Difference between revisions of "MAT4233"
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Groups: Definition and elementary properties. | Groups: Definition and elementary properties. | ||
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Groups of Permutations. Permutations of finite sets. | Groups of Permutations. Permutations of finite sets. | ||
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Group isomorphisms and orders of elements. | Group isomorphisms and orders of elements. | ||
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Homomorphisms and quotient groups. | Homomorphisms and quotient groups. | ||
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Quotient rings and integral domains. | Quotient rings and integral domains. | ||
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The integers. Factorization into primes. | The integers. Factorization into primes. | ||
Revision as of 10:45, 25 March 2023
Modern Abstract Algebra
MAT 4233. Modern Abstract Algebra. (3-0) 3 Credit Hours.
Prerequisites: MAT3233. Basic properties and examples of semigroups, monoids, and groups, detailed study of permutation, dihedral, and congruence groups, cyclic groups, normal subgroups, quotient groups, homomorphism, isomorphism theorems, direct products of groups, rings and fields and their basic properties, ideals, polynomial rings. Generally offered: Spring. Differential Tuition: $150.
Text
Charles C. Pinter. A Book of Abstract Algebra. (Reprint of 2nd.\ ed.\ originally published in 1990) Dover Publications, NY (2010). ISBN-10: 0-486-47417-8.
Topics
1| Date | Sections | Topics | Student Learning Outcomes | ||
|---|---|---|---|---|---|
|
1 & 2 |
Binary operations on sets. |
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|
2 |
3 & 4 |
Groups: Definition and elementary properties. |
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|
3 |
5 |
Subgroups. |
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|
4 |
7 & 8 |
Groups of Permutations. Permutations of finite sets. |
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|
5 |
9 & 10 |
Group isomorphisms and orders of elements. |
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|
6 |
--- |
Review. First midterm exam. |
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|
7 |
11 |
Cyclic groups. |
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|
8 |
13 |
Counting cosets. |
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|
9 |
14 & 15 |
Homomorphisms and quotient groups. |
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|
10 |
--- |
Review. Second midterm exam. |
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|
11 |
16 |
The fundamental theorem of homomorphism. |
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|
12 |
17 |
Rings and ideals. |
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|
13 |
18 |
Ring homomorphisms. |
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|
14 |
19 & 20 |
Quotient rings and integral domains. |
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|
15 |
21 & 22 |
The integers. Factorization into primes. |
|
Wrap-up and review. Student Study Day. |
