Math 4281: News and Announcements, Spring 2011

o 05/11/11: Here is some Exam III statistics: mean = 18.77, median = 19, maximum = 35, out of 40 total. Thanks for a semester of hard work. Good luck to you in the future!

o 05/05/11: I have added solutions to 6.2.15 and 6.3.7 to the selected solutions to the last homework. Refresh your browser or erase cache to see the latest version.

o 05/05/11: I have posted selected solutions to the last homework.

o 05/04/11: I have added solutions to the last problems on the Sample Exam III.

o 05/03/11: I will be having extra office hours today, Tuesday, May 3, from 4 to 5 p.m.

o 05/01/11: I have revised the Practice Exam III and added a necklace problem to it. Make sure to reload the page, so as to have a version of the test with a necklace problem.

o 04/30/11: A Practice Exam III is posted. Sorry about a delay. Get it from here or refresh the class web page to see a link to it.

o 04/29/11: The third midterm is coming: Friday, May 6. Coverage: Sections 2.6-7, 3.1, 3.3 (3.6 in the on-line edition), 5.1, 5.2 (omitting 5.2.5), 6.1-3. How to get ready: the more problems you solve, the better you will be prepared. Solve the sample exam, which will be posted soon, and problems from the homeworks again (if you feel you do not remember how to do them), as well as similar problems from the text (for example, if problem 11 was on the homework, problems 10 or 12 will likely be similar). Also, look for similar exams, for similar Modern or Abstract Algebra classes, on the web. If you know you need only 3 minutes to get an idea on how to solve at least 50% of random exam problems you find for similar classes on the internet, only then you may be sure you will do well our test.

o 04/27/11: I have just posted solution to Exercise 6.1.16.

o 04/26/11: Ignore the first columns of tables in Section 5.2: they are confusing for us and not at all essential for figuring out the sizes of sets Fix(g).

o 04/25/11: I will be having extra office hours tomorrow, Tuesday, April 26, from 10:15 till 11:30 a.m.

o 04/25/11: I have revised the homework due this coming Wednesday: removed Exercises 5.2.4 and 5 and added 5.2.1, so that homework for Section 5.2 consists of Exercises 1 and 2. The thing is that I wanted us to have a different example on using Burnside's lemma, apart from the examples with necklaces, but the examples with cubes and dodecahedra need some mastery of symmetries of those polyhedra, which we have not studied.

o 04/20/11: Exercise 3.1.12 (on-line edition), which we discussed today in class, is indeed asking you to do an impossible thing. If you look at elements of order two in GL(2,C) and C*× SL(2,C), you will find out there are infinitely many of them in the first group and only three in the second. I have asked the grader to assign full credit for this problem to those who tried. I apologize about the confusion. I was raised to trust books, in general. I still find our textbook much better than any other Algebra text suitable for Math 4281. Errors like this are unavoidable in math textbooks, unfortunately.

o 04/19/11: Hint for Exercise 3.3.5 (Edition 2): You may either use the fundamental theorem of finite abelian groups, Theorem 3.3.13 (Edition 2) or Theorem 3.6.22 (Edition 2.5) and concentrate on a prime p shared by a and b. Figure out which cyclic subgroup of p power order must be in the decomposition on Zab into a direct product of cyclic groups of prime power order. Another way to do this problem is to look at the maximal order of an element in ZaxZb.

o 04/18/11: When I was telling you in class how to identify the groups Φ(pn) for primes p, I forgot to mention that the case p = 2 was exceptional and identification in this case was somewhat different, see Proposition 3.3.19(b) of the printed edition of the textbook. This is important to remember when doing homework problem 3.3.10.

o 04/18/11: I am going to post a copy of Section 3.3 from the printed edition on our class web page shortly.

o 04/11/11: Beware: the printed edition of the textbook contains an error in Example 2.7.20, which we discussed in class. To factor out a scalar from an invertible matrix X, so that the determinant of the remaining factor X' is 1, you need to factor out an nth root of (det X)^{-1}, as I pointed out in class. The on-line edition has that error corrected.

