Introduction to Abstract Algebra with Notes to the Future Teacher
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
• To the Teacher sections:
– Draw connections from the number theory or abstract algebra under consideration to secondary mathematics
– Help students make appropriate connections between the advanced mathematics they are learning and the secondary mathematics they may be teaching,
• In the Classroom sections addressing classroom concerns in each chapter – Optional for the non-teacher.
• From the Past sections in each chapter – Provide historical context; students experience historical thinking and technique.
• Worksheets that outlines the framework of a topic in most chapters:
– Asks students to provide the details and exposition.
– Worksheets are suitable for group work and for development as student presentations in a capstone experience.
• Examples in the text drawn from linear algebra – Can be omitted for students without that background.
Table of Contents
1. Topics in Number Theory
2. Modular Arithmetic and Systems of Numbers
4. A First Look at Group Theory
5. New Structures from Old
6. Looking Forward and Back