Self resources for Math 113.

Professor Mariusz Wodzicki

LEC 001MWF 3:00P-3:59P | 289 Cory

Alternative Texts

Brief "History of Algebra."

The homework problems assigned, and the Midterms, are a good indicator of what is going to be on the Final Exam.

I will be expecting you to be able to draw the diagram of subgroups for some simple enough groups like Dn, for n=3,4,5,6 and Sn or An for n=3 and 4. You should be able to determine which subgroups are normal, and which are conjugate to each other.

In particular, I may ask you to find Sylow p-subgroups for such groups, to say how many are they, and what familiar groups are they isomorphic to. You may be also asked to find the normalizer of a given subgroup of such a group.

You should be able to determine the number of conjugacy classes of permutations of given order in Sn. For example: find the number of conjugacy classes of permutations of order 6 in S10.

Past homework:


Mathematics 113
homework assignments

due May 4
Find the centralizer CG(σ) in group S9 of the permutation σ in the following two cases:
a)  σ = (3 9 4 2)
b)  σ = (2 7) (3 1 8)
c)  σ = (1 5)(3 8)
d)  σ = (1 2)(3 4)(5 6)
Section 36:  17  18  22
Read short Section 20 and do the following exercises: 2  8  12  14  27
due April 27
Read Section 18 and do the following exercises:  2  4  12  20  34  40  41  44  46
due April 20
Section 36:  2  4  6  11  12  13  14  15
due April 13
Section 15:  26  36  37  40
Section 16:  2  9bc  10ab  11  12

due April 6 (more than usual, but many are very short)
Section 13:  8  10  16  26  28  36  38  42  44
Section 14:  4  8  10  14  27
Section 15:  4  8  10  12  14  16

due March 23
The exercises accompanying Section 11 are an excellent learning material. Do as many as you can.
Section 11:  2  4  6  8  10  12  14  16  20  22  24  26  28

due March 16
Section 9:  18  29  30
Section 10:  2  4  6  12  16  28  30  31  32  33

due March 9
Section 8:  45  49  51(this is the opposite group structure we have been talking about in the class)  53
Section 9:  2  8  10  12   14  16  27a

due March 2
Section 8:  18  22  30  32  36  40  42   46  48

due February 23
Section 6:  34 46  48  55
Section 7:  2  4  6
Section 8:  2  4  6  8  10  12

due February 16
Section 6:  12  14  16  18  20
22  24  26  28  36  40  44  50

due February 9
Section 5:  12  14  16  18  20
22  24  26  28  30  32  34  36  38

due February 2
Section 2: 26 Section 3: 24  26  27  33  34
Section 4: 8  14  19ab  20  35

due January 26
Study Sections 0-1 and do the following exercises:
Section 0: 12 14 16cd 18 19 28 32 34 36
Section 1: 22 30 32 36