Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Ask HN: How can I learn to read mathematical notation?

news.ycombinator.com

Post reply on HN
Print view View original

131–140 of 148 posts

Re: Ask HN: How can I learn to read mathematical notation?

#131

Post by imjustsaying »

starbeast wrote: post #83

I run into the same problem, am much better at understanding maths stated as code than in mathematical notation. 3blue1brown's animated maths channel is pretty good. - https://www.3blue1brown.com/ Khan Academy's maths section covers a lot of stuff - https://www.khanacademy.org/math math.stackexchange is excellent for specific questions - https://math.stackexchange.com/ One thing that works for me is to try and find s…

I always wondered why math notation hasn't been replaced by code.

While math notations can be interpreted in different ways, code is going to give an unambiguous result.

Why don't mathematicians, especially those writing in machine learning or computer science domains, do this? Is it just a problem of agreeing on a common language?

Re: Ask HN: How can I learn to read mathematical notation?

#132

Post by [deleted] »

eldavido wrote: post #122
crawfordcomeaux wrote: post #113

Earlier quoted context omitted.

"The best" is purely subjective. I look at indigenous cultures who were able to resolve conflicts and share resources without hierarchical governments. They developed approaches to doing things western culture is only now relearning. Also, your "best people" developed systems to addict us with little concern for their systemic impacts. If that's your version of best, I want better.

> "The best" is purely subjective Bullshit. Find me one "indigenous culture" as advanced as a modern developed western country (or China) and I'll believe you. I don't care whether your metric is life expectancy, scientific progress, quantity and quality of art produced, fairness of our legal system, political/religious freedom, lack of food scarcity, or corruption. You pick. We in the West have it as good as anyone…

[deleted]

Re: Ask HN: How can I learn to read mathematical notation?

#133

Post by the_rock_says »

woodson wrote: post #105

John von Neumann once said, "Young man, in mathematics you don't understand things. You just get used to them." While probably not the originally intended meaning, you can take the quote as saying that, after reading a lot of papers in a given field, you will “get used to it” and recognize recurring patterns and what they mean. This is particularly important as more often than not, part of the math is left out (presu…

Thank you for bringing the Neumann's quote. At times I get so bogged down because of these complex mathematical notations. This was particularly frustrating as mathematics is an area where I shine. I started reading between the lines and rewriting those equations in a way I understand. I'm glad to know that many people resonate with this and I'm not the only one that struggles. Thanks HN!

Re: Ask HN: How can I learn to read mathematical notation?

#134

Post by crawfordcomeaux »

eldavido wrote: post #122
crawfordcomeaux wrote: post #113

Earlier quoted context omitted.

"The best" is purely subjective. I look at indigenous cultures who were able to resolve conflicts and share resources without hierarchical governments. They developed approaches to doing things western culture is only now relearning. Also, your "best people" developed systems to addict us with little concern for their systemic impacts. If that's your version of best, I want better.

> "The best" is purely subjective Bullshit. Find me one "indigenous culture" as advanced as a modern developed western country (or China) and I'll believe you. I don't care whether your metric is life expectancy, scientific progress, quantity and quality of art produced, fairness of our legal system, political/religious freedom, lack of food scarcity, or corruption. You pick. We in the West have it as good as anyone…

We don't have a fair legal system, so I'd say that's a place where we could learn from them. Also, being connected to the land. Consent practices, as well. How to learn principles of life from observing nature.

Oh, and we totally have food scarcity, too.

There's stuff there to learn, if you're willing to accept the idea that perhaps your culture has room to grow.

Re: Ask HN: How can I learn to read mathematical notation?

#136

Post by princeb »

kazinator wrote: post #127
SomewhatLikely wrote: post #121

Earlier quoted context omitted.

When I first began writing papers I tried to describe using prose. I found that readers were confused and there was much more ambuigity than I anticipated. By using mathematical notation, it becomes a lot less likely that you are misinterpetted and often takes less space. It's kind of like the difference between providing code versus a written description of the algorithm.

The problem is assuming that the reader is already familiar with the notation, and consequently not explaining it.

the other problem is assuming the reader knows nothing, going too deep into the foundations supporting the conclusion.

mathematical knowledge is like scaffolding. a reader has to gradually build up and buttress the lower layers before attempting to move up. skipping steps does no one any favours.

