Instructor
Luis von Ahn
Teaching Assistants
Drew Besse (F)
Adam Blank (D)
Dmitriy Chernyak (B)
Jimmy Koppel (G)
Margaret Meyerhofer (G)
Tim Self (E)
Abhinav Sharma (C)
Tim Wilson (A)
Office Hours
TA Office Hours are held at the Wean 8th Floor Couches
Sunday
Dmitriy and Jimmy: 6-8pm
Monday
Adam and Drew: 6:30-8:30pm
Tuesday
Tim and Tim: 4:30-6:30pm
Wednesday -- Verification Office Hours
Adam: 1:00-3:00pm
Thursday
Luis: 4:30-5:30pm
Margaret and Abhinav: 6:30-8:30pm
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Welcome to 15-251!
If you are verifying in the last hour, you should NOT be creating new mistakes.
REMEMBER: You will lose fewer points if you don't create a new mistake than if you do.
Quick Check on Current Verifications
General Advice
- Any mistakes you do enter should be neither too specific nor too vague. You should, in particular, not rely on terms defined in the submission -- students and TAs who have not read that particular submission will need to understand what it means.
Guest Week: Danny Sleator (Part A) [mmeyerho]
- Most people did pretty well on this. The most common mistakes were
in the definiton of big O (or Theta, or Omega). $f(n) \in \mathcal{O}(g(n)) \Rightarrow \exists c > 0, n_0 \in \mathbb{N}$ s.t. $f(n) \leq g(n)$ $\forall n > n_0$. People commonly forgot to specify $c > 0$ and often pulled
$n_0$ out of thin air.
- It is correct to say "for sufficiently large n" rather than specify some $n_0$.
- Many people did not use the fact that $f$, $g$, and $c$ are positive when squaring inequalities or multiplying through by something. $x\geq y \Rightarrow x^2 \geq y^2$ if and only if $x\geq y\geq 0$ and $x\geq y \Rightarrow cx\geq cy$ if and only if $c \geq 0$
If You Think the Seconds are Long For You... [dbesse]
- The question asks to list the sets, not say how many there are.
Saying "An infinite number" should be a warning sign, as there could
be an uncountable or countable number of sets. Students who say this
will potentially avoid showing the proper sets are the *only* ones
that work
- As always, watch out for edge cases. These don't need really
need to be (as the trivially hold), they just need to be listed.
The problem never states there has to be one happy and one sad
number. Especially the "everyone's sad" case is often ignored.
- Beyond that, the mistakes really are just the way people argue
things. Namely:
- Listing the solutions that work and showing they work is one
thing, the important part is showing any set that works has to
have one of the provided forms. Most of you were good about this,
but its still something to watch out for.
- A bunch of students will show happy times happy is happy, but
then not actually use that to claim while all multiples of the
smallest happy number are happy. Watch out for minor mistakes like
this.
- You can't have two inductive proofs that recursively use each
other's results. Often the arguement will be fine if the induction
is done in in one proof, but trying to do it in two makes it invalid.
There are a lot of subtle ways to wind up with circular reasoning
on this problem so take the time to fully understand each proof.
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