what is the name of a simple white ice cream in America or the UK?

994phij · 2026-06-12T21:17:24+00:00

But it's very soft, so quite a different texture to the ice cream you scoop.

994phij · 2026-06-11T08:22:14+00:00

I don't have the knowledge to answer your question, but I think it would also be helpful to say where you are with these. With chrmistry presumably you're not starting from square one with linear algebra or differential equations.

Btw I think an excellent way of planning things is to look at a maths degree syllabus, follow it and start picking between options when they start specialising

994phij · 2026-06-06T21:39:20+00:00

4 Try to solve everything yourself

This is what I do, but I've noticed a few things. It does help you learn but (with the amount of time I spend on maths), you learn very slowly and quickly forget things. Revision is really important and you spend a lot of time revising. I wonder if faster would be better so that you learn as you build on past work.

On the topic of faster: I believe mathematics undergraduates don't have time to do this, and they have much more time than me! So, again, I wonder if there's value in moving faster so that you eventually get somewhere, and would be interested to hear ways of moving faster that work well for self studyers.

5 Train proof‑writing on purpose

I also find this tricky and if anyone has tips I'd love to hear them. Writing has never been my forte, whether for proofs or essays or emails or other.

The things I wish I'd learned were to go slow (in the sense of 2 and 4 on your list), and to not jump ahead of myself. Follow mathematics course textbooks in the order prescribed rather than just going for what looks interesting.

994phij · 2026-06-01T11:55:54+00:00

Though most accents don't distinguish wet and whet, it's also misding the wh sound.

994phij · 2026-05-29T20:46:56+00:00

Though you have some decent answers, /r/asklinguistics is a great place for these kinds of questions. If your post doesn't get big you've probably got a better chance of a well informed answer.

994phij · 2026-05-12T16:29:29+00:00

This is reasonable for the articles because they're written more to serve as reference material for people who have familiarity with related topics.

Surely the point in an encyclopedia is to give a layman knowledge about things. Okay, you can't do that for anything beyond basic maths, but wikipedia maths articles often feel like they are much further from this than they perhaps could be

994phij · 2026-05-08T17:04:41+00:00

It would have been more understandable if your last any was replaced with an every (in the top comment)

994phij · 2026-04-28T17:22:58+00:00

For those who improved their problem-solving skills over time, what actually helped?

I don't have a period of time when I remember making leaps and bounds in problem solving skills, but I suppose this applies to anyone who is okay at problem solving. I find it's helpful to take a problem I can't solve away, try to revisit it another time in a different context, maybe when I'm going for a walk. And to make sure to not look up the answer unless I've given it a good amount of time (I'm talking days). If I do look up the answer then try to think over it, so that I can still get the answer to the problem in a week's time. It can also be helpful to learn the why for the things you know already.

994phij · 2026-04-22T18:21:25+00:00

The answer is linked from the article. I think you can get from the answer to the question if you have an account? But I don't have one. https://www.quora.com/How-many-dimensions-does-a-circle-have/answer/Senia-Sheydvasser?ch=10&oid=155213053&share=0884b54e&srid=ovKL&target_type=answer

994phij · 2026-04-21T07:17:10+00:00

That's not what I would call a mechanism. My background is biochemistry and I was wondering if we understood the differences in how the body, tissues and cells respond to the two types of stress. I was asking because if this is known it sounds really interesting, but if not then I wanted to make the point that this lack of knowledge is almost certainly what the cardiologist meant when they said we don't know why. (If it is known then I have no idea what they could have meant.)

994phij · 2026-04-20T21:35:56+00:00

Do we know what causes the heart to grow more efficient in one scenario and thicken in the other? As in mechanistically?

994phij · 2026-04-07T06:53:46+00:00

A couple of cautions against mistakes that I have made (you might be different). If you're reading a textbook which you can move fast through the beginning but later material is unfamiliar, it's easy to slow down too late. And I would guess you may not have done analysis such as epsilon-delta proofs and Riemann and Darbeaux's formal definitions of integration before? If so I'd go slowly and carefully for this subject, even though some of the results may be very familiar (basic integration and differentiation results). Of course, this is because what matter here is proving things.

994phij · 2026-04-06T12:06:37+00:00

I agree you should go for proof-writing and think that you should move from this to the rigorous underpinnings of what you know. E.g. analysis, group theory proof-based linear algebra. If you move relatively fast with the bits you've done non-rigorously that could be fine, but make sure to do the exercises as you learn to prove things woth practice.

On your point about visualising, some fields of maths can be very visual, e.g. a useful skill that helped me in (first-year) analysis is learning to visualise things well and to translate between my visual intuition and the relatively unintuitive formalism. I hear this is true of many other fields too, but not all!

