Department of Mathematics Part I: PRELIMINARIES 1. SET THEORY 2. RELATIONS 3. MAPPINGS 4. MATRICES 5. BINARY OPERATIONS 6. INTEGERS Part II: GROUP THEORY 7. GROUPS 8. SUBGROUPS 9. PERMUTATIONS 10. NORMAL SUBGROUPS 11. ISOMORPHISM OF GROUPS 12. CYCLIC GROUPS 13. HOMOMORPHISM: 1 Part III: RING THEORY 14. RINGS 15. INTEGRAL DOMAINS 16. IDEALS: 1 17. HOMOMORPHISM: 2 18. FIELDS 19. POLYNOMIALS 20. IDEALS: 2 21. FINITE FIELDS 22. UNIQUE FACTORIZATION DOMAIN AND EUCLIDEAN RING Appendices A: De Moivre’s Theorem B: Three Famous Problems Supplementary Problems • References • Index