o 04/07/11: Here is some Exam II statistics: mean = 28.91, median = 29, maximum = 40. You have done a great job, again!

o 04/07/11: Here is some Exam II statistics: mean = 28.91, median = 29, maximum = 40. You have done a great job, again!

o 03/31/11: I have a cold and need to cancel my office hours for tomorrow, but I will be there to give the test. And it is not an April 1st joke!

o 03/31/11: I have sent a note to Professor Frederick Goodman, the author of our textbook, suggesting him to change Exercise Problem 2.2.15. And he did. He added a condition that the cyclic subgroups <a> and <b> intersect trivially (i.e., only over identity e). In this case, the answer is indeed o(ab) = lcm (o(a),o(b)). See the new wording in the online Edition 2.5.

o 03/31/11: I have added a solution to Problem 6 on the Practice Exam II. Refresh the page, if you do not see it.

o 03/25/11: A Practice Exam II is posted. Get it from here or refresh the class web page to see a link to it.

o 03/24/11: The second midterm is coming: Friday, April 1. Coverage: Sections 1.5, 1.10-11, and 2.1-5. How to get ready: the more problems you solve, the better you will be prepared. Solve the sample exam, which will be posted soon, and problems from the homeworks again (if you feel you do not remember how to do them), as well as similar problems from the text (for example, if problem 11 was on the homework, problems 10 or 12 will likely be similar). Also, look for similar exams, for similar Modern or Abstract Algebra classes, on the web.

o 03/24/11: I am moving the due date of Homework 8 to Wednesday, March 30, and removing one problem (2.4.10) from the homework, because of the slowdown caused by Problem 2.2.15 on Monday.

o 03/21/11: I have to reschedule my office hours just for Wednesday, March 23, to 12 to 1 p.m.

o 03/12/11: As we agreed during the last class meeting, Homework 7 will be due on Wednesday, March 23.

o 03/08/11: Homework for the coming 12 days, including the Spring Break is posted. If you do not see it, refresh your browser.

o 03/06/11: Hint to Exercise 1.10.5: You need to verify the axioms of a group for all the isometries with respect to composition. This means, you need to check that if you compose two isometries, you will get another isometry. You need to mention that the composition law is associative, find an isometry which will serve as the identity for the group, and show that every isometry has an inverse isometry.

o 03/04/11: Hint to Exercise 1.10.10: When showing that the set of fractional linear transformations is closed under composition, observe that composition of fractional linear transformations is given by matrix multiplication. Use this to find the condition for a fractional linear trasnformation to be invertible.

o 03/04/11: Beware: there is a difference in the printed and online editions for homework for Section 2.1. The homework was given first referring to the printed edition, now corrected to refer to both.

o 02/23/11: Here is some Exam I statistics: mean = 38.13, median = 39, maximum = 50. You have done a great job!

o 02/20/11: I am in Texas for a Math conference, and my tonight's flight back home to Minneapolis has gotten canceled because of the snow storm. In fact, all flights tonight to Minneapolis are canceled. For this reason, I have no choice but to cancel tomorrow's (Monday, February 21) Math 4281 class meeting. I apologize about any inconvenience that may cause.

o 02/16/11: I have added selected solutions to Practice Exam I on the web. Make sure to reload the page to see the version with solutions!

o 02/14/11: Reminder: I have to reschedule my office hours just for Wednesday, February 16, before the first exam, to 12 to 1 p.m.

o 02/14/11: In homework Exercise 1.4.2, you do not need to complute all the 36 products to verify that matrix multiplication corresponds to multiplication of symmetries. Just check that for RA, you get symmetry c, for R2A, you get symmetry b, and for AR, you get again symmetry b.

o 02/13/11: On Friday, February 25, all University of Minnesota campuses will partner to host the 2011 University of Minnesota Job and Internship Fair. I encourage those of you interested in job and internship opportunities to attend the event.