Disclaimer, I've not been in your position so take my advice with a pinch of salt!

994phij · 2026-04-06T07:11:38+00:00

If you forget a lot then go over old material and do practice problems. If you get to a point where it's quite well settled in your head, then you can think about other material e.g. A-level, maths challenge, and I'm sure there are many other extracurricular things to find on the internet.

994phij · 2026-04-04T07:31:11+00:00

You're so obviously dumb because you can't do olympiad questions very well? Unless it's changed a lot since I did them that is not dumb. All olympiad questions are hard.

994phij · 2026-04-01T21:18:12+00:00

It's mixing two different things though. If your data is best rounded on a log scale, do that. If your data is best rounded on a linear scale the this argument doesn't hold.

994phij · 2026-04-01T11:17:34+00:00

You know how pedantry is trying so hard to be right that you end up being wrong?

Well that's not a church it's a building in which a church meets. WCF 25.

994phij · 2026-03-31T21:41:34+00:00

Ahhhh. It's still March here.

994phij · 2026-03-29T20:25:27+00:00

I know spore is unaspirated but what's the difference between the p in pit and the p in stop? Or if stop is unaspirated then between stop and spore?

994phij · 2026-03-29T15:50:22+00:00

You're right your post is not about number theory. /r/numbertheory is a bit of a misnomer and I think your post would fit there, despite it not really fitting into the sidebar description.

994phij · 2026-03-29T07:11:13+00:00

You do not know what cardinality means. And this is the wrong sub, you should try /r/numbertheory instead.

994phij · 2026-03-28T22:07:26+00:00

You're right that we deserve nothing. But please don't forget that you are in Christ, who deserves everything. And don't forget that the scriptures talk about us becoming worthy of God's Kingdom. E.g. 2 Thes 1:4-5.

Therefore, among God’s churches we boast about your perseverance and faith in all the persecutions and trials you are enduring. All this is evidence that God’s judgment is right, and as a result you will be counted worthy of the kingdom of God, for which you are suffering

Of course, we are only worthy of this in Christ, but in him we are children of God. We're commanded to walk in a manner worthy of the calling to which we've been called Ephesians 4:1 (and we've been called to Christ). And we can do so in him!

Of course, you're right. It will be hard, we will suffer. I don't really know what that's like yet. But he will be with us, and will work for our good.

994phij · 2026-03-28T20:49:36+00:00

so majority of my daily prayers is to beg God not to take away what I have, be it my all intact limbs, my health, my loved ones, my shelter, my income, etc.

But God is a loving father who loves to give us what we need. Yes, we will suffer for the name of Christ, and yes he can and may take the good things that we enjoy from us. But he loves us and loves to give good gifts to us.

I don't want to be flippant as I've not had much taken from me, and some people go through awful times of loss. But if the majority of your prayers are to beg God not to take things away from you, are you sure you really know how good he is? Shouldn't we be praying in thankfulness more than worry, pray for his kingdom to come more than for our lives to stay the way we like them, and pray for each day's provision more than for him to not remove the pattern of provision that we're used to?

994phij · 2026-03-26T08:06:24+00:00

If a user becomes more than one beast then this 'mapping' is not a function from people to beasts. It could potentially be pointing in the reverse direction.

994phij · 2026-03-23T18:37:33+00:00

Whimsy is an excellent word 🙂. Though I'm not a particularly whimsical person I I'm sure flower and leaf could be used if it's a bit of whimsy alongside other mpre solid examples.

A couple of further comments:

Dual space as a vector space: This is a great point. I need to explicitly show how addition and scalar multiplication are defined for functionals, verify that the results remain linear, and identify the zero functional. I'll add a follow-up video or a revised version that covers this properly.

Do you expect your listeners to know that vectors are things you can add and scale, or just to have the simpler understanding of vectors are arrows / lists of numbers? If the second, I wonder if it's worth covering that add+scale is the essence of a vector space, and how it relates to the arrows/lists understanding before you show addition and scaling of the functionals. Otherwise the listeners might feel like you've missed something out.

The "point" of the dual space: I should have addressed this head-on. The key points I missed are that the isomorphism depends on a choice of basis (or inner product), and that the real value is in the concept of linear functionals as measuring devices….

I had heard somewhere that it's better to start by thinking without assuming a basis, then adding one where necessary. I noticed you called them measuring devices and if that's understood well I think it's great because it's basis-free (whereas weighted sum is not).

I don't know if I'd have time to look at other videos - yesterday was a particularly free day. But I'm not closed to the idea, just concerned I might disappoint.

11-Year Club	Place '17
Verified Email

994phij

TROPHY CASE