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Nov
7
comment Proving a function is one-to-one
Coming from someone who does exactly that themselves sometimes this might seem like amusing advice but so there.
Nov
7
comment Induction on a Sequence
You have $|x_{n+1}| < k |x_n|$ for all $x_n$. You have to use this information. So what happens if you replace $n$ with $1$?
Nov
7
comment Induction on a Sequence
Your case $n=1$ is wrong: if $n = 1$ you have $x_{2}$ on the left.
Nov
7
comment Is it possible to find the digit sum of $n!$ ($n \in \mathbb{N} \text{ and } n \le100$) without actually computing the factorial?
Related: stackoverflow.com/questions/1469529/…
Nov
2
comment “Best practice” innovative teaching in mathematics
@percusse: A great teacher just doesn't work with 300 people half of which talking about how hot the guy in the second row on the left is. I think it's an imposition that I'm forced to listen to all of this while actually wanting to do maths!
Nov
2
comment “Best practice” innovative teaching in mathematics
@AdamSmith: I couldn't disagree more. Why should someone unmotivated study at all? University is not primary school where you motivate your kids to play ball and draw pictures. Besides the major reason why these people shouldn't be around is because they disturb others.
Nov
2
comment “Best practice” innovative teaching in mathematics
@BillCook: It seems to me that lecturers want to do lectures because they see it as kind of exercise for them. Also, a lecture is passive and therefore boring.
Nov
2
comment “Best practice” innovative teaching in mathematics
@JimConant: I think unmotivated students should be ignored. An unmotivatd person is the sort of person that sits behind me in the lecture talking to his buddy about whatever. VERY disturbing.
Nov
2
comment “Best practice” innovative teaching in mathematics
@BillCook: the question is asking about 1st year math and engineering courses. And the lectures I've been to (many!) explained things worse than a good book.
Nov
2
comment “Best practice” innovative teaching in mathematics
@percusse: I don't understand your point at all.
Nov
2
comment “Best practice” innovative teaching in mathematics
@Gordon: That's great! I wish other universities did the same. I was thinking a bit further though in the sense that if you have zero-lecture and zero-tutorial courses the cost to run the course become almost zero.
Nov
2
comment Fourier series of $f(x,y)$
I ended up having $a_n = K + a_n$. Maybe I made a mistake, although I did it twice...
Oct
30
comment Good book for self study of functional analysis
+1: I'm using Kreyszig and the book is just so good!!
Oct
28
comment Any converging sequence is bounded
Did you mean to write $n > 1$? If yes then $a_n$ is bounded by 1.
Oct
25
comment Radon Nikodym derivative proof
@t.b.: OK. I can't go to the library right now but I'll try to find it online...
Oct
25
comment Radon Nikodym derivative proof
@t.b.: You said "of informative value $0$" -- is this not a correct answer? I think using Riesz there is nothing left to show. Is this wrong?
Oct
25
comment Radon Nikodym derivative proof
@t.b.: I posted my tentative answer below... thanks for your help!
Oct
25
comment Radon Nikodym derivative proof
@MichaelHardy: Thanks!
Oct
25
comment Mean ergodic theorem
Thank you. I thought you might leave me to it because it's homework and then I started to panic because I have to hand it in by tomorrow and I still didn't really know what I was doing.
Oct
24
comment Mean ergodic theorem
@t.b.: I would like to show for $x \in I^\bot$ $\forall a_\bot \in A^\bot: \langle x, a_\bot \rangle = 0$. And to do that I was thinking of decomposing $x = a_\bot^\prime + a_{\bot \bot}^\prime$-- am I on the right track?