HN Books @HNBooksMonth

> You underestimate how hard the problem is.

It's hrd, but it's not that hard. Character recognition is half the problem, the other half is context recognition - and there's abundant reference material available. I think we'll see 'copilot for math' aimed at AP/college level users within a few years.

It's not something that any human can do, bu something that any human can do with help. The first killer app will be 'I found this formula, please tell me how to read it.' Not in the sense of being a math tutor (although that may come, but simply in the sense of helping students to read it out loud, identify symbols like hats or bars and son so on. Most math books are terrible in this respect because they assume the student already knows all the notation or has someone who can lecture or tutor them about it. This massively inhibits solo learners who can't engage in the practice of 'teaching themselves' by verbally walking through formulae or discussing them fluently, unless they're lucky enough to have found a good reference for notation.

If you are not in the latter group, Wikipedia has OK summary articles on notation; and these two books offer variously concise and in-depth tools to built mathematical literacy:

https://www.amazon.com/Mathematical-Notation-Guide-Engineers...

https://www.amazon.com/Programmers-Introduction-Mathematics-...

I've found this book to be very helpful: Mathematical Notation: A Guide for Engineers and Scientists [0]. It's compact, very well organized, and has several indexes to make symbol lookups easier and good summaries of what they mean.

[0] https://www.amazon.com/gp/product/1466230525

The rhino book is a good dead tree reference.

https://www.amazon.com/Mathematical-Notation-Guide-Engineers...

It's not really comparable to the yellow book and its meant as a glossary for an older audience, but I've found Mathematical Notation: A Guide for Engineers and Scientists [1] to be useful, especially for reading CS and ML papers.

[1] https://www.amazon.com/Mathematical-Notation-Guide-Engineers...

There is a good book for math notation that I like:

"Mathematical Notation: A Guide for Engineers and Scientists"

https://www.amazon.com/Mathematical-Notation-Guide-Engineers...

⬐ jongold

This book single handedly saved my butt a few years ago when I was diving deep into deep learning without a math background. It’s very slim, which is a huge selling point in a world of 9000 page textbooks. I love it.

⬐ binarymax

An upvote isn’t enough for this book, so I need to comment that it’s the best I’ve come across for my needs. When I was getting into the more mathematical aspects of coding when I was getting started with machine learning 5 years ago, this book was invaluable.

Having thought in code (with verbose variables and structure) for many years, I needed a Rosetta Stone for the ambiguous symbology of mathematics - and this is it!

It’s tinier than you’d think, but is an absolutely incredible reference. An absolute requirement for any engineers bookshelf.

As someone in the same boat I've found this book to be very helpful.

https://www.amazon.com/gp/product/1466230525 - Mathematical Notation: A Guide for Engineers and Scientists

⬐ alexbanks

I purchased this. I've been trying to brush up on CS fundamentals (it's been a long time since college), but I get stuck just on trying to understand what I'm being asked to learn.

Thank you

This might help https://www.amazon.com/dp/1466230525

The following is a decent and reasonably priced reference:

"Mathematical Notation: A Guide for Engineers and Scientists"

https://www.amazon.com/Mathematical-Notation-Guide-Engineers...

>learning math is just really, really hard.

I'll accept the premise, but I still wonder if there are things that can be done to make it easier for someone. In my case, I've been trying to learn some more mathematics recently, and one of the most annoying things is coming across notation that isn't defined in a paper, presumably because "everyone" who can read the paper is familiar with the context and knows what the "skinny long arrow" means (good luck with that internet search). I wonder if there could be a wiki-like / forum / stackoverflowish site, which people could use to discuss and provide running commentary on a paper/book. Especially useful would be the ability for people to be able to annotate the paper by translating the formulas in to a formal language where you could track down the definition of the various operators, and try to figure out why the author used both of → and ↦ in the paper, when they both appear to be for functions/maps. (Just to preempt the easy objections, I'm not trying to suggest that each paper be formalized and proven in something like Isabelle/Coq).

