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All the Mathematics You Missed by Lori Pedersen, Thomas A. Garrity

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Chapter 11

Algebra

Basic Objects:

Groups and rings

Basic Maps:

Group and ring homomorphisms

While current abstract algebra does indeed deserve the adjective abstract, it has both concrete historical roots and modern day applications. Central to undergraduate abstract algebra is the notion of a group, which is the algebraic interpretation of the geometric idea of symmetry. We can see something of the richness of groups in that there are three distinct areas that gave birth to the correct notion of an abstract group: attempts to find (more accurately, ...

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