The Fair is open to all U of M undergraduates, graduate and professional students, and recent graduates. It's held from 10 a.m. to 4 p.m. at the Minneapolis Convention Center.

Please refer to www.umjobfair.org for all the information you need about registration, getting to the fair, and how to prepare. Registration is $10 for those who register online prior by February 22, or $25 at the door on the day of the event.

The Job and Internship Fair connects students with employers and organizations seeking to recruit them for diverse jobs and internships. In this economic environment, it is a particularly important opportunity for the students.

o 02/11/11: I have to reschedule my office hours just for Wednesday, February 16, before the first exam, to 12 to 1 p.m.

o 02/09/11: Since we are slow in starting sections on Symmetry, I have decided to put off the next homework due date till Wednesday, February 16.

o 02/09/11: A Practice Exam I is posted. Get it from here or refresh the class web page to see a link to it. I have also adjusted coverage for the first exam, see below.

o 02/08/11: The first midterm is coming: Friday, February 18. Coverage: Sections 1.1-4 and 1.6-9, skipping Examples 1.9.13-14. How to get ready: the more problems you solve, the better you will be prepared. Solve the sample exam and problems from the homeworks again (if you feel you do not remember how to do them), as well as similar problems from the text (for example, if problem 11 was on the homework, problems 10 or 12 will likely be similar). Also, look for similar exams, for similar Modern Algebra classes, on the web.

o 01/31/11: Since I will be out of town the rest of this week, the next homework will be due on Wednesday, February 9.

o 01/30/11: A little hint for 1.7.7: guess the answer to be yes, there can, and present a base n and three distinct congruence classes modulo n so that [a][b]=[a][c] = [0].

o 01/29/11: A little clarification for the homework (in particular, for Exercises 1.7.6 and 1.7.7): [2] = [8] are not distinct residue classes modulo 6, because they both consist of numbers 2, 8, 14,... and -4, -10, -16,...

o 01/29/11: I will be out of town February 2 through 4. I have asked Professor Webb to substitute for me in the Wednesday and Friday classes. There will be no office hours, while I will be out of town, but you are welcome to ask Professor Webb questions during and after class and send me e-mail, which I will be responding to while out of town.

o 01/26/11: I have changed my office hours again because of popular demand and moved my Wednesday hours to 2-3 p.m. My office hours are now MF 10-11 and W 2-3.

o 01/24/11: I have changed my office hours because of popular demand and moved my Wednesday hours to 1-2 p.m. My office hours are now MF 10-11 and W 1-2.

o 01/19/11: One of you pointed out that the wording of the make-up policy on the the syllabus was confusing. I have reworded it as follows:

MAKE-UP TESTS: There will be no make-up tests. If you have to miss an hour exam, your grade on it will be the prorated grade of the following exam. If you have to miss the last exam, the grade on it will be the minimum of your grades on the first and the second exam. If you miss two tests, one of them will be graded as zero. If you miss three, they will all be graded as zero. You have to tell me before the exam (e-mail is fine) that you want to exercise this option and skip the test.

o 01/19/11: I have changed the link to where you can purchase the textbook to the following one: DealOz.com, where the prices are cheaper.

o 01/19/11: I will be out of town February 2 through 4. I have asked Professor Webb to substitute for me in the Wednesday and Friday classes then.

o 01/19/11: I recommend the following way to study. Before each class study the corresponding part of the text. You can find out which part of the text at the Class Outlines page. After the class study your class notes. Next, reread the corresponding section of the text. Then do relevant homework problems. Then read the material that we will be discussing during the next class meeting.

o0 01/19/11: If you need to register for this class, please, send a message to Ms. Lawson at ugrad@math.umn.edu and ask for a permission number. Then go to OneStop and register.

o 01/19/11: Homework will be collected before each class, starting Monday, January 24, and a small selection of problems will be graded. ("Small," because the grader will allocate only 4 hours per week for our class.)


Last modified: Wed Jan 19 11:34:25 CDT 2011