[Verse 1]
When structures tangle, maps unclear
First isomorphism cuts through fear
Quotient by kernel reveals the truth
Image emerges, clean and proof
Like peeling layers from ancient stone
What's left behind stands on its own
[Chorus]
Ten strategies carved in algebra's heart
Decompose, classify, set them apart
Universal counting guides the way
Correspondence shows what patterns say
Exact sequences tell their tale
Symmetry's where answers never fail
[Verse 2]
Break into pieces, irreducible parts
Abelian groups and representation arts
Invariants whisper the secret code
Dynkin diagrams light the road
Characters dancing in finite space
Each classification finds its place
[Chorus]
Ten strategies carved in algebra's heart
Decompose, classify, set them apart
Universal counting guides the way
Correspondence shows what patterns say
Exact sequences tell their tale
Symmetry's where answers never fail
[Bridge]
Localize the problem, make it small
Functors translate, connecting all
From Galois dreams to Yoneda's lens
Where one proof ends, another begins
[Verse 3]
Count the elements, feel the constraint
Lagrange and Sylow, elegant and faint
Homology flows through exact arrays
Module theory in its tangled maze
When structure fights against the change
Symmetry keeps truth within its range
[Chorus]
Ten strategies carved in algebra's heart
Decompose, classify, set them apart
Universal counting guides the way
Correspondence shows what patterns say
Exact sequences tell their tale
Symmetry's where answers never fail
[Outro]
From kernel's core to functor's flight
Ten paths converge in abstract sight
PATH 2 complete, the tools are yours
Unlock the mathematical doors