Survey Of Modern Algebra, A

Preface to the Fourth Edition 1. The Integers 2. Rational Numbers and Fields 3. Polynomials 4. Real Numbers 5. Complex Numbers 6. Groups 7. Vectors and Vector Spaces 8. The Algebra of Matrices 9. Linear Groups 10. Determinants and Canonical Forms 11. Boolean Algebras and Lattices 12. Transfinite Arithmetic 13. Rings and Ideals 14. Algebraic Number Fields 15. Galois Theory Bibliography List of Special Symbols Index

This classic text introduces abstract algebra using familiar and concrete examples that illustrates each concept as it is presented. It covers such topics as the role of careful proof in algebra; linear algebra as grounded in geometry; groups as expressions of symmetry; subgroups and subsystems leading to lattice theory; and much more. To develop the student’s power to think for himself in terms of these new concepts, the authors have included a wide variety of exercises on each topic. Some of these exercises are computational, some explore further examples, and others give additional theoretical development. This fundamental text, now in its fifth edition, continues to show that the vital aspects of abstract algebra as they relate to the body of modern mathematics can be presented to undergraduates in an effective and innovative manner.