Area II
Groups, polynomials, linear maps, rings, and the homology that measures exactness.
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Pathway VII
Magmas, groups, homomorphisms — a set with an operation, and the maps that preserve it.
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Pathway IX
Finite combinations of powers, then the infinite ones that still multiply.
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Pathway VIII
Arrows, machines that move the plane, and the area they span.
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Pathway X
Rings, ideals, quotients — then Spec, and a cubic that is a group.
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Pathway XI
Groups acting linearly. Exact sequences that measure kernels and images.
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