Introduction to Abstract Algebra

Instructor: Prof. Ilya Kapovich

Spring 2008 ; MATH 417 Section C13

MWF, 10am; Altgeld Hall 145

http://www.math.uiuc.edu/~kapovich/417-08/417-08.html

The final exam has been graded and the results have been posted via Score Reports. The Final Exam Solutions are available. I have also assigned the final course grades and you should be able to see them in the Score Reports as well. I added the extra credit problem totals to your midterm results so that the extra credit scores are no longer shown as separate items. The course components were weighted as follows: each of the midterms 100 points, h/wk 100 points, final exam 200 points and quizzes 75 points, for the maximum point total of 100+100+100+200+75=575 points. You should be able to see your weighted course point total in the Score Reports next to your course letter grade. One low quiz score and two low h/wk scores were dropped when computing the point totals.

The course letter-grade cut-off levels were:

Grade	A+	A	A-	B+	B	B-	C+	C	C-	D+	D	D-	F
Range	548-575	521-547	495-520	468-494	441-467	414-440	382-413	351-381	320-350	300-319	280-299	260-279	0-259

alert I will be have office hours on Monday, May 12, 10am-11:45am. You can come and take a look at your final exams then if you are interested.

alert LAS and Engineering students enrolled in Math 417 are permitted to drop this course without academic penalty and without petition through Friday, April 11, 2008. LAS students who wish to drop this course by the April 11 deadline should see the receptionist in the LAS office and ask to be directed to a COAR user, who will process the late drop without a grade of "W". Engineering students are directed to the Engineering College Office, 206 Engineering Hall, for assistance with the late drop.

alert The first midterm exam has been graded and the results are posted in Score Reports. Solutions are available below.
The high score was 100, the low score was 32, the median score was 71, the mean score was 66 with the standard deviation 25%.
Formal letter grades are not assigned for midterms but you can approximately interpret your scores as follows:
A: 90-100; B: 75-89; C: 60-74; D: 45-59; F: 0-44.

alert The second modterm has been graded and the results have been posted via Score Reports. Solutions are available below. The high score was 96 and the low score was 43; the median score was 69.5 and the average score was 72.7, with the standard deviation 15.2%. Formal letter grades are not assigned for midterms but you can approximately interpret your scores as follows:

A:88-100; B:73-87; C: 57-72; D: 43-56; F:0-42.

Anonymous on-line feedback form is available

SCORE REPORTS -Math Department gradebook program where you can look up your quiz, h/work and exam grades. (You will be prompted for your NetId and password).

My office hours are Tuesday 10am-11:30am, Thursday, 10am-11:30am (and at other times by appointment). You DO NOT need to tell me in advance if you want to see me during the office hours. If you want to come at a different time, you need to schedule an appointment. My office is located in Altgeld Hall, room 365.

The FINAL EXAM for this course is scheduled for 8:00-11:00 am, Tuesday, May 6 in our usual classroom. Please make sure now that this time is acceptable for you (if not, you urgently need to register for another section!!!) Keep in mind that I will not entertain any requests for "conflict" final exams from people who do not have what the university officially recognizes as a "conflict". See the official university rules regarding exam conflicts here.

We will be using a Math Department "gradebook" program called the "Score Reports". It will allow you to check on your quiz, h/works and exam scores. I'll post a link here as soon as the Math Office sets up the program for us.

Text:      Papantonopoulou, Algebra, Pure and Applied

Telephone: 265-0633
e-mail: kapovich@math.uiuc.edu. (Preferred method of reaching me!)
Office location: Altgeld Hall, room 365
Office hours:   Tue 10am-11:30am, Th 10am-11:30am, or by appointment
Grader:    Chanyoung Jun, cjun2@uiuc.edu

Homework assignments:

