Topics in Algebraic Structures/Graduate Algebra
- Homework Assignment #1:
- Exercises: 1.1-1.22.
- Homework Assignment #2:
- Exercises: 2.1-2.25.
- Homework Assignment #3:
- Exercises: 3.5, 3.9-3.17.
- Homework Assignment #4:
- Exercises: 5.1, 5.3-5.17.
- Homework Assignment #5:
- 6.1-6.16.
Turn-in HW#1: 1.14, 1.22, 2.2, 2.13, 2.19, 3.15, 5.5, 5.9, 5.12, 6.8, 6.9, 6.16.
The HW is due on Wednesday, February 7th.
- Homework Assignment #6:
- Chapter V: 1.1-1.9.
- Homework Assignment #7:
- Ch. V: 1.11-1.16.
- Homework Assignment #8:
- Ch. V: 2.1-2.9.
- Homework Assignment #9:
- Ch. V: 2.9-2.10 (these characterize Neotherian UFDs), 2.12, 2.14, 2.15-2.18 (these are on Euclidean valuations), 2.22.
- Homework Assignment #10:
- Ch. V: 4.2-4.4, 4.18-4.23. Study (read and understand) Sect. V.4. Do as many as you can from the suggested Exercises.
After the Break, we are discussing Sect. V.5 and V.6. After that - Ch. VI.
- Homework Assignment #11:
- Ch. V: 6.1-6.8.
- Homework Assignment #12:
- Ch. VI: 1.1-1.16, 1.19, 1.20.
- Homework Assignment #13:
- Ch. VI: The exercises after sect 2, with 4 exceptions, contain facts that are generally known from the standard linear algebra course.
Do as many of these as you like. The exceptions are 2.13, 2.14 (Algebraic Geometry and Topology related), and 2.18, 2.19.
Try to do the former two, and do do the latter two.
- Homework Assignment #14:
- Ch. VI: 4.1-4.5.
- Homework Assignment #15:
- Ch. VI: 5.1, 5.2, 5.10, 5.13, 5.14, 5.15, 5.17.
- Homework Assignment #:
- Final Exam: 5.9, 5.13, 5.17, 6.4 (det(R) is det(\alpha)), 6.6, 7.6, 7.7, 7.10, 7.11, 7.12.
Due date: April 22nd.
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Florida International University
Mathematics Department, FIU