Álgebra abstrata larpcal Álgebra larpcal Algebra, Abstract Commutative rings Group rings Number theory Universelle Algebra (DE-588)4061777-4 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4061777-4 (DE-588)4001156-2 |
| title | A first course in abstract algebra with applications |
| title_auth | A first course in abstract algebra with applications |
| title_exact_search | A first course in abstract algebra with applications |
| title_exact_search_txtP | A first course in abstract algebra with applications |
| title_full | A first course in abstract algebra with applications Joseph J. Rotman |
| title_fullStr | A first course in abstract algebra with applications Joseph J. Rotman |
| title_full_unstemmed | A first course in abstract algebra with applications Joseph J. Rotman |
| title_short | A first course in abstract algebra |
| title_sort | a first course in abstract algebra with applications |
| title_sub | with applications |
| topic | Álgebra abstrata larpcal Álgebra larpcal Algebra, Abstract Commutative rings Group rings Number theory Universelle Algebra (DE-588)4061777-4 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Álgebra abstrata Álgebra Algebra, Abstract Commutative rings Group rings Number theory Universelle Algebra Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015652041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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