the calm hedonist

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 |