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Ask HN: How did you learn math notation?

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Re: Ask HN: How did you learn math notation?

#91

Post by zwerdlds »

My suggestion to you is going to sound pithy, but its what worked for me: do problems. Lots and lots of problems.

Pick a direction (maybe discrete math, if you're trying to do CS) and get a book (I like EPP, as it is super accessible) and go, in order, through each chapter. Read, do the example problems, and do EVERY SINGLE PROBLEM in the (sub)chapter section enders.

Its a time commitment, but if you really want to learn it, this is one way to do so. IMO finding the right textbook is key.

Re: Ask HN: How did you learn math notation?

#92

Post by kergonath »

readme wrote: post #80

the notation you need to know should be defined somewhere in the book or paper you're reading if it's not, try intuition if that fails, email your mathematician friend and ask don't have a mathematician friend? there's your next goal, go make one.

> if it's not, try intuition

If it’s not, the book is badly written. Most of the time, you can’t rely on a specific bit of notation to be consistent across books or articles. Smart arses who try to impress the readers with their fancy unique notations are the bane of scientists doing literature reviews.

90% of the time, there needs to be a keyword when a symbol is introduced, e.g. “where Λ is the time-dependent foo operator” so you can get a textbook to find what the fuck a “foo operator” is. Then, the first time you spend a day learning what it is, and the next million times you mumble “what a stupid notation for such a straightforward concept”.

Re: Ask HN: How did you learn math notation?

#93

Post by zoomablemind »

>... I'd really like to learn "higher level than highschool" math...

This sounds somewhat abstract, as the math field is vast. If you consider the next level from where you believe your present standing is, I would try to revisit the college-level math which you probaby experienced back in time.

Generally, the textbooks rely on previous knowledge and gradually feed the new concepts, including the math notation as needed in the new scope.

I find it easier to get the feel for the notation by actually writing it by hand. Indeed it's just an expression tool. Also, you may develop your own way of making notes, as you go on dealing with math-related problems.

But in the core of this you are learning the concepts and an approach to reasoning. Of course, for this path to have any practical effect, you would need to memorize quite a bit, some theorems, some methods, some formulas, some applications. Internalizing the notation will help you condense all of that new knowledge.

Picking a textbook for your level is all that is needed to continue the journey!

Re: Ask HN: How did you learn math notation?

#94

Post by Jensson »

throwaway31338 wrote: post #81
pjc50 wrote: post #74

Earlier quoted context omitted.

> because programs can't work without being specified. Someone hasn't read the C spec, with all its specified as undefined behavior. Programs working on real systems is very different from those systems being formally specified. I suspect that if you only had access to the pile of documentation and no real computer system - if you were an alien trying to reconstruct it, for example - you'd hit serious problems.

Undefined behavior isn't a feature. A spec isn't an implementation, either. All behavior in an implementation can be teased-out if given sufficient time. > if you were an alien trying to reconstruct it, for example - you'd hit serious problems. I can't speak to alien minds. Considering the feats of reverse-engineering I've seen in the IT world (software security, semiconductor reverse-engineering) or cryptography (th…

> All behavior in an implementation can be teased-out if given sufficient time.

Can it? Given what? You would need to understand how the CPU is supposed to execute the compiled code to do that. In order to understand the CPU you would need to read the manual for its instruction set, which is written in human language and hence not any better defined than math. At best you get the same level of strictness as math.

If you assume you already have a perfect knowledge of the CPU workings, then I can just assume that you already have perfect knowledge of the relevant math topic and hence don't even need to read the paper to understand the paper. Human knowledge needs to come from somewhere. If you can read a programming language manual then you can read math. Every math paper is its own DSL in this context with its own small explanations for how it does things.

Re: Ask HN: How did you learn math notation?

#95

Post by kergonath »

db48x wrote: post #35
solmag wrote: post #5

Earlier quoted context omitted.

You can also get sufficiently angry and just write out linear algebra books and what not in Agda / Coq / Lean if it pisses you off so much (I've done a bunch of exercises in Coq)

I like the approach they took in Structure and Interpretation of Classical Mechanics, where the whole book is done in Scheme: (define ((Lagrange-equations Lagrangian) q) (- (D (compose ((partial 2) Lagrangian) (Gamma q))) (compose ((partial 1) Lagrangian) (Gamma q))))

I have no idea what the hell that means, and I am quite familiar with Lagrangian mechanics.

Re: Ask HN: How did you learn math notation?

#96

Post by tedunangst »

throwaway31338 wrote: post #81
pjc50 wrote: post #74

Earlier quoted context omitted.

> because programs can't work without being specified. Someone hasn't read the C spec, with all its specified as undefined behavior. Programs working on real systems is very different from those systems being formally specified. I suspect that if you only had access to the pile of documentation and no real computer system - if you were an alien trying to reconstruct it, for example - you'd hit serious problems.

Undefined behavior isn't a feature. A spec isn't an implementation, either. All behavior in an implementation can be teased-out if given sufficient time. > if you were an alien trying to reconstruct it, for example - you'd hit serious problems. I can't speak to alien minds. Considering the feats of reverse-engineering I've seen in the IT world (software security, semiconductor reverse-engineering) or cryptography (th…

All meaning of math notation can be teased out if given sufficient time.

Re: Ask HN: How did you learn math notation?

#97

Post by amelius »

I have a notation problem. I want to write "approximately 24 volt" on my printed circuit board, but I have little space. I could write "≈24V", but the wavy symbol makes it look like it is AC instead of DC. How to solve this without adding more characters or changing my circuit?

Re: Ask HN: How did you learn math notation?

#99

Post by simiones »

wrycoder wrote: post #36
rullopat wrote: post #19

Earlier quoted context omitted.

Sorry I didn't mean to make you work for me, but it's a PDF and I didn't know how to explain better the position (maybe I should have told you the first formula on page X). For you it was a D, for me it was a triangle and I didn't get the meaning of that Dt. Maybe it's just a too advanced paper for my knowledge.

The triangle, or “delta”, is used to indicate a tiny change in the following variable. Let’s say you go on a journey, and the distance you’ve travelled so far is “x” and the time so far is “t”. Then your average velocity since the beginning is x / t . But, if you want to know your current velocity, that would be delta x divided by delta t . The delta is usually used in a “limiting” sense - you can get a more accurate…

I would say that delta is typically used to mean difference of any magnitude (i.e. Δt could mean 2 hours).

Re: Ask HN: How did you learn math notation?

#100

Post by solmag »

db48x wrote: post #35
solmag wrote: post #5

Earlier quoted context omitted.

You can also get sufficiently angry and just write out linear algebra books and what not in Agda / Coq / Lean if it pisses you off so much (I've done a bunch of exercises in Coq)

I like the approach they took in Structure and Interpretation of Classical Mechanics, where the whole book is done in Scheme: (define ((Lagrange-equations Lagrangian) q) (- (D (compose ((partial 2) Lagrangian) (Gamma q))) (compose ((partial 1) Lagrangian) (Gamma q))))

I should really pick that one up some day. It had an inspiring story, I believe the author wanted to understand the classical mechanics and just wrote them out in Scheme.
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