Lec 3 | MIT 6.042J Mathematics for Computer Science, Fall 2010

Lec 3 | MIT 6.042J Mathematics for Computer Science, Fall 2010

35 thoughts on “Lec 3 | MIT 6.042J Mathematics for Computer Science, Fall 2010”

  1. Inversion problem doubt – is any order of the letters having odd parity of number of inversions possible if the starting parity was odd?

  2. how the relative position of g doesn't change?? in initial position it was adjacent to d but in the later its position with respect to d is different.

  3. First of all, I can't thank you enough for all these great videos and free courses! Thank you!
    Is there any chance I can find these "hand outs" he was talking about?
    If I am not mistaken they are not on the website.

  4. Benedict Voltaire

    I've always had an issue with the name "Strong" induction. In maths, the more assumptions we make, the less powerful the theorem. So if we are assuming more for our induction hypothesis, I think the method should rather be called weak induction. Just a thought.

  5. Ibrahim El Mountasser

    40:00 from lemma 3, can we say if we have two inversions we can solve the puzzle? go from 2 to -> 0

  6. A B C A B C
    D E F D F
    H G H E G
    in the 1 st case above only 1 pair was inverted(G H) but after the column move 3 pairs are inverted(H G, E F & H E). How does the c part of lemma 3 follow????

  7. Have you ever noticed a spinning object such as a side view of a wagon wheel or an airplane prop
    as it turns different speeds? I would like to see it explained by
    Mathematics why it slows then
    turns the opposite direction.

  8. i may not be able to afford to get the type of education these these students and teachers are lucky enough to be admitted into thus qualify for better paying job offerings that come with attending a prestigious college BUT i can use this information to start my own business, the path less traveled, and create my own success, circumventing the "gate-keeper" access academia has on information and qualifications. I am sincerely thankful for the lectures but no thanks for your perpetuation of the strangle hold of qualifications and therefore reduced employment opportunity.

  9. guys can some one please help me out here?
    In reference to the problem set 2 i have a solution to the beaver flu problem that i am unable to get any check on if i'm in the right direction— I have set my invariant to be S= max{ min(r*), min(c*) }. Here min(r*) is the minimum no.of rows required to contain/represent the intial no.of infected students and min (c*) is the minimum number of columns required to represent the no.of initial infected students.

  10. With reference to cases of lemma 3, can somebody please explain to me how the number of inversions decreased by two in case B and didn't change in case C? I'd be beholden to you.

  11. Everyone on here is gushing. If he assigned you a homework set, the tone would completely change. Lol.
    "He never showed us this in class!" Hahaha

  12. It may have been nicer to restate lemma 4 as: for any move, the parity of the state stays the same (so if it is odd before it is odd after, and if it is even before it is even after), cause now the theorem simply says that the first configuration (with H G) which has parity 1 and the second which has parity 0 cannot ever be changed into each other though any set of moved. Lemma 4 now finishes the proof because the first has odd and the second even stated.

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