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% (date TBD)
• Exam 2: 20% (date TBD)
• Final Exam: 20%

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

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 \(\mathbb{Z}/n\mathbb{Z}\)

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