MATH 3010 Abstract Algebra

Fall 2024

Instructor

• jthartwig.net
• Office 470
• Email jth@iastate.edu
• Office hours: MWF 3:10pm–4:00pm

Time and Place

• Lectures: MWF 11:00pm–11:50pm in Carver 128

Texts and Resources

• Main text: Algebra — Notes from the Underground by Paolo Aluffi

Exams and Grading

• Homework: 40%

• Exam 1: 20% (September 27, 2024) Chapters 1–3 Study Guide for Exam 1

• Exam 2: 20% (November 8, 2024) Chapters 4, 5, and 7 Study Guide for Exam 2

• Final Exam: 20%

• In-Class Worksheets: 10%

• Worksheet 1

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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