[yazzku]

Propositional and first-order logic along with Algebra and basic proofs by induction, reduction to absurdity, etc, should beat the logical, pedantic motherfucker out from your inner self. At least that is what we did at uni -- along with physics, calculus, discrete mathematics, and theory of computation -- but I'd argue the first list should be a sufficient starting point.

Not really sure about "better programmer", but I think it makes you at least more logical and helps develop a keener attention to detail. "Better programmer" entails an array of many other qualities outside of the scope of "better thinker".