Self resources for Math 113.

Professor Mariusz Wodzicki

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

Alternative Texts

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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.
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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
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