101–110 of 148 posts
Other people have listed great books and resources. What I don't see, however, is to ask a friend. Find someone who is familiar with the notation, if not the material, and ask questions. You'll likely get a more clear answer.
You say: > What I don't see, however, is to ask a friend. From https://news.ycombinator.com/item?id=18510564 : > ... get a few examples, and ask some friends, colleagues, or on-line forums ...
I think you've got this backwards. You don't need to understand the notation, you need to understand the math. If you don't understand the notation then you probably don't understand the math in the first place so learning notation won't help. Learning how a matrix is written is useless without understanding what a matrix is. You need to find out exactly what type of math is used in the paper and learn that. Learning…
1) Logical quantifiers: ∃ ("there exists") and ∀ ("for all"). Quantifiers can get confusing when they get strung together. I like to think of them as challenge-response games. For example, your real analysis textbook asserts that a function f is continuous at x if ∀ e>0, ∃ d>0 such that if |x0-x|disprove and the ∃ player (Daniel) trying to prove the statement. Since the definition asserts "∀ e>0", all Ella needs is a single counterexample e' such that no matter what d'>0 Daniel chooses, the condition is false. Or mathematically written, Ella's objective is to prove "∃ e'>0 such that ∀ d'>0, the condition doesn't hold." Notice how taking the converse flips the quantifiers.
2) Set notation: S = { x∈R | 0<x<1 } reads as "S is the set of real numbers that are between 0 and 1". You can also think of this as {x ∈ domain | filter_condition(x,y,z,...)}. You'll see many mathematical objects represented as sets, so it's pretty important to know how sets are defined.
Okay, if you're reading a physics paper and you encounter 'c', that's probably the speed of light, 'm' is likely mass, and so on. There's context and culture involved, and that's usually fine.
But if you're wading through something less mainstream, say some denotational semantics or queuing theory, and the author starts dragging in undefined alphabet soup, what's the reader supposed to do? Sometimes the answer is to get more culture in the subject area, or read some of the same author's previous papers, or just forge ahead in the paper and hope that understanding will come anyway.
Don't get me started on formula that use single character variables nearly everywhere, but have zingers like 'hz' -- which is not 'h' times 'z', but Hertz. If math is supposed to be so rigorous, how come there's no agreed upon grammar, with reasonable ways to extend it to specialized domains?
Many papers, especially im engineering, use a lot of mathematical notation that doesn’t benefit the reader, it’s just there to show off. Often, there are mistakes in there too, because no reviewer typically goes to the trouble of checking every single equation. When reading a paper, don’t get bogged down by all the equations. Read it once or a few times before getting down to that level. Often it’s helpful to read other descriptions of a particular algorithm, for example in a student’s thesis, which contain more detail and contextualize some of the math.
While you may not find this comment particularly helpful, as I’m not pointing to a guide or something, you could take away from it that it takes practice and that one shouldn’t be discouraged when you don’t understand the math in a paper, as I guarantee you there are maths professors that couldn’t make sense of it either.
You learn while studying math. There is no way around it.
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…
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.
I love how there are these two parallel threads going in HNville: (1) COLLEGE SUCKS BURN IT DOWN and (2) "I'd like to learn complex things like machine learning and math that take more than reading 5 blog posts to master, how do I do it"? Sometimes this place just cracks me up. I honestly think the answer is pretty simple: go to college. It doesn't have to be expensive. Take a community college course in calculus or…
The paradox disappears when you stop anthropomorphizing HN and remember that a community of millions of people has a lot of different subgroups.
Most days I appreciate its uniqueness, but I find myself rolling my eyes at least once/week at some of the comments here.
Here are some of what I'd call the "HN tropes":
"Oh that hard thing? It's not that hard. I have never worked on that problem before, but can surely replicate that entire system in a week, because everyone working on it is an idiot and doesn't know what they're doing."
"That traditional human behavior (e.g. marriage, buying a house, going to college)? I can squeeze 5% more efficiency out of life by completely ignoring the reality of human behavior, because my superhuman, almost robotic levels of conscientiousness and diligence that make it a horrible idea for 99% of the population, somehow don't apply to me. I beat the averages in everything I do." (I see that a bit in this thread. See also: playing games with credit card balance transfers, renting vs. buying "because I'll save the difference", trading options and thinking you won't fall into well-known behavioral traps)
"Hard problem from another discipline (finance, accounting, medical science)? I can reinvent a clever algorithm ten times smarter than that, despite my complete lack of domain knowledge. No problem."
"Incumbents are stupid. Anyone can beat them if they're clever."
"I don't need to read history. Humans are irrelevant, if we just apply the right combination of game theory, economics, and some clever code, we can fix any problem. Politics and governance are stupid, avoidable problems if we just used the right system." (I see this a lot in Bitcoin discussions)
I see these with alarming frequency here. You can certainly say I'm painting with too broad a brush but I've been here since 2009 and it comes up over and over. More than anything, I just laugh at it these days (not get mad).
Earlier quoted context omitted.
Don't listen to this asshat. There are 2 great resources for self education on Math. https://www.encyclopediaofmath.org/index.php/Main_Page and http://people.math.sfu.ca/~cbm/aands/abramowitz_and_stegun.p... Have a nice day.
Happy Thanksgiving to you, too.
Earlier quoted context omitted.
The paradox disappears when you stop anthropomorphizing HN and remember that a community of millions of people has a lot of different subgroups.
That is true. But you also have to acknowledge that this community isn't in any sense, "normal" (representative, average, etc) Most days I appreciate its uniqueness, but I find myself rolling my eyes at least once/week at some of the comments here. Here are some of what I'd call the "HN tropes": "Oh that hard thing? It's not that hard. I have never worked on that problem before, but can surely replicate that entire s…
Seriously: do you routinely see eye-rolling comments that don’t get downvoted or rebutted? I don’t. That’s what I like/appreciate about this place; yes you’ll get the tropes you mention, but you’ll invariably get an articulate response that points out the weakness or conceit.