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Algebra: Abstract and Concrete

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Linear algebra over Z 3. Symmetries of Polyhedra 4. Rotations of Regular Polyhedra 4. Rotations of the Dodecahedron and Icosahedron 4. Linear Isometries 4. Actions of Groups 5. Group Actions on Sets 5. Group Actions—Counting Orbits 5.

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Symmetries of Groups 5. Group Actions and Group Structure 5. Application: Transitive Subgroups of S5 5. Additional Exercises for Chapter 5 Chapter 6. Rings 6. A Recollection of Rings 6. Homomorphisms and Ideals 6. Quotient Rings 6. Integral Domains 6. Unique Factorization Domains 6. Noetherian Rings 6. Irreducibility Criteria Chapter 7. Field Extensions — First Look 7. A Brief History 7. Solving the Cubic Equation 7. Adjoining Algebraic Elements to a Field 7. Splitting Field of a Cubic Polynomial 7. Modules 8.

The idea of a module 8. Homomorphisms and quotient modules 8. Multilinear maps and determinants 8. Rational canonical form 8. Jordan Canonical Form Chapter 9. Field Extensions — Second Look 9.

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Finite and Algebraic Extensions 9. Solvability Composition Series and Solvable Groups Commutators and Solvability Simplicity of the Alternating Groups Cyclotomic Polynomials The Equation x n b D 0 Solvability by Radicals Radical Extensions Chapter Isometry Groups More on Isometries of Euclidean Space Finite Rotation Groups Crystals Appendix A. Almost Enough about Logic A.

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  • Statements A. Logical Connectives A. Deductions Appendix B. Almost Enough about Sets B. Families of Sets; Unions and Intersections B. Induction C. Proof by Induction C. Multiple Induction Appendix D. Review of Linear Algebra E. Linear algebra in K n E. Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

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