MAT 370 – Algebraic Structures I

MAT 370 – Algebraic Structures I
Catalog description: (A) Abstract algebra with an emphasis on group theory. Prerequisite: a grade of Cor better in MAT 224 and MAT 272. Fulfills: LASR. (3 cr. hr.)
Goals / Objectives
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To develop abstract reasoning (e.g., variables representing matrices, permutations, etc., as well as
numbers)
To improve proof-writing skills
To gain an understanding of groups, knowledge of rings and fields
To gain an understanding of structure preserving maps (homomorphism/isomorphism)
To be proficient in the use of integers (such as Euclidean algorithm, GCDs/LCMs) and modular
arithmetic
Required Topics
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Groups: definition, basic properties
Subgroups
Cyclic groups
Permutation groups, dihedral groups
Homomorphisms and isomorphisms
Cosets and Lagrange’s Theorem
Direct products
Fundamental Theorem of Finite Abelian Groups
Factor groups
Rings and ideals: definition, basic properties