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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?

#21

Post by sonabinu »

gmiller123456 wrote: post #14

Understanding the notation is only the first little step in understanding the underlying principles. There are a lot of machine learning books/classes that will cover the underlying principles you need to understand what's covered in the book. Exactly which one to recommend depends on your background, but Andrew Ng's Coursera Course [1] has been a staple for people without a lot of math background. [1] https://www.co…

I tried to overcome the notation issue by taking a ML class as a non- degree seeking student from the CS dept of a good university. I took it for credit, so invested a lot of time on hw and paper reading. I’m more comfortable with the notation now and am better at learning independently. I also did calc, linear algebra and Differential equations classes at a community college prior to this.

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

#22

Post by sqrt17 »

gmiller123456 wrote: post #14

Understanding the notation is only the first little step in understanding the underlying principles. There are a lot of machine learning books/classes that will cover the underlying principles you need to understand what's covered in the book. Exactly which one to recommend depends on your background, but Andrew Ng's Coursera Course [1] has been a staple for people without a lot of math background. [1] https://www.co…

Ng's Coursera course will teach you what happens in Deep Learning and Machine Learning, but at least the Deep Learning course is very very light on the math side and avoids scary mathematics rather than making it accessible.

Without having read it, I'd recommend the "preliminary maths" part of Bengio et al's Deep Learning book - it teaches both the letters and the language, so to speak, and if the language isn't for you, you'd better throw away the papers and completely concentrate on reading and understanding the implementations that are our there, using the implementation first and foremost and the paper only as a backup to provide explanations when the implementation does mysterious or unexplained things.

You can do deep learning productively without having a PhD, but you won't be able (nor obliged) to read and understand PhD-level academic papers unless you have a solid (i.e., maths or physics or math-rich CS BSc) maths background.

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

#24

Post by BucketSort »

This is the beguiling thing about mathematics: it is right there on the page in front of you, yet often so far from your grasp. How could a statement said so simply as "a^n + b^n = c^n has no solutions for n > 2" be so difficult to reason about? This duality of having something and not having it is something I've only experienced in mathematics and bad relationships.

It's not about understanding the notation, as others have said, it's about understanding the principles expressed by the notation. You may learn the grammar of a language, but that is a far journey from understanding its poetry, which is full of norms and views beyond what is captured by its grammar.

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

#27

Post by arsalanb »

erwan wrote: post #16

Hard to answer without knowledge of prior background or exposure that you might have. As a rule of thumb, I would advise to start with elementary linear algebra, statistics, and probability. Edit: As pointed out by a reply comment, these require a good grasp of calculus. Notation is only syntactic, most importantly you want to understand the semantics (i.e the significance of the construction your are studying). To a…

This. I mean you can google stuff like "what does the curly L mean" and it would tell you that it's a Lie derivative, but that wouldn't mean much to you unless you understood that it did.

So you need to understand the work and the math behind it and you will get an idea about the notations used. Not the other way round.

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

#28

Post by williamstein »

rocqua wrote: post #20
williamstein wrote: post #15

Earlier quoted context omitted.

"There is no Royal Road to Geometry." -- Euclid I've spent time studying number theory (Ph.D. Berkeley, wrote 30+ papers and 3 books), and it really is very deep. If understanding some notation or mathematics doesn't come easily to you, that's normal. It often takes Ph.D. students years of fulltime study just to understand a single research paper. This is because mathematics is a very deep subject, certainly much dee…

> pretty much all mathematics does make sense, and can be truly 100% understood if you're willing to invest enough time Inter-universal Teichmüller theory seems to be a counter-example.

To me it is an example, not a counterexample, because the IUT papers have been completely understood and judged to be incorrect by recent fields medalist Peter Scholze (and several other top mathematicians).

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

#29

Post by DoctorOetker »

erwan wrote: post #16

Hard to answer without knowledge of prior background or exposure that you might have. As a rule of thumb, I would advise to start with elementary linear algebra, statistics, and probability. Edit: As pointed out by a reply comment, these require a good grasp of calculus. Notation is only syntactic, most importantly you want to understand the semantics (i.e the significance of the construction your are studying). To a…

I would definitely add calculus to that list first univariate, then multivariate

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

#30

Post by [deleted] »

rocqua wrote: post #20
williamstein wrote: post #15

Earlier quoted context omitted.

"There is no Royal Road to Geometry." -- Euclid I've spent time studying number theory (Ph.D. Berkeley, wrote 30+ papers and 3 books), and it really is very deep. If understanding some notation or mathematics doesn't come easily to you, that's normal. It often takes Ph.D. students years of fulltime study just to understand a single research paper. This is because mathematics is a very deep subject, certainly much dee…

> pretty much all mathematics does make sense, and can be truly 100% understood if you're willing to invest enough time Inter-universal Teichmüller theory seems to be a counter-example.

[deleted]
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