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Date |
Homework & Suggested
Problems
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| 8/29 |
Ch 0: 7, 8, 10, 11,
13, 19, 20, 22, 41, 43, 45, 48, 52
I realized that to me, Number
Theory, Geometry, and the Theory of Algebraic Solutions were
only shadows cast in different directions by some central solid
essence. I tried to reconstruct that central object and
came up with Abstract Algebra.
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| 8/31 |
All good, but
here are the great ones: Ch 2: 7, 8, 9, 11, 17, 23, 29, 33, 35, 37 (11
& 35 require some Linear Algebra background)
I realized that to me, the
symmetries of the equilateral triangle, the hexaflexagon, and
the propeller were only shadows cast in different directions
by some central solid essence. I tried to reconstruct that
central object and came up with the concept of a group.
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| 9/5 |
Ch 1: All great
problems, but esp. 5, 6, 8, 17, 19, 22
Using 3 colors, how many non-isomorphic
Cayley tables can you color in?
Try to find ALL the subgroups of D_3
Read Ch. 3
I realized that to me, the
symmetries of the propeller, the equivalence classes mod 4, and
the color wheel group were only shadows cast in different
directions by some central solid essence. I tried to
reconstruct that central object and came up with the concept
of group isomorphism.
|
| 9/7 |
Start looking at
problems Ch 3: 4, 13, 14, 21, 22, 29, 32, 35, 36, 41, 42, 46,
50, 51, 53, 54
Read chapter 4
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| 9/12 |
Ch 4 problems
are all so great, I can't chose. Maybe read through them
all and pick the 20 hardest sounding problems
I realized that to me, all cyclic
groups of order n were only shadows cast in different
directions by some central solid essence. I tried to
reconstruct that central object and realized that all cyclic
subgroups of order n are isomorphic to Z_n. |
| 9/21 |
Ch 5: 9, 13,
14, 15, 19, 21, 23, 30, 31, 33, 35, 39, 41, 43, 45, 49, 50, 55
Read chapter 6
I realized that to me, all groups
were only shadows cast in different
directions by some central solid essence. I tried to
reconstruct that central object and realized that every group
is isomorphic to a group of permutations. |
| 9/24 |
Take-Home
Problem Packet, Due Friday October 5th
pdf file,
tex file |
| 9/26 |
Ch. 6: 2, 3,
7, 9, 10, 12, 17, 18, 21, 22, 24, 25-27, 30, 31, 33, 34, 37, 38,
43
Read chapter 7
"Cayley's Theorem tells us that
abstract groups are not different from permutation groups.
Rather, it is the viewpoint that is different. It is this
difference of viewpoint that has stimulated the tremendous
progress in group theory and many other branches of mathematics
in the twentieth century." -Gallian, pg. 127
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| 9/28 |
Ch. 7: 1, 4,
7, 8, 9, 10, 11, 15, 16, 18, 20, 23, 27, 29, 20, 31, 32, 33, 36,
38, 40, 41, 42, 43, 44, 45
Read chapter 8
|
| 10/3 |
Ch. 8: 1, 2,
11, 14, 15, 17, 20, 31, 33, 34, 35, 37, 43, 44, 47, 49, 53, 54,
55, 57, 59-63
Read chapter 9
I realized that to me, the finite
Abelian groups were only shadows cast in different
directions by some central solid essence. I tried to
reconstruct that central object and came up with direct
products of cyclic groups of prime-power order.
|
| 10/5 |
Ch. 9: 1-5,
7-11, 15, 17, 19, 27, 31, 33, 38, 39, 41-43, 45, 48, 49-51,
55-58, 61-63, 66, 68, 69, 71
Outline (due Monday 10/8) .pdf,
.tex |
| 10/10 |
Read Chapter
10
The universe is an enormous direct
product of representations of symmetry groups. - Steven Weinberg |
| 10/12 |
Ch. 10/ 7, 9,
11, 15, 17, 19, 39, 43, 48 (LA of DEQ), 49, 54, 57
I realized that to me, the normal
subgroups of a group G were only shadows cast in different
directions by some central solid essence. I tried to
reconstruct that central object and came up with kernels of
group homomorphisms. |
| 10/17 |
Read Ch. 11
& Start Studying for the Midterm |
| 10/22 |
Ch. 11/ 3, 5,
7, 9, 11, 12-15, 17, 19, 21, 25, 29, 35, 36
Write 2 problems for midterm with
justification, Due: Wednesday, Oct. 24
Rewrites of Take Home Packet 1 Due:
Friday, Nov. 2nd
I realized that to me, the finite
Abelian groups were only shadows cast in different
directions by some central solid essence. I tried to
reconstruct that central object and came up with direct
products of cyclic groups of prime-power order. |
| 10/26 |
Relax and
Read Ch. 12 |
| 10/29 |
Ch.
12/ 2-4, 6, 7, 11, 17, 18, 19, 26, 27, 36, 37, 38, 41, 43, 50,
52
Read Ch. 13
I realized that to me, the
integers, the integers mod n, n-by-n matrices with integer
entries, continuous real-valued functions passing through the
point (1,0), etc. were only shadows cast in different
directions by some central solid essence. I tried to
reconstruct that central object and came up with the concept
of a ring. |
| 10/31 |
Take
Home Mid-Term
Due Monday, Nov. 5th |
| 10/31 |
Ch.
13/ 7, 8, 10, 20, 24, 26, 27, 28, 29, 31, 34, 35, 41, 43, 46,
49, 50, 55, 60
I realized that to me, the
integers mod p, the reals, the rationals, the complex numbers,
etc. were only shadows cast in different
directions by some central solid essence. I tried to
reconstruct that central object and came up with the concept
of an field. |
| 11/2 |
Read
Ch. 14, Study for Group Exam |
| 11/7 |
Ch.
14/ 3, 6, 7, 9-13, 24, 26, 30, 33, 35, 37, 41, 47, 53, 55
Read Ch. 15 for 11/12 |
| 11/9 |
Take
Home Packet 2, Due Wednesday 11/21 |
| 11/12 |
Ch.
15/ 4, 10, 18, 26, 31, 33, 35, 38-40, 41(a), 43, 44, 48,
52, 53, 58, 60, 61
Read Ch. 16 for 11/19 |
| 11/19 |
Ch.
16/ 4, 9, 10, 12, 13, 15, 21, 22, 27, 29, 31, 32, 36-40, 42-44,
48
Read Ch. 17 for 11/26 |
| 11/26 |
Visualizations
of D6 Due |
| 12/3 |
Take-home
Final Exam: .pdf, .tex
Due: Noon, Saturday 12/15 |
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