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Full Description
For courses in Abstract Algebra.
Designed for future mathematics teachers as well as mathematics students who are not planning careers in secondary education, this text offers a traditional course in abstract algebra along with optional notes that connect its mathematical content to school mathematics. Elementary number theory and rings of polynomials are treated before group theory. Prerequisites include some experience with proof. (A brief appendix reviews certain basics of logic, proof, set theory, and functions.) Students should also have access to a Computer Algebra System (CAS), or a calculator with CAS capabilities
Contents
1. Topics in Number Theory
2. Modular Arithmetic and Systems of Numbers
3. Polynomials
4. A First Look at Group Theory
5. New Structures from Old
6. Looking Forward and Back