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FLMPotD
Let K/k be the splitting field of an irreducible quintic over k. Show that K cannot contain a root of any irreducible cubic over k. -
FLMPotD
Compute \sum_{k=0}^n (-1)^k \binom{n}{k}/(k+1). -
FLMPotD
Find a commutative ring R, a multiplicative subset S \subset R, and finitely generated R-modules M and N such that the natural map S^{-1}Hom(M,N) \to Hom(S^{-1}M,S^{-1}N) is not an isomorphism. -
FLMPotD
Show that a finite p-group G can be recovered from the mod p cochains on BG, as an E_\infty-algebra ( Read more... ) -
FLMPotD
Show that if the homology of a spectrum is free, then its Atiyah-Hirzebruch spectral sequence for any (co)homology theory with torsion-free coefficients degenerates at E_2. -
On cleverness in LARPs
While I've never written a LARP, one of the subtler points about writing them that I've noticed from playing is that it is difficult to make plots that require people to be clever in character. The basic difficulty is that if I'm presented with a challenge to which I (the player) see an obvious solution (or even just first step towards a solution ( Read more... ) -
Bah
I don't understand why people ever say things in math without accompanying them with an explanation of what's actually going on in them. It's just so...why ( Read more... ) -
FLMPotD
Prove Picard's big theorem (in a neighborhood of an essential singularity, a holomorphic function's image misses at most one point of C) using only the fact that the holomorphic universal cover of C-{0,1} is the unit disk, elementary complex analysis, and covering space theory ( Read more... ) -
FLMPotD
Show that the ring Q[sin,cos] (say as a subring of the ring of functions on R) is spanned by the functions sin nx and cos nx as n varies.
(This one's from somthng2remembr. There's an unenlightening trivial solution using obscure trig identities, and then a more interesting conceptual solution.) -
FLMPotD
Show that x^4-16x^2+4 is reducible mod p for every prime p.
(Stolen from a comment by secret_panda on a post on somthng2remembr's facebook. Yay stalking!)
(PS: Actually, my argument should work for anything of the form x^4+bx^2+c^2 for b and c integers and p odd.)