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MATH 500 C1 - Abstract Algebra I

Campus: Urbana-Champaign


Isomorphism theorems for groups. Group actions. Composition series. Jordan-Holder theorem. Solvable and nilpotent groups. Field extensions. Algebraic and transcendental extensions. Algebraic closures. Fundamental theorem of Galois theory, and applications. Modules over commutative rings. Structure of finitely generated modules over a principal ideal domain. Applications to finite Abelian groups and matrix canonical forms. Course Information: Prerequisite: MATH 417 and MATH 418.

Special Instructions:

Students from the following programs must contact the Director of Graduate Studies in Mathematics rdeville@illinois.edu to request permission to register for the course: Restrictions will be removed May 7th. MS:Economics:Policy Econ -UIUC or MS: Financial Engineering. Undergraduates seeking approval to enroll should go to 313 Altgeld Hall for information. Restricted to Graduate - Urbana-Champaign. Not intended for MS:Economics:Policy Econ -UIUC, MS:Economics:Policy Econ -UIUC, MS: Financial Engineering, MENG:Mechanical Enginerng-UIUC, MENG:Elec & Computer Eng-UIUC, or MENG:Engineering:Comp Eng-UIUC

Academic Program Restrictions:

PHD:Mathematics -UIUC

Option 1

Number of Required Visit(s): 0

Course Level: Graduate

Credit: 4

Term(s): Fall


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