MATH 3010 Abstract Algebra

Fall 2024

Instructor

Time and Place

Texts and Resources

Exams and Grading

Homework

Homework sets will be posted here. They are due most Wednesdays.

  1. (Due Sep 4) Homework 1
  2. (Due Sep 11) 1.4, 1.5, 1.8, 1.9, 1.10, 1.11, 1.12, 1.15, 2.1, 2.6
  3. (Due Sep 18) 1.25, 1.26, 2.2, 2.5, 2.8, 2.9, 2.12, 2.13, 2.15, 2.16
  4. (Due Sep 25) 2.19, 2.22, 3.1, 3.2, 3.3, 3.5, 3.10, 3.11, 3.12, 3.17
  5. (Due Oct 9) 3.15, 3.19, 3.22, 4.1, 4.2, 4.6, 4.7, 4.8, 4.10, 4.17
  6. (Due FRIDAY Oct 18) 4.18, 4.19, 5.2, 5.3, 5.4, 5.5, 5.6, 5.8, 5.9 (three parts, each graded as a separate problem), 5.15
  7. (Due Oct 23) 5.19, 5.20, 5.24, 5.25, 5.27, 5.32, 5.36 (each problem worth 7 pts)
  8. (Due Oct 30) 6.10, 7.2, 7.3, 7.5, 7.8, 7.9, 7.14, 7.18, 7.19, 7.33 (\(p\le 20\) is sufficient)
  9. (Need not be handed in) 4.4, 4.9, 4.17, 5.2, 5.6, 5.28, 7.21, 7.25, 7.29, 7.30

Lecture Summary

We will cover Appendix A.5–A.8, and Chapters 1–5, 7, 11, and parts of Chapter 12. A short summary of each lecture will be posted here.

  1. Set operations (A.5), functions (A.6, A.7)
  2. Compositions, identity (A.6, A.7); relations, equivalence classes (A.8)
  3. §1.1 Well-Ordering Principle and Induction
  4. (Labor Day)
  5. §1.2 Division with Remainder
  6. §1.3 Greatest Common Divisors
  7. §1.4 The Fundamental Theorem of Arithmetic
  8. §2.1 Equivalence Relations and Quotients, §2.2 Congruence mod \(n\)
  9. §2.3 Algebra in \(\mathbb{Z}/n\mathbb{Z}\), §2.4 Properties of + and \(\cdot\) on \(\mathbb{Z}/n\mathbb{Z}\)
  10. §2.4 (continued) Zero-divisors and multiplicative inverses in \(\mathbb{Z}/n\mathbb{Z}\). Fermat’s Little Theorem
  11. §2.4 (continued) RSA encryption algorithm, §3.1 Definition and examples of rings
  12. §3.1 Definition and Examples of Rings
  13. §3.2 Basic Properties
  14. §3.3 Special Types of Rings
  15. Review
  16. Exam #1 Friday September 27, during lecture
  17. §4.1 Cartesian Products of Rings
  18. §4.2 Subrings
  19. §4.3 Ring Homomorphisms
  20. §4.4 Isomorphisms of Rings
  21. §5.2 Kernel and Ideals
  22. Worksheet 1
  23. §5.3 Quotient Rings
  24. §5.4-§5.5 The First Isomorphism Theorem
  25. §7.2 Polynomial rings over fields
  26. §7.2 (continued)
  27. §7.2 (continued) \(F[x]\) is a PID, §7.3 Irreducible polynomials
  28. §7.3-§7.4

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