Math 546, Spring 2023, Professor Kustin
Announcements
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- In class on Wednesday, April 19, we covered pages 38-41 of the class notes.
- The final exam is Friday, April 28 4:00-6:30. Please take the final exam very seriously. The final covers the whole course from day 1 until chapter 8, rings and fields.
- Up to date as of April 19, 2023, 6:01 PM.
Syllabi
Other Resources
Old Announcements
- In class on Monday, January 9, we covered (more or less) as far as Example 2, which ends on the top of page 6 of the Class Notes.
- In class on Wednesday, January 11, we finished example 2 on page 6 of the class notes covered Examples 3, 4, 5, 6, 7, and 8; and started Example 9.
- Quiz 1 is Wednesday, January 18. The quiz will consist of one of the homework problems 1--6.
- In class on Wednesday, January 18, we showed that each rigid motion of the plane is invertible on page 6 of the class notes.
- By the end of class on Monday, January 23, we covered everything in the class notes until the end of Example 9 on page 8.
- Quiz 2 is Wednesday, January 25. The quiz will consist of one of the homework problems 7, 8, 9, 10, 12, 13.
- At the end of class on Wednesday, January 25, we started to think about the group U_n of n-th roots unity. This is example 11 at the bottom of page 9 in the class notes.
- Exam 1 is Wednesday, February 1. The exam covers everything we do between the first class and the exam.
Here are notes about the exam. Here are the instructions for the exam.
- On Monday, February 6, we covered pages 9--12 in the class notes.
- On Wednesday, February 8, we covered pages 12--15 in the class notes.
- On Monday, February 13, we covered pages 15 and 16 in the class notes.
- Quiz 3 on February 15 will be one of the homework problems 11, 14, 15, 16, 17, or 18.
- Solutions, Exam 1, Spring 2023
- On Wednesday, February 15, we covered pages 16--18 in the class notes.
- Quiz 4 on February 22 will be one of the homework problems
28, 29, 30, 35, 36, 37 from the List of Homework problems or Question 3.11 or 3.12 from the Class Notes.
- On Monday, February 20, we covered pages 18--19 in the class notes.
- On Wednesday, February 22, we proved that every infinite cyclic group is isomorphic to the group on integers under addition.
- On Monday, February 27, we covered as far as the end of Example 5.8 on page 22 of the Class Notes.
- Exam 2 on March 1 covers from Day 1 until the statement and proof of Cayley's Theorem. Notes about Exam 2.
- In class on Monday, March 13, we covered pages 22-25 of the class notes.
- In class on Wednesday, March 15, we covered pages 25-27 of the class notes.
- Quiz 5 is Wednesday, March 22. The quiz will be one of the problems 19, 20, 27, 33, 38, or 39.
- In class on Monday, March 20, we covered pages 28-29 of the class notes. (These pages were recently re-written. Be sure to look at the new pages.)
- In class on Wednesday, March 22, we covered page 30 of the class notes.
- In class on Monday, March 27, we covered pages 31 and 32 of the class notes.
- Quiz 6 is Wednesday March 29 on HW 40, 41, 42, 49, 50, 54, 55.
- Solutions to Exam 2
- In class on Monday, March 29, we covered page 33 of the class notes.
- In class on Monday, April 3, we covered Observation 6.5 and pages 33-34 of the class notes.
- Exam 3 is Wednesday, April 5. The exam will cover everything from Day 1 until the end of section 6. Notes about Exam 3.
- In class on Monday, April 10, we covered pages 35 and 36 of the class notes.
- In class on Wednesday, April 12, we covered page 38 of the class notes.
- Quiz 7 is Monday April 17. The quiz will be one of the questions: Prove that the smallest subgroup of S_4 which contains (1,2) and (1,2,3,4) is all of S_4 (This is essentially 1.c.iii.), 84, 85, 86, or 87 from the homework list or 6.13, 6.18, or 7.10 from the class notes.
- Solutions to Exam 3.
- In class on Monday, April 17, I answered questions.