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### Algebra by Michael Artin

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Abstract Algebra eBooks . We hope mathematician or person who’s interested in mathematics like these books. Algebra written by Michael Artin , Massachusetts Institute of Technology.
According to Michael Artin:
This book began about 20 years ago in the form of supplementary notes for my algebra classes. I wanted to discuss some concrete topics such as symmetry, linear groups, and quadratic number fields in more detail than the text provided, and to shift the emphasis in group theory from permutation groups to matrix groups. Lattices, another recurring theme, appeared spontaneously. My hope was that the concrete material would interest the students and that it would make the abstractions more understandable, in short, that they could get farther by learning both at the same time. This worked pretty well. It took me quite a while to decide what I wanted to put in, but I gradually handed out more notes and eventually began teaching from them without another text. This method produced a book which is, I think, somewhat different from existing ones. However, the problems I encountered while fitting the parts together caused me many headaches, so I can't recommend starting this way.
The main novel feature of the book is its increased emphasis on special topics. They tended to expand each time the sections were rewritten, because I noticed over the years that, with concrete mathematics in contrast to abstract concepts, students often prefer more to less. As a result, the ones mentioned above have become major parts of the book. There are also several unusual short subjects, such as the ToddCoxeter algorithm and the simplicity of PSL2•

Algebra written by Michael Artin cover the following topics.

• 1. Matrix Operations
1. The Basic Operations
2. Row Reduction
3. Determinants
4. Permutation Matrices
5. Cramer
s Rule
EXERCISES

• 2. Groups
1. The Definition of a Group
2. Subgroups
3. Isomorphisms
4. Homomorphisms
s.Equivalence Relations And Partitions
6. Cosets
7. Restriction of a Homomorphism to a Subgroup
8. Products of Groups
9. Modular Arithmetic
10. Quotient Groups
EXERCISES

• 3. Vector Spaces
1. Real Vector Spaces
2. Abstract Fields
3. Bases and Dimension
4. Computation with Bases
5. Infinite-Dimensional Spaces
6. Direct Sums
EXERCISES

• 4. Linear Transformations
1. The Dimension Formula
2. The Matrix of a Linear Transformation III
3. Linear Operators and Eigenvectors
4. The Characteristic Polynomial
5. Orthogonal Matrices and Rotations
6. Diagonalization
7. Systems of Differential Equations
8. The Matrix Exponential
EXERCISES

• 5. Symmetry
1. Symmetry of Plane Figures
2. The Group of Motions of the Plane
3. Finite Groups of Motions
4. Discrete Groups of Motions
5. Abstract Symmetry: Group Operations
6. The Operation on Cosets
7. The Counting Formula
8. Permutation Representations
9. Finite Subgroups of the Rotation Group
EXERCISES

• 6. More Group Theory
1. The Operations of a Group on Itself
2. The Class Equation of the Icosahedral Group
3. Operations on Subsets
4. The Sylow Theorems
5. The Groups of Order 12
6. Computation in the Symmetric Group
7. The Free Group
8. Generators and Relations
9. The Todd-Coxeter Algorithm
EXERCISES

• 7. Bilinear Forms
1. Definition of Bilinear Form
2. Symmetric Forms: Orthogonality
3. The Geometry Associated to a Positive Form
4. Hermitian Forms
5. The Spectral Theorem
7. The Spectral Theorem for Normal Operators
8. Skew-Symmetric Forms
9. Summary of Results, in Matrix Notation
EXERCISES

• 8. Linear Groups
1. The Classical Linear Groups
2. The Special Unitary Group SU2
3. The Orthogonal Representation of SU2
4. The Special Linear Group SL2(lR)
5. One-Parameter Subgroups
6. The Lie Algebra
7. Translation in a Group
8. Simple Groups
EXERCISES

• 9. Group Representations
1. Definition of a Group Representation
2. G-Invariant Forms and Unitary Representations
3. Compact Groups
4. G-Invariant Subspaces and Irreducible Representations
5. Characters
6. Permutation Representations and the Regular Representation
7. The Representations of the Icosahedral Group
8. One-Dimensional Representations
9. Schur
s Lemma, and Proof of the Orthogonality Relations
10. Representations of the Group SU2
EXERCISES

• 10. Rings
1. Definition of a Ring
2. Formal Construction of Integers and Polynomials
3. Homomorphisms and Ideals
4. Quotient Rings and Relations in a Ring
6. Integral Domains and Fraction Fields
7. Maximal Ideals
8. Algebraic Geometry
EXERCISES

• 11. Factorization
1. Factorization of Integers and Polynomials
2. Unique Factorization Domains, Principal Ideal Domains, and Euclidean Domains
3. Gauss
s Lemma
4. Explicit Factorization of Polynomials
5. Primes in the Ring of Gauss Integers
6. Algebraic Integers
7. Factorization in Imaginary Quadratic Fields
8. Ideal Factorization
9. The Relation Between Prime Ideals of R and Prime Integers
10. Ideal Classes in Imaginary Quadratic Fields
12. Some Diophantine Equations
EXERCISES

• 12. Modules
1. The Definition of a Module
2. Matrices, Free Modules, and Bases
3. The Principle of Permanence of Identities
4. Diagonalization of Integer Matrices
5. Generators and Relations for Modules
6. The Structure Theorem for Abelian Groups
7. Application to Linear Operators
8. Free Modules over Polynomial Rings
EXERCISES

• 13. Fields
1. Examples of Fields
2. Algebraic and Transcendental Elements
3. The Degree of a Field Extension
4. Constructions with Ruler and Compass
6. Finite Fields
7. Function Fields
8. Transcendental Extensions
9. Algebraically Closed Fields
EXERCISES

• 14. Galois Theory
1. The Main Theorem of Galois Theory
2. Cubic Equations
3. Symmetric Functions
4. Primitive Elements
5. Proof of the Main Theorem
6. Quartic Equations
7. Kummer Extensions
8. Cyclotomic Extensions
9. Quintic Equations
EXERCISES

• Appendix Background Material
1. Set Theory
2. Techniques of Proof
3. Topology
4. The Implicit Function Theorem
EXERCISES

• Notation
Index

• ##### Math Books ABSTRACT ALGEBRA

Algebra by Michael Artin
• Free
• English
• PDF
• Page 634

• Algebra (2nd Edition) by Michael Artin
• Free
• English
• PDF 111
• Page 559

• A First Course on Abstract Algebra by John B. Fraleigh
• Free
• English
• Page 523

• Abstract Algebra by Joseph A Gallian
• Free
• English
• PDF 48
• Page 664

• Notes on Algebra by Donu Arapura
• Free
• English
• PDF 89
• Page 77

• Abstract Algebra by Robert B Ash by Robert B. Ash
• Free
• English
• PDF (Chapter wise) 71
• Page 200

• Abstract Algebra Lecture Notes by Dr David R Wilkins
• Free
• English
• PDF (chapter wise) 64
• Page 150

• Fields and Galois Theory by J.S. Milne
• Free
• English
• PDF 57
• Page 138

• Abstract Algebra by Irena Swanson
• Free
• English
• PDF 50
• Page 102

• Intro Abstract Algebra by Paul Garrett
• Free
• English
• PDF 49
• Page 200

• A History of Abstract Algebra by Jeremy Gray
• Free
• English
• PDF 38
• Page 412
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##### Worksheets (Solved)

###### Integration     