My used to be a 5th grade teacher. She divided her class according to ability – slower kids worked at the level they could handle, the average kids worked on 5th grade stuff (and helped the slower kids (i.e., tutor them) and the really bright kids had special projects. One of those special projects was to work all the way thru a 5th grade teacher’s edition of a new math book. They were to list any wrong examples, explain why they were wrong and give my mom a report as to whether the book was appropriate for the 5th grade or not and why. She would also let them work on stuff at higher grade levels. I wanted her as my teacher so bad! (My sister and I went to the same school she taught at)
Definition 1.1. Let H1,H2 be Hilbert spaces and T:dom(T)−→H2 be a densely defined linear operator, i.e. dom(T) is a dense linear subspace of H1. Let dom(T∗) be the space of all y∈H2 such that x7→(Tx,y)2 defines a continuous linear functional on dom(T). Since dom(T) is dense in H1 there exists a uniquely determined element T∗y∈H1 such that (Tx,y)2= (x,T∗y)1 (Rieszrepresentation theorem). The map y7→T∗y is linear and T∗:dom(T∗)−→H1 is the adjoint operator to T. And so on and so on.
Templo S.U.D. over 5 years ago
a head start too fast to get to the honor roll
Jogger2 over 5 years ago
Fifty five or more chapters in a middle school math book?
Auntie Socialist over 5 years ago
He’s going to be hella disappointed when he gets to the end of the book in October
rmercer Premium Member over 5 years ago
next chapter: Unbounded Operators on Hilbert Spaces. Hot damn!
BiggerNate91 over 5 years ago
I swear, I wish I could do this.
the lost wizard over 5 years ago
Figures.
contralto2b over 5 years ago
My used to be a 5th grade teacher. She divided her class according to ability – slower kids worked at the level they could handle, the average kids worked on 5th grade stuff (and helped the slower kids (i.e., tutor them) and the really bright kids had special projects. One of those special projects was to work all the way thru a 5th grade teacher’s edition of a new math book. They were to list any wrong examples, explain why they were wrong and give my mom a report as to whether the book was appropriate for the 5th grade or not and why. She would also let them work on stuff at higher grade levels. I wanted her as my teacher so bad! (My sister and I went to the same school she taught at)
HappyDog/ᵀʳʸ ᴮᵒᶻᵒ ⁴ ᵗʰᵉ ᶠᵘⁿ ᵒᶠ ᶦᵗ Premium Member over 5 years ago
Unbounded operators on Hilbert spaces
Definition 1.1. Let H1,H2 be Hilbert spaces and T:dom(T)−→H2 be a densely defined linear operator, i.e. dom(T) is a dense linear subspace of H1. Let dom(T∗) be the space of all y∈H2 such that x7→(Tx,y)2 defines a continuous linear functional on dom(T). Since dom(T) is dense in H1 there exists a uniquely determined element T∗y∈H1 such that (Tx,y)2= (x,T∗y)1 (Rieszrepresentation theorem). The map y7→T∗y is linear and T∗:dom(T∗)−→H1 is the adjoint operator to T. And so on and so on.
And the rest is obvious. ☺
Sailor46 USN 65-95 over 5 years ago
I had a friend like that, the good thing it made my homework easier to do.
Dianne50 over 5 years ago
I did that in 2nd grade, worked through the entire math book in two weeks. Of course, 2nd grade math is easy. You don’t even need your toes.
Lightpainter over 5 years ago
I am so opposite Jason on this..I would have looked for any excuse to not open that math book!