| Modern Algebra II - MA542 - Spring 2020 |
| Course Home Page |
Course: MA 542, Modern Algebra II
Instructor: Jared Weinstein
Lectures: MWF 1:25 pm - 2:15 pm in FLR 123
Discussion Sections: M 12:20 pm - 1:10 pm in FLR 123
Office Hours: F 10:00 am - 11:00 am in MCS 238
This course is the second half of the abstract algebra sequence. MA 541 dealt with groups, whereas MA 542 deals with rings. Rings are algebraic structures which have two operations: addition and multiplication. Examples include the integers, the rational numbers, the real numbers, the complex numbers, and polynomial rings. The theory of rings (and especially fields) is used to answer the question of how to solve polynomial equations. This will lead us to the final topic, Galois theory, which establishes a relationship between solutions of a polynomial equation and properties of a group associated to that equation.
Now that BU is conducting lectures online, I'll be posting lecture notes here.
March 16,18,20: Splitting Fields and separable extensions.
March 23, 25: The main theorem of Galois theory.
March 27, 31, April 1: Illustrations of Galois theory.
April 3, 6, 8: Some algebraic number theory.
April 10, 13: Solvability by radicals.
April 15, 17, 22, 24: Some more algebraic number theory.
April 27, 29: A crash course in algebraic geometry.
April 27 was not recorded in error, sorry.
John B. Fraleigh, A First Course in Abstract Algebra, 7th ed., Addison-Wesley.
Resources relevant to this course can be found here.
In order to gain mastery of the concepts it is crucial to do many exercises. I will be assigning problem sets every week which will usually be due on Wednesdays. You are allowed and encouraged to work together on homework assignments, but you must hand in solutions which are written in your own words. Select problems from each problem set will be graded and returned to you the following week.
The midterm and final exams will be take-home. You are not allowed to work together on the exams. The first midterm will be due on Wednesday, March 25, and the final will be due Wednesday, May 6.
| HW | Assignment | Due |
|---|---|---|
| #1 |
§18: 1, 5, 7-13, 14, 15, 20, 27, 37, 46, 55. §19: 1,2, 14, 29. §20: 1, 6, 27. |
Jan. 29 |
| #2 |
§21: 1, 2. §22: 2, 3, 6, 11, 12, 13, 22, 25. §23: 5,7, 9, 34, 36. |
Feb. 5 |
| #3 |
§24: 4, 6, 9, 10, 12. §26: 1, 3, 9, 12, 13, 14, 20, 24, 30. | Feb. 12 |
| #4 |
§26: 34, 35, 36. §27: 5, 15, 16, 24, 28, 37. §29: 1, 2, 14, 16, 17, 25. | Feb. 19 |
| #5 | §29: 29, 30, 31, 32, 34. §30: 4, 6, 21, 23. | Feb. 26 |
| #6 | §31: 7, 10, 13, 24, 33, 35, 37. §32: 3, 4, 8. | Mar. 4 |
| #7 | §33: 8, 9, 10, 11, 12, 13, 14. | Mar. 18 |
| No HW | Midterm due | March 27 |
| #8 |
§50: 1, 2, 5, 7, 8, 9, 18, 24. §51: 1,3,11. | Apr. 3 |
| #9 |
§51: 16,17. §53: 1-11. | Apr. 10 |
| #10 | §53: 16, 17, 19, 22, 24. | Apr. 17 |
| #11 | §54: 4, 5, 7, 8, 11, 12. | May 8 |
| #12 | §55: 2, 6, 10, 11. §56: 1, 2, 3, 4, 8. | May 8 |
The grading scheme is: Homeworks 70%, Midterm 10%, Final 20%. Because doing homework assignments regularly is so important for this class, I have given them a high weight in the grading scheme. It may be the case that an emergency prevents you from handing in an assignment on time. That is why I will drop the lowest score from your homework average. Late homework will not be accepted.
At this stage I cannot be very specific about how many points you must get to achieve each letter grade. An A grade will only be given to those students who have a very deep understanding of the material, who not only know the definitions and theorems but can easily apply them to various situations. To achieve this understanding, I recommend the following: Attend every lecture, read every page of the text, attempt every assignment, come to office hours, and discuss the material with each other.
| MA542 Home Page | Jared Weinstein | Department of Mathematics | Boston University |