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

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11–20 of 148 posts

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

#11

here's a dirty seceret: we (people that have mathematical training) don't read the notation very closely either. it's very much like reading code: i don't look very closely unless there's a pattern i don't recognize or one that's broken. so ironically reading notation is about ignoring notation :) the problem for you is that you simply haven't had enough exposure to know what the "patterns" are and hence don't have t…

I was a college math major, and I can't read math the way I can read text or even sheet music. I familiarized myself sufficiently by writing out my own derivations and treating the textbook as a reference while working the problems. The act of writing the stuff out and manipulating it with my hands is how I learned it.

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

#12

here's a dirty seceret: we (people that have mathematical training) don't read the notation very closely either. it's very much like reading code: i don't look very closely unless there's a pattern i don't recognize or one that's broken. so ironically reading notation is about ignoring notation :) the problem for you is that you simply haven't had enough exposure to know what the "patterns" are and hence don't have t…

[deleted]

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

#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.coursera.org/learn/machine-learning?authMode=log...

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

#15

https://en.wikipedia.org/wiki/List_of_logic_symbols https://en.wikipedia.org/wiki/Table_of_mathematical_symbols These might help a bit. But as someone with similar problems, I'm beginning to think there's no real solution other than thousands of hours of studying.

"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 deeper than everything else I've encountered in academia. The good part is that pretty much all mathematics does make sense, and can be truly 100% understood if you're willing to invest enough time, unlike the case with many other things in life! An added bonus is that much of mathematics is also incredibly beautiful, when you understand it.

Listening to lectures by excellent speakers (many are on youtube now) helps a lot.

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

#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 achieve this, you need to do the proper background work and the rest will follow naturally.

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

#17
I've been eyeing this book to help bridge some gaps in the same area for me: https://amzn.to/2OZUIlE It talks more fully about mathematical proofs in general, but it gives a really good introduction to the notation and such in a much more compact space than most other ones I've seen.

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

#18
Sort of copy-pasting one of my earlier comments, apologies, but I highly recommend the book "Mathematical Notation: A Guide for Engineers and Scientists" by Edward Scheinerman (Amazon link: http://a.co/c1jcvLH ). It's short, and perfect for looking up symbols, brackets, subscript/superscript conventions etc. for science and engineering math (for me, the stuff I encounter in my programming life, when I read papers & books that deal with graphics programming, DSP, cryptography, etc.).

It's difficult to google mathematical stuff, especially since each symbol has many different meanings depending on which branch of mathematics you're dealing with - this book solves that problem nicely by letting you look up by the roman letter a symbol is similar to, by mathematical discipline, etc.

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

#20

https://en.wikipedia.org/wiki/List_of_logic_symbols https://en.wikipedia.org/wiki/Table_of_mathematical_symbols These might help a bit. But as someone with similar problems, I'm beginning to think there's no real solution other than thousands of hours of studying.

"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.

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