| Date |
Lectures |
Chapter(s) in Text |
Brief Description |
Homework/
Practice Problems |
| June 26 |
Day |
1, 6, 2 |
History of algebra, functions, binary operations |
|
| June 29 |
|
2, 3 |
Binary operations, definition of groups |
|
| July 1 |
|
4, 5 |
Properties of groups, subgroups |
|
| July 3 |
|
6, 7, 8 |
Functions, permutation groups |
|
| July 6 |
|
8 |
Permutations |
|
| July 8 |
|
9,14 |
Homomorphisms, Isomorphisms |
|
| July 10 |
|
9 |
Summary of basic groups, Cayley's Theorem |
|
| July 13 |
|
10,11 |
Cyclic groups, order of an element, exponent laws |
|
| July 15 |
|
12 |
Equivalence relations |
|
| July 17 |
|
13 |
Equivalence relations, and cosets |
|
| July 20 |
|
13 |
Lagrange's Theorem, normal subgroups |
|
| July 22 |
|
15, 16 |
Quotient groups, fundamental homomorphism theorem |
|
| July 24 |
|
16 |
Decomposition theorem for finite abelian groups |
|
| July 27 |
|
17 |
Group review, definition of rings and fields |
|
| July 29 |
|
18 |
Homomorphisms, ideals, subrings |
|
| August 1 |
|
19 |
Quotient rings |
|
| August 3 |
|
20 |
Integral Domains |
|
| August 5 |
|
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| August 7 |
|
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| August 10 |
|
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| August 12 |
|
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| August 14 |
|
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| August 17 |
|
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| August 19 |
|
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| August 21 |
|
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| August 24 |
|
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| August 26 |
|
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