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) ]|
|EX5||2009.10.03||(Punctual) transitivity of implication|
|EX5a||2009.10.04||Distributivity of implication|
|EX6||2009.10.14||[ (X => Y) \/ (Y => Z) ]|
|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|