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21-373 Algebraic Structures

Department:Mathematical Sciences
Prerequisites:(21-241 or 21-341) and 21-127
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Groups: Homomorphisms. Subgroups, cosets, Lagrange's theorem. Conjugation. Normal subgroups, quotient groups, first isomorphism theorem. Group actions, Cauchy's Theorem. Dihedral and alternating groups. The second and third isomorphism theorems. Rings: Subrings, ideals, quotient rings, first isomorphism theorem. Polynomial rings. Prime and maximal ideals, prime and irreducible elements. PIDs and UFDs. Noetherian domains. Gauss' lemma. Eisenstein criterion. Fields: Field of fractions of an integral domain. Finite fields. Applications to coding theory, cryptography, number theory. 3 hours lecture.

  Popularity index
Rank for this semester:#220
Rank in this department:#23

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  Spring 2005 times

Sec Time Day Instructor Location  
A 10:30 - 11:20 am M Owen DH 2105 Add course to my schedule
W Owen DH 2105
F Owen DH 2105

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