Due Wednesday, January 23: Exercise 0.3 (pp. 22-24), no. 2, 5, 6, 16, 17, 23, 24, 27
Due Wednesday, January 30: Exercise 1.1 (pp. 48-50), no. 5, 7, 10, 12, 14, 17, 18, 21
Due Wednesday, February 6: Ex. 1.2 no. 5, 15, 21, 24, 33; Ex. 1.3 no. 2, 9, 17, 23
Due Wednesday, February 13: Ex. 1.4 no. 10, 12, 14, 16, 18, 21, 32, 35
Due Wednesday, February 20: Ex. 2.1 no 5, 16, 19, 27, 32; Ex. 2.2 no. 7, 10, 16, 29
Due Friday, February 29: Ex 2.2 no 43, 44; Ex. 2.3. no 5, 12, 15, 18; Ex 2.4 no. 6, 11, 23,
Due Wednesday, March 5: Ex. 3.1 no 3, 5, 14, 18; Ex. 3.2 no. 4, 5, 11, 17.
Due Wednesday, March 12: Ex. 4.1 no. 1, 5, 8, 15; Ex. 4.2 no. 3, 8, 10, 11
Due Wednesday, March 26: Ex. 4.6 no. 3, 4, 7, 13, 14, 15, 16
Due Wednesday, April 2: Ex. 6.1 no. 3, 9, 15, 19, 20; Ex. 6.2 no. 6, 7, 12, 13
Due Friday, April 11: Ch 6.3 no 2, 8, 19, 20, 24, 29; Ch 7.1 no. 5, 14, 18, 23
Due Wednesday, April 16: Ch. 7.2 no. 5, 10, 16, 19, 21, 25, 27, 28, 31, 34
Due Wednesday, April 23: Ch. 7.3 no. 7, 10; Ch. 8.1 no 9, 21, 22; Ch. 8.2 no. 1, 4, 7, 10, 12
Due Wednesday, April 30: Ch. 8.4 no 3, 6, 8; Ch 8.6 no 3, 5, 9, 12, 21, 25

Optional Extra Credit Problem Assignments:

Set 1, due Friday, March 7.
Set 2, due Friday, March 28
Set 3, due Friday, April 11
Set 4, due Friday, April 18
Set 5, Due Friday, April 25

Approximate Syllabus:

The integers: Division algorithm. Greatest common divisor. Fundamental theorem of arithmetic. Con-
gruence arithmetic.
Permutations: Cycle decomposition. Order of a permutation. Even and odd permutations.
Group Theory: Definition and examples. Subgroups, cosets and Lagrange's theorem. Normal subgroups
and quotient groups. Homomorphisms. The Isomorphism Theorems.
Group Actions: Cayley's theorem. Burnside's theorem. Conjugacy classes and centralizers. Applications
of group actions, eg. to Sylow's theorem or Polya counting.
Ring Theory: Definition and examples. Polynomial rings. Subrings, ideals and quotient rings. Homo-
morphisms of rings. The Isomorphism Theorems for rings. Integral domains and fields.
Division algorithm for polynomial rings over a field. Roots of polynomials and the Remain-
der Theorem. The Fundamental Theorem of Algebra (without proof). Maximal ideals in
polynomial rings over fields, with application to the construction of ¯elds.

Available course material:

How this course is graded.

There will be two one-hour midterm exams during the semester. Each of them counts a maximum of 100 points.
The 1-st midterm is currently scheduled for Monday, February 25. The 2-nd Midterm is currently scheduled for Monday, April 7.
The final exam counts a maximum of 200 points. The final exam will take place on Tuesday, May 6, 8am-11am.
The homework will be collected on Wednesdays. Homework will be checked for completeness and several selected problems from each homework will be graded for correctness. Homework contributes a maximum of 100 points towards you final score. For the h/work assigned during a particular week the due date will be Wednesday of the following week. Late homework is generally not accepted!! At the end of the term two low h/work grades will be dropped.
There will be a quiz almost every Friday (except for the 1-st week and the weeks of the midterms). Quizzes contribute a maximum of 75 points towards the final score. At the end of the course your lowest quiz grade is dropped. Make-up quizzes are administered provided you give me a compelling and convincing (to my satisfaction) explanation as to why you had to miss a regular quiz. Make-up quiz problems will be harder than the regular ones.
A modest number of "extra credit" problems may be assigned.
Thus your final course score will be a maximum of 100+100+100+75+200=575 points. The final curve determining letter grade cut-off levels for the course will only be determined at the end of the term, but you should use the scale of the first midterm as a guide.
Although I expect you to regularly attend classes, non-attendance will not be penalized provided you do all the required course-work on time. HOWEVER, I take a very dim view of people coming in late or exiting the classroom early!!
For each of the midterm exams and for the final exam you are allowed to use: one two-sided 8''x11'' "cheat-sheet" of notes and formulas and a calculator. The final exam is an open book exam and you can use both the textbook and the lecture notes, as well as a calculator during the final.
No textbooks or lecture notes are allowed on the midterm exams.
The final exam will be cumulative and will include all the material covered during the course.
The final curve will be determined only at the end of the course.

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