Tentative Syllabus We will primarily study groups, roughly covering chapters 0 until 10 or 11, and perhaps a chapter or two of part 3 (special topics). The following is a tentative syllabus, which probably will be modified a few times during the course.

Homework assignments

Homeworks need to be turned in on or before the stated date, usually a Friday, by 2pm. There is a drop box on the 6th floor of APM. No homework needs to be turned in in weeks when a midterm is scheduled. However, some of the listed problems may also be part of the material being asked for the midterm. It is very important that you do the homework problems as most of the exam problems will be variations of homework problems.

for Sept 30: : Chapter 0: #8, 10, 12, Use Euclidean algorithm to calculate gcd(34, 126) and express it as a linear combination of 34 and 126; 20, 21, 28, 36, 38, 54,

for Oct 7:: Chapter 1: #4, 6, 10. Chapter 2: #6, 11, 12, 16, 20, 22, 24, 28, 35 Note: You may assume without proof in #11 that multiplication of matrices is associative.

Additional Problem: We have seen that the rational numbers Q with multiplication can only be made into a group if we remove 0. Question: Could we make Q into a group with the usual multiplication if we add to it an inverse of 0 called \infty? What would be the multiplication with \infty? Either show that all group axioms would be satisfied, or find a contradiction.

for October 14: Chapter 3: #2, 8, 10, 12, 18, 25, 28, 42, 52, 59a,b, Chapter 4: #1, 4, 8, 12, 14, 16, 18

for October 21: Chapter 4: #22, 40, 45, 54 (hint: consider the order of an element in the intersection), 56 (hint: prove first that it is enough to show that U(2^n) contains two distinct elements of order 2, using theorems in the book) Chapter 5: #3d, 4, 18, 28, 36, 6 (we will define A_n on Wednesday, or look it up on page 105/106), 8, 12, 24,

for November 4: Chapter 6: #4, 10, 18, 20, 22, 24, 25 Extra problems for practice (do not hand in): Chapter 6: #1, 3, 5, 7, 19 (or wait with looking at the problems until preparing for next midterm). It is recommended that you start looking at the problems of the next assignment, which will be longer, and you have to turn the problems in sooner due to a holiday).

for November 11 (Friday is a holiday): Chapter 7: #2, 6, 8, 10, 16, 20, 22, 24, 26, Chapter 9: #8, 10, 12, 16, 18

for November 23 (Wednesday, because of Thanksgiving): Chapter 9: #37, 38, 70, Chapter 10: #2, 10, 14, 20, 24,

for December 2: Chapter 10: #32, 54, Chapter 8: #2, 4, 6, 12, 26, 28, 50, 56, 64

Remark about homomorphisms

Final: Essentially the same rules apply for the final as they do for the midterms: You are allowed one hand-written cheat sheet (both sides), but no other notes, books or calculators. The material will go over what we covered in class and homework from Chapter 0 until including Chapter 10. The problems will be similar to assigned problems or problems from practice exams. Below is a practice exam

Practice final

Midterm I: The first midterm will take place Wednesday, October 26, in class. You are allowed one hand-written cheat sheet (both sides), but no calculators or books. The material will go until this homework assignment; however, you will only need to know very basic things from Chapter 5, such as how to do calculations with permutations. Below you find a practice midterm from a previous class. Cover the solutions first. If you can not do the problem, you should have spent thinking about it for at least ten to 15 minutes before looking at the solutions.

Practice test for Midterm I

You may ask questions on Monday in class, or in my and the TA's office hours, or in the TA section. Don't be shy about it.

Midterm II The material will go until the last homework assignment, but without the material of Chapter 9. So you only need to know material until Chapter 7. The same rules will apply as for Midterm I. The problems will be similar to homework problems or problems in the practice exam below. Please start with preparing now for your exam, so that you can ask questions in class, section and/or office hours next week.

Practice test for Midterm II