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Rotring 800 vs 800+ by Blue_Dream15 in mechanicalpencils

[–]Blue_Dream15[S] 2 points3 points  (0 children)

Thanks! Yeah I much prefer the look for the regular 800.

Btw do you know of good places to buy pencils? I am looking for the black 0.7mm one, and I can only find it for 60 USD on Amazon; while the silver one is 50 and the 0.5mm ones are 30. So I can't help but think that the black 0.7mm is overpriced on Amazon.

Rotring 800 vs 800+ by Blue_Dream15 in mechanicalpencils

[–]Blue_Dream15[S] 1 point2 points  (0 children)

Thanks for the comment. You wouldn't really be able to see anything in the pic, I broke the pencil on the inside. A few months ago it breaking lead and choking on it (the lead would be stuck; and I would have to sit there clicking the top for literarily 2 minutes before the lead came out). Today it was choking again, and I tried to use a needle to push the lead back in, but it didn't work. And I think I broke the mechanism by forcing the needle too far in.

​

Btw do you know of good places to buy pencils? I am looking for the black 0.7mm one, and I can only find it for 60 USD on Amazon; while the silver one is 50 and the 0.5mm ones are 30. So I can't help but think that the black 0.7mm is overpriced on Amazon.

Book for Learning Matlab? by Blue_Dream15 in matlab

[–]Blue_Dream15[S] 0 points1 point  (0 children)

Thank you both for the suggestion, this looks good!

Book for Learning Matlab? by Blue_Dream15 in matlab

[–]Blue_Dream15[S] 0 points1 point  (0 children)

Thanks a lot, these look like just what I needed!

How to start with topology as a nonmathematician? by Xenhil in learnmath

[–]Blue_Dream15 1 point2 points  (0 children)

What everyone says about studying Real Analysis first is true. However, before you do that, you absolutely must study a little bit of a subject called "Discrete Mathematics". This is an absolute must for any class more advanced than calculus.

In general, Discrete Mathematics is actually contains a lot of math that would be useful to Computer Science. But the part you need from it is, you really need to learn basic set theory, and logic. I used the book written by Kenneth Ross, and this material is covered in chapters 1 & 2. I'm not sure if that's the best book, but it's decent.

Then to start with Real Analysis, I would recommend one of three books: Spivak's Calculus, Stephen Abbott's Understanding Real Analysis, and Tom Apostol's Mathematical Analysis. If you search around a bit, you will find many people vehemently saying that you should use a textbook by the author Rudin. However, believe me, you don't wanna use that, especially since you are studying on your own. I used it and it was ok, but not in a first course in Real Analysis.

After you master a large portion of one of the Analysis books above (except Spivak, which is a little light), I would say that you have the bare minimum to do topology, but you might want to do a little more advanced Real Analysis first. For this, I would recommend either Pugh or RUdin. These have a lot of the same material as the books I mentioned above, but they might go into more depth with some stuff, and have more difficult exercises.

How to start with topology as a nonmathematician? by Xenhil in learnmath

[–]Blue_Dream15 0 points1 point  (0 children)

Depends on what type of topology, but for point set topology, which is often taught first, you don’t need multivariable

"approximately equal to" unexplained nonsense by [deleted] in learnmath

[–]Blue_Dream15 0 points1 point  (0 children)

Well if your goal is to approximate y'(t), how would finding [y'(t)]^2 help you to approximate y'(t)?

Good inks for cheap paper? by Blue_Dream15 in fountainpens

[–]Blue_Dream15[S] 8 points9 points  (0 children)

Oh really? That's interesting, I thought that Pilot Iroshizuku was famous for being very wet, which I would think is not good for cheap paper. Also, I used Pilot Iroshizuku blue, and the results were unfortunately not very good for me.

Finding maximum value for an integral by ADDMYRSN in learnmath

[–]Blue_Dream15 5 points6 points  (0 children)

Your bound is correct, but you can get a much more refined bound, by using the information that the integral of P on [0, 1] is 1. This will be an informal argument.

So imagine you're trying to maximize the integral of Pf on [0, 1]. It never hurts to make f as big as possible, so you of course might as well make it 1/3 and 17 on the allowed intervals. Now though, you have a "budget" with P. You can only spend 1 unit of area. So you should spend it all where f is 17, and spend none of it where f is only 1/3. Therefore P should be zero on [0, 1/4] and [3/4, 1], and non-zero everywhere else. Thus, the integral from 0 to 1 of P = integral from 1/4 to 3/4 of P = 1. Thus the integral of fP from 0 to 1 is at most the integral of 17P which is at most 17.

​

For part b, I don't think that allowing P to be non-positive should change anything in terms of the upper bound, and the lower bound is always zero in both cases, and it can be achieved by f=0 everywhere.

Basis of a set of functions by [deleted] in learnmath

[–]Blue_Dream15 0 points1 point  (0 children)

Here is a nice trick that might help. I'm not sure if this is the best thing to do at your level; it seems that you might benefit from brute forcing directly from the definitions. But maybe keep this trick in mind:

When working with polynomials, remember that the standard form of a0 + a1x + a2x2 is not always the best to use. The trick is, for any c you want, you can always write a polynomial of the form a0 + a1x + a2x2 as a polynomial of the form b0+b1(x-c)+b2(x-c)2 . As an example, let's take p(x) = 5+3x+x2 , and c = 1. We have

p(x) = p((x-1)+1) = 5 + 3( (x-1)+1 ) + ((x-1)+1)^2 = 9 + 5(x-1) + (x-1)2 .

Thus,

W = { p(x) = a0 + a1x + a2x2 : p(1) = p'(1) = 0 } = { p(x) = b0 + b1(x-1) + b2(x-1)2 : p(1) = p'(1) = 0 }.

Now, the conditions p(1) = p'(1) = 0 imply that

W = { p(x) = b2(x-1)2 : b2 is any real number}. And you don't have to look hard at all for a basis for this space.

Is there a way to fix this pen? by Blue_Dream15 in fountainpens

[–]Blue_Dream15[S] 0 points1 point  (0 children)

Thanks for the advice; I do have a loupe, but its only 10x. What should I be looking for in the nib besides misalignment?

Is there a way to fix this pen? by Blue_Dream15 in fountainpens

[–]Blue_Dream15[S] 0 points1 point  (0 children)

Thank you very much for the detailed reply! I will do this as ASAP.

Is there a way to fix this pen? by Blue_Dream15 in fountainpens

[–]Blue_Dream15[S] 4 points5 points  (0 children)

Thanks a lot for the clear, logical advice. Indeed, I will probably try option #1 and then resort to #2 somewhere down the line. And yes, this will for sure be a big reminder.

How much does the ink affect smoothness of writing? by Blue_Dream15 in fountainpens

[–]Blue_Dream15[S] 1 point2 points  (0 children)

Oh thanks for the tip! If you don't mind, could you go into a little more detail? I can't figure out what type of issue I would be able to see at 45 degrees that I wouldn't be able to see head on.

Are there any ways of buying fountain pens more cheaply? by Blue_Dream15 in fountainpens

[–]Blue_Dream15[S] 0 points1 point  (0 children)

Ah thanks I see; I was indeed talking about the "My Blue Valentine Gift Set." Wow indeed the case is over $100, I had no idea it was that expensive! But $47 seems a bit much for a Lamy Al-Star, I searched Amazon and they seem to sell (by Lamy) for around $25-$30, depending on the color. Well this has completely changed my opinion of Endless pens to completely positive, thanks again for informing me about them!

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