In the ideal form, this website would allow you to see the paper or book page in question, and then see all the people who commented or had questions on each particular sentence (in the margin?). There could be filtering and voting so that experts could bypass the newbie commentary, etc..

I suppose part of my problem would be solved by getting a book like:

https://www.amazon.com/Mathematical-Notation-Guide-Engineers...

...(which I just came across when composing this message).

Maybe someone has a other suggestions for something like this? Maybe a site similar to this already exists?

And on a slightly related note to making things easier to learn, I think learning programming is much easier than math, because even though both are abstract, at least with programming you get a tangible, concrete thing (the program) that you can run and modify and extend, and the computer will tell you when you went wrong (e.g. won't compile, output result is unexpected, etc.).

⬐ sn9

Forgive me if I'm making incorrect assumptions about your background, but usually you learn math from books of varying degrees of difficulty which naturally force you to become accustomed to various kinds of notational conventions.

You wouldn't try to learn math from papers until you've built that foundation (unless you have access to a tutor/mentor), at which point the notation usually shouldn't be an issue.

⬐ GregBuchholz

That sounds like the traditional method of learning math. I was wondering if we could leverage technology and our experiences with teaching/learning the formal systems of programming languages to make more math more accessable. For instance, I'm thinking this little instance of geometric algebra:

http://www.shapeoperator.com/2016/12/12/sunset-geometry/

...might be easier for me to understand if I could use Haskell to implement the wedge and geometric product operators on an algebraic data type describing the scalar/vector/bi-vector thingy. There is probably an applied vs. pure thing here as well. My motivations for investigating geometric algebra is to see if geometric algebra makes synthesizing mechanical linkages easier, whereas maybe most expositions on geometric algebra are focused on teaching geometric algebra to advance the state of geometric algebra. That's probably a long winded way of saying that mathematicans are writing for mathematicians (whether by design or accident). I suppose I should re-read Mindstorms again, but this time in the context of adult learning.

⬐ sn9

I'm not sure if this is what you're looking for, but I've had this book on my wishlist for a quite a while and it seems to fit: http://www.geometricalgebra.net/

⬐ GregBuchholz

Yes, that looks to be exactly the type of thing I'm thinking of. Thanks.

⬐ GregBuchholz

I also what a running commentary would do for authors. Would they get ideas for improving their next paper, by looking at what had people confused? Surprised by who is reading their papers (especially those outside of their field)? Would they merely be horrified by YouTube style commenters?

⬐ kmill

That is a question you can ask https://math.stackexchange.com/

Unlike mathoverflow, it is meant for every kind of math question below research level.

(Regarding $\to$ vs $\mapsto$, I think of it as type-level vs lambda expression. I think you can find it in any introductory abstract algebra book that assumes you still need to learn a thing or two about functions.)

In my experience, it seems the usual way people in the math community resolve these issues is to ask an expert, or at least a knowledgeable grad student.

⬐ binarymax

Based on this post: https://news.ycombinator.com/item?id=13951399

...and my comment: https://news.ycombinator.com/item?id=13951623

...I thought I would just submit the book to root. Highly recommended.

I bought this book [1] a couple years ago to help with the notation, and it's awesome. I've been able to walk through papers that I never would have understood without this rosetta stone.

[1] https://www.amazon.com/Mathematical-Notation-Guide-Engineers...

⬐ badtuple

Thank you! I looked for something similar a while ago and came up empty. Whenever I asked math friends the answer was always "there's too much variation so a book couldn't tell you everything", which is probably true but even common things would help.

Someday I'd love to see a similar thing that's simply an operator to function index where you can read in code/pseudocode what an operator does on a (bounded for ease of reading) datatype.

⬐ binarymax

A tool that parses equations in CS papers and outputs pseudocode is an amazing idea!

⬐ fdupoo

Thanks, I'll be checking this book out ASAP

⬐ tucaz

Thank you! I got to the comments to find exactly something like this.

About the post, though, it would be way more constructive if the author would propose a way for people to learn what their lacking instead of just complain about it.