Free Abelian Groups and Homomorphisms

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Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Explores active learning through homomorphisms, exact sequences, and comparisons of presentations in Abelian groups.

Covers exact sequences of homomorphisms in abelian groups, including injective sequences and split sequences.

Covers vector spaces, topology, and proof methods like the pigeonhole principle in R^n.

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.

Explores the isomorphism between Hom(A, B) and Hom(A, B) for any abelian group B.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.