← Theoretical / proof-based

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In this program

Binary operations and equivalence relations
Modular arithmetic
Groups: definitions, examples (Z, Z_n, dihedral, symmetric groups)
Subgroups and cyclic groups
Cosets, Lagrange's theorem, and index
Normal subgroups and quotient groups
Group homomorphisms
The first isomorphism theorem
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Groups

Binary operations and equivalence relations

Abstract algebra · Theoretical / proof-based

Topic

Binary operations and equivalence relations

Practice by unit: Groups

Undergraduate Abstract Algebra — scope drawn from open algebra texts (e.g. Judson Abstract Algebra: Theory and Applications, AIM-approved) and typical US undergraduate algebra syllabi.

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