MATH 403 (Abstract Algebra)
| DESCRIPTION |
This course discusses the basic elementary facts about the
integers,
groups, rings, integral domains, and fields. It is recommended strongly
for all students planning to go to graduate school in mathemetics.
Credit
will only be given for one of Math 402 and 403. |
| PREREQUISITES |
MATH 240 and 241 |
| TOPICS |
Groups
Definition and examples
Subgroups
Normal subgroups and quotient groups
Homomorphisms
Isomorphism theorems
Cyclic groups
Permutation groups, Cayley's Theorem
Rings
Definition and examples
Polynomial rings
Ideals and quotient rings
Integral domains
Euclidean domains, unique factorization
Prime ideals, maximal ideals
Fields
Quotient fields
Extensions
Algebraic extensions
Impossibility of trisection of angle,
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| TEXT |
Text(s)
typically used in this course. |
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