Instructor | Keith Conrad | ||||
kconrad at math dot uconn dot edu. (When you send an email message, please identify yourself at the end.) | |||||
Office hours | MSB  318; Mon. 1:00-2:00, Wed. 3:30-4:30. | ||||
Course info |
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Text | Abstract Algebra, 3-rd ed. (Wiley), by Dummit and Foote. There is a list of errata for the book at Foote's website. | ||||
Other references | There are notes on Galois theory at the website of Milne. |
Course handouts
Dimension
Zorn's Lemma
(revised)
Definitions related to rings
The Minimal Polynomial and Some Applications
Dual Modules
A Non-Free Stably Free Module
Universal Identities
Splitting of Short Exact Sequences for
Modules
Splitting of Short Exact Sequences for
Groups (Optional)
Tensor Products
Tensor Products, II
Exterior Powers
Roots of Irreducible Polynomials
Separability without Tensor Products
Separability with Tensor Products
Perfect Fields
Constructing Algebraic Closures
Galois Correspondence
Applications of Galois Theory
Brief course description: This is the second semester of a year-long course which will prepare graduate students for future work where algebra is needed. In the second semester we will cover topics from linear and multilinear algebra, field extensions, and Galois theory. This corresponds to Parts III and IV in the course text. If time permits, we may discuss commutative algebra (in Part V) or representation theory (in Part VI).
Prerequisites: Math 315 and a basic undergraduate course in linear algebra.
Course grade: This will be based on the following weighting:
Homework: Homework assignments will be posted on the bottom of this web. Due dates will be marked on each assignment. All homeworks and exams must be prepared using LaTeX. No late homeworks will be accepted.Exams: There will be 1 midterm and a final.
- Computational homework problems should present a complete calculation, starting with the data of the problem. Do not just give the answer.
- There are no makeup exams.
- If you need exam accommodations based on a documented disability, you need to speak with both the Center for Student Disabilities and the course instructor within the first two weeks of the semester.
Due Week of | Homework Assignment |
1. Jan. 21 |
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2. Jan. 28
Avg: 76.1/80 |
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3. Feb. 4 |
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4. Feb. 11 |
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5. Feb. 18
Avg: 88.7/100 |
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6. Feb. 25 |
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7. Mar. 3
Avg: 75.4/100 |
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8. Mar. 10 | Spring Break |
9. Mar. 17
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10. Mar. 24 |
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11. Mar. 31
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12. Apr. 7 |
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13. Apr. 14
Avg: 81.1/100 |
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14. Apr. 21
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15. Apr. 28
Avg: 87.2/100 |
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16. May 5 |
Final Exam Week
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