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

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

#121

Post by SomewhatLikely »

Koshkin wrote: post #107
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…

> it’s just there to show off That is true, unfortunately, in much of the mathematical literature. Way too often authors use the formalized language where the plain language would suffice. This kind of abuse is extremely widespread. It is one thing when a formula is used to represent, say, a complicated integral; it is another when a formula is used to express something just as easily said in a couple of words.

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.

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

#122

Post by eldavido »

crawfordcomeaux wrote: post #113
eldavido wrote: post #52

Earlier quoted context omitted.

It's not about being "fed information". It's the reality that being around a motivated group of peers confers real advantage. I look at the history of art (e.g. Impressionists), YC, winning athletics programs, Silicon Valley, or just about any well-regarded academic department as evidence. These places don't do well just because they select the best, they also MAKE the best by creating an environment that fosters it.

"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 ever did in the history of the world. Tell me one thing "western culture is only new relearning", I'd be interested to hear?

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

#123

Post by lp251 »

Koshkin wrote: post #107
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…

> it’s just there to show off That is true, unfortunately, in much of the mathematical literature. Way too often authors use the formalized language where the plain language would suffice. This kind of abuse is extremely widespread. It is one thing when a formula is used to represent, say, a complicated integral; it is another when a formula is used to express something just as easily said in a couple of words.

Can you give an example?

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

#124

Post by deytempo »

The real problem is people who understand machine learning don’t know how to describe it in terms of anything except math. You don’t really need math to do it just like you don’t need math to understand neurons or how they function. Every concept in machine learning can be demonstrated in simple programming without any math. Why it is not is because most people who are doing it at the experimental level are at a university and they don’t start learning it until they already have a tremendous math background but to say it requires math is ridiculous

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

#125

Post by diffeomorphism »

Mathematical notation is not anything magical and mostly there to allow for easy discussion. Also equations are only a small part of notation and words and definitions are much more important, e.g. "isomorphism".

Since mathematics is abstract anything used necessarily has be precisely defined. Thus, the best way to learn mathematical notation is to get some beginner level rigorous mathematics book for mathematicians, e.g. Rudin's real analysis or Lang's Linear Algebra, and read through chapter 0 and 1. Books like these tend to start entirely from scratch: What is a number? What does '+' mean? What is a sum symbol?

While each field tends to have some further notation, that is often explained within the paper or in standard references and you should be able to read mostly everything after reading up on basic notation sections in analysis, linear algebra and maybe category theory.

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

#126

Post by deytempo »

empath75 wrote: post #25

To me it’s exactly the same as learning to work with an unfamiliar code base. Just pick some small part of it and start tracing back until you find definitions.

Yea except you are supposed to compile it and run each line and iteration in your head

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

#127

Post by kazinator »

SomewhatLikely wrote: post #121
Koshkin wrote: post #107

Earlier quoted context omitted.

> it’s just there to show off That is true, unfortunately, in much of the mathematical literature. Way too often authors use the formalized language where the plain language would suffice. This kind of abuse is extremely widespread. It is one thing when a formula is used to represent, say, a complicated integral; it is another when a formula is used to express something just as easily said in a couple of words.

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.

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

#129

Post by terrycody »

I recommend you read this article about how to learn CS and become a computer scientist or machine learning expert, from 0 ground.

In the article, author recommend u have to have a very strong knowledge base of math, statistics, probability, and linear algebra in order to read those things.

https://www.afternerd.com/blog/learn-computer-science/

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

#130

Post by stillbourne »

eldavido wrote: post #118
stillbourne wrote: post #109

Earlier quoted context omitted.

As a high school dropout that is self educated, I don't appreciate people dogging those who take the effort to forge their own path. You can learn complex topics outside a formal education system and your comment offered no specific assistance. So in the spirit of the holiday, thanks for nothing.

So here's the thing: apart from you and maybe a few friends, nobody really cares about your "forging your own path". It may give your life meaning, which is important. But in any sort of professional / market context, people just emphatically. Do. Not. Care. Speaking from experience, I have often taken the hard path. I've always regretted it and often, if I'm being honest, it's out of a misguided sense of stubbornnes…

I have no idea what point you are trying to make, my point is simple, a poorly taught college course is worse for comprehension than reading the source material and coming to your own understanding. As a Sr. Dev, I have mentored many people that are still in college. I have seen the struggle that they have endured in classes such as Discrete Math. I have held their hands through poorly constructed math courses that have bad or misleading information, and not from the same school. Maybe you were privileged enough to go to a good school where they had their shit together but not all colleges are made equal. I learned most of what I know from reading the material myself. I'm not bragging. This is not coming from a position of, look at me, I am so fucking cool because I did it on my own. No, this is a statement that not all educational systems are built the same, that there are faults in our general education system and some people are better off picking it up and running with it, forging their own path, than to have is spoon fed to them by an idiot that doesn't know what he is talking about or by a broken online courseware spewing bad information. So spare me the bullshit of feeling sorry for yourself, or about life not dealing you the fair hand. Because I don't believe that for a fucking moment.
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