Re: Ask HN: How can I learn to read mathematical notation?

#137

Post by yesenadam »

imjustsaying wrote: post #131
starbeast wrote: post #83

I run into the same problem, am much better at understanding maths stated as code than in mathematical notation. 3blue1brown's animated maths channel is pretty good. - https://www.3blue1brown.com/ Khan Academy's maths section covers a lot of stuff - https://www.khanacademy.org/math math.stackexchange is excellent for specific questions - https://math.stackexchange.com/ One thing that works for me is to try and find s…

I always wondered why math notation hasn't been replaced by code. While math notations can be interpreted in different ways, code is going to give an unambiguous result. Why don't mathematicians, especially those writing in machine learning or computer science domains, do this? Is it just a problem of agreeing on a common language?

You mean, "Why don't they use a language you understand, instead of one you don't?"... Why expect they should?

I don't think math notations can be interpreted in different ways usually is right. That would defeat the purpose of using them, if the meaning wasn't exactly clear. And maths notation is more compact, a lot more. Even assuming a translation between the 2 always is possible or makes sense.

Re: Ask HN: How can I learn to read mathematical notation?

#138

Post by sn9 »

lucb1e wrote: post #116
cowboysauce wrote: post #56

I think you've got this backwards. You don't need to understand the notation, you need to understand the math. If you don't understand the notation then you probably don't understand the math in the first place so learning notation won't help. Learning how a matrix is written is useless without understanding what a matrix is. You need to find out exactly what type of math is used in the paper and learn that. Learning…

Partly, perhaps. For me, a large part is the notation. I know conditionals, I know loops (as in for loops), I know SQL... but if you show me logic, set theory, a sigma, or, uh, what's this sigma but for multiplication, I wouldn't have known what you meant a few years ago. It's not only understanding the math, it's also the notation. I still don't know how to read things like curly braces or matrices or a dozen other…

Pretty much every math textbook I've read has defined the notational conventions early on.

(I'm not saying this is the case with every math text, just the ones I've read that are intended to teach the reader the subject.)

I see all these comments about reading papers with confusion and I get the impression that they didn't read the prerequisite information from textbooks for whom they're the right audience as that's generally how you pick up notation.

Re: Ask HN: How can I learn to read mathematical notation?

#139

Post by ssijak »

kazinator wrote: post #127
SomewhatLikely wrote: post #121

Earlier quoted context omitted.

When I first began writing papers I tried to describe using prose. I found that readers were confused and there was much more ambuigity than I anticipated. By using mathematical notation, it becomes a lot less likely that you are misinterpetted and often takes less space. It's kind of like the difference between providing code versus a written description of the algorithm.

The problem is assuming that the reader is already familiar with the notation, and consequently not explaining it.

If it is a mathematical paper it is targeted at other mathematicans eho should be able to understqnd the notation.

Re: Ask HN: How can I learn to read mathematical notation?

#140

Post by MaxBarraclough »

nvarsj wrote: post #68
MaxBarraclough wrote: post #53

Earlier quoted context omitted.

> I don't know any way I'd have learned all the complex topics in math, stats, probability, etc., I did without attending a big 10 engineering school This is something the MOOC crowd often overlook. It's based on a misunderstanding of what a university gives you: university entry doesn't grant you access to some members-only club where they hide away the knowledge to keep it from the plebs (ignoring the open access m…

You ignore the possibility that MOOCs can have peer interaction. In OMSCS at least, there is loads of peer interaction (via slack, email, forums) - more in fact than I ever had at my undergrad (which was a top 10 engineering school).

That's a fair point, but I put a lot of stock in physical interaction. I suspect that being physically part of a class greatly reduces odds of drop-out, and improves group study.

(Of course, this is an empirical claim, and I can't say I'm basing my opinion on a published study.)

More cynically: some undergrads struggle to get out of bed for their midday lectures. They would not thrive in a MOOC, where there is less immediate pressure to drive their studies. I can see it working far better in the context of a masters degree, as you allude to.

Post reply on HN