Files
Download Full Text (807 KB)
Download Preface (134 KB)
Download 34 RSA Encryption (269 KB)
Download 35 Check Digits (223 KB)
Download 36 Games: NIM and the 15 Puzzle (232 KB)
Download 37 Groups of Order 8 and 12: Semidirect Products of Groups (285 KB)
Download Appendix A: Functions (292 KB)
Download Appendix B: Mathematical Induction and the Well-Ordering Principle (291 KB)
Download Appendix C: Methods of Proof (255 KB)
Download Appendix D: Proof that R[x] is a Ring (211 KB)
Download Appendix E: The Cubic Formula (275 KB)
Download Appendix F: The Fundamental Theorem of Algebra (247 KB)
Download Appendix G: Complex Roots of Unity (233 KB)
Download Index (79 KB)
Description
This text is a supplement to Abstract Algebra: An Inquiry-Based Approach, Second Edition. It includes applications of algebra to RSA encryption, check digits, the games of NIM and the 15 Puzzle, and the determination of groups of small order. In addition, reference material that could be useful for some students appears in the appendices, such as background material on functions, methods of proof (including the equivalencies of the Well-Ordering Principle and different versions of mathematical induction), and complex roots of unity. The appendices also contain a complete proof that polynomial rings are rings, a proof of the Fundamental Theorem of Algebra, and a derivation of the formula for solving any cubic equation.
Publication Date
6-2023
Publisher
Grand Valley State University Libraries
City
Allendale, MI
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Keywords
abstract algebra, modern algebra, RSA encryption, check digits, mathematical games, mathematical induction, methods of proof
Disciplines
Mathematics
