Jeremy Weissmann :
the calm hedonist

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In August 2009, my colleague Apurva Mehta mentioned that he was looking for ways to incorporate mathematical exercise into his routine. I suggested that he take very simple problems and do them very well. With simple problems, one can focus more easily on perfecting one's thought process.

About a month later, I decided it might be fun do these exercises myself; after all, I hadn't written on calculational mathematics in a long time. I decided I would use the simple predicate calculus exercises from WF122 (link) to begin with. I would take an exercise from that document, and approach it completely top-down, designing solutions with nearly the same strictness I would be held to in a session of the Tuesday Afternoon Club (link 0, link 1).

Below you can find the fruits of my labors. I hope that they will inspire my readers to embark on similar "exercise regimens". This can be done, no matter what field you are in: mathematics, sciences, humanities, arts. The idea is to take something simple and try to do it as close to perfectly as you can.


Number Date (Y.M.D) Brief Description
EX0 2009.09.09 /\ almost over ==
EX1 2009.09.10 [ X /\ (X == Y) == X /\ Y ]
EX2 2009.09.11 [ (X == X /\ Y) \/ (Y == X /\ Y) ]
EX3 2009.09.12 Modus Ponens
EX4 2009.09.14 Shunting
EX5 2009.10.03 (Punctual) transitivity of implication
EX5a 2009.10.04 Distributivity of implication
EX6 2009.10.14 [ (X => Y) \/ (Y => Z) ]
EX7 2009.10.30 Mutual implication
EX8 2009.11.05 'true' is the weakest predicate
EX9 2009.11.14 Strengthening to 'true' as a proof shape
EX10 2009.11.14 'Equivales' implies 'implies'
EX11 2010.07.10 After a hiatus