Introduction to group theory. Isomorphism theorems. Permutation groups and Cayley's theorem. Conjugacy classes. Lagrange's theorem and the Sylow theorems. principle ideal domains. Polynomial ring.
Algebra I (MATH 511)
Programs\Type | Required | Core Elective | Area Elective |
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CONTENT
OBJECTIVE
Studying groups and rings
LEARNING OUTCOME
Define and use Subgroups, Ideals, Homomorphisms and other basic concepts about Groups and Rings,
Analyze and produce proofs of statements involving Groups and Rings,
Use some fundamental examples such as the Symmetric Group and its Subgroups, Cyclic Groups, Matrix Groups, and Polynomial Rings,
Distinguish basic Algebraic structures from each other up to Isomorphism,
Use the three Isomorphism theorems for Groups and Rings,
Use Direct and Semi-direct Product Constructions,
Use Group Actions to study structures of Groups and to do effective counting in Groups,
Apply Sylow Theorem and the Structure Theorem on Finitely Generated Abelian Groups,
State basic Ring types such as Local Rings, Principal Ideal Domains, Unique Factorization Domains.
Update Date:
ASSESSMENT METHODS and CRITERIA
Percentage (%) | |
Final | 40 |
Midterm | 60 |
RECOMENDED or REQUIRED READINGS
Textbook |
dummit and foote: algebra |