دانلود کتاب Applied Abstract Algebra

فهرست مطالب :

Title
Contents
Preface
1. Sets and binary relations
1.1. Sets
1.2. Binary relations
1.3. Functions
1.4. Order relations
1.5. Boolean matrices and graphs
1.6. Arrow\'s impossibility theorem
2. Semigroups and groups
2.1. Semigroups
2.2. Generators and relations
2.3. Green\'s relations
2.4. Blockmodels
2.5. Finite state machines
2.6. Recognition of machine languages by finite state machines
2.7. Groups
2.8. Subgroups
2.9. Homomorphisms
2.10. Permutation groups
2.11. Systems of distinct representatives and flows on networks
2.12. Orbits and conjugations
2.13. Symmetries
2.14. Polya enumeration
2.15. Kinship systems
2.16. Lattices of subgroups
3. Vector spaces
3.1. Vector spaces
3.2. Basis and dimension
3.3. Matrices
3.4. Linear transformations
3.5. Determinants and characteristic polynomials
3.6. Eigenvalues, eigenvectors, similarity
3.7. Symmetric and unitary matrices
4. Rings
4.1. The integers and divisibility
4.2. Euclidean domains and factorization
4.3. Ideals and congruences
4.4. Structure of Zn
4.5. Simple and semisimple rings
5. Group representations
5.1. The group ring and representations
5.2. Modules and representations
5.3. Irreducible representations
5.4. Group characters
5.5. Tensor products
6. Field theory
6.1. Finite dimensional extensions
6.2. Applications of extensions of the rationals
6.3. Finite fields
6.4. Coding theory
6.5. Cyclic codes
6.6. Latin squares
6.7. Projective planes and block designs
Open problems
List of special symbols
References
Index