I find that reading anything "mathy" can quickly become hard to follow. Sometimes it seems the authors are being very obtuse by introducing variables and not specifying what they represent (also doesn't help that they are all greek letters which I forget the names of). But regardless, I'd love to be able to read pages of mathematics as easily as I can read pages of source code.
Anyone got tips for that? Is there some sort of bootcamp for learning the language of maths?
I feel the language part can be disentangled from the problem solving part. The same way one doesn't need to be able to come up with brand new algorithms to read and understand the algorithms used in computer science. I don't want math superpowers, just math fluency...
The intro is about 150 pages, and somewhat dense, but with work definitely accessible to someone with little knowledge of mathematics. I wish they would sell it separately from the rest of the book because it's that good, but unfortunately it comes attached to another thousand pages of material you probably won't have a use for unless you get into mathematics research.
I am not sure of any particular source that makes this easy, but the majority of technical things written are written by people who don't really have a reason to have especially strong communication skills, especially communication skills for people that might not be familiar with some of the basics.
Since this is HN --- I actually think this is a business opportunity. People would pay plenty for the best educational resources, at varying times in their life, and having good explanations of things is a valuable resource.
Mathematics is dense. Period.
However, you might be mistaken about language and problem solving being independent.
You can't understand mathematics without doing mathematics anymore than you can understand a complicated program without having a commensurate amount of experience in programming.
EDIT: Apparently the similarly-titled MIT Press book is freely available as PDF. Now that the course isn't currently running, I'd probably prefer the book. https://mitpress.mit.edu/books/street-fighting-mathematics
"Dead Reckoning: Calculating Without Instruments"
I find it to be a little addictive, and sometimes find it a bit hard to stop. I always feel like wanting to improve my skills a little more, become a little faster at it, and increase the number of digits and terms I can handle without making a mistake.
The soroban is a great tool for developing concentration, a memory for numbers, a facility for performing a relatively complex series of steps in a certain sequence, and eventually for lightning fast mental arithmetic.
In Japan, soroban use is taught to young kids, who after a while develop enough proficiency not to need the physical device any longer and can perform the calculations on an imaginary soroban, and eventually can achieve some really amazing feats of mental arithmetic, such as this example from their national competitions: 
Forward to the 1'45" mark in the following video for another really impressive display of soroban-trained mental math prowess: 
Finally, there's a great subforum for mental math in the Art of Memory Forum: 
 - https://en.wikipedia.org/wiki/Soroban
 - https://www.youtube.com/watch?v=Px_hvzYS3_Y
 - https://www.youtube.com/watch?v=7ktpme4xcoQ
 - https://www.youtube.com/watch?v=rPTKZ4PLkMc
 - http://mt.artofmemory.com/forums/mathematics-and-mental-calc...
What was really weird was doing the abacus work, moving beads, all in chunks of 5 or 10, and then looking at the final results without any preconceived notion of what the results were. Totally fresh eyes as I counted the final set of beads.
The manual movement was one thing, but the motion didn't cause me to visualize "numbers" as I understand them. Completely separate pathway to the same answer.
This can be more generally thought of as using exponentiation.
12 * 8 = 12 * 2^3
Using the more general rule, again.
12 * 9 = 12 * 3^2. Or 12 * 3 * 3.
12 * 8 = 10 * 8 + 2 * 8 = 96
12 * 9 = 12 * 10 - 12 = 108
That said, most of the things in the article are things I've picked up more or less automatically. If you could train yourself to do them, I think it could help, but I think most people who do them just figured them out on their own.
I disagree entirely with "Memorizing building blocks", mostly because I see the huge dichotomy among students between those who try to memorize and those who attempt to learn concepts. Those who memorize do worse on tests, because if they forget, they can't just apply their knowledge. They also seem to forget the material faster after the class. Those who learn the concepts are usually okay, even if they forget a detail they can often work it out. I also think that someone who needs to memorize that 3/5 = 0.6 is unclear on some deeper concept somewhere.
Sure. It's just another tool.
> I disagree entirely with "Memorizing building blocks", mostly because I see the huge dichotomy among students between those who try to memorize and those who attempt to learn concepts.
Do you find the best students are fluent with the techniques and have an understanding?
It would seem to me, spending time pondering meaning also has the benefits of remembering 'building blocks'; because they're the primitives involved in the struggle for understanding.
Being fluent with techniques is not strictly necessary, but is generally important and can aid in helping to understand concepts by demonstrating relationships. But a student who prioritizes concepts is probably better off than one who only understands techniques.
My objection to the article is that it is advocating memorizing facts. Figuring out that 3/5 == 0.6 is trivial if you already understand the concepts and knowing that 3/5 == 0.6 is pointless if you don't know what it means.
 - Anecdotally, I breezed through calc 1 in high school. First done with every test, always aced those tests, never studied. Had no idea what I was doing, because I was just memorizing and applying rules. Knowing just the techniques was equivalent to knowing nothing.
I suppose so. If you wrote some code to carry out the rules, you wouldn't say the computer knows anything.
1111128 = 1111118+8=888896
Sorry for being irrelevant.
Asia is a big continent, what kinda countries or areas are you talking of?
Chinese and korean are more serious about teaching in my perspective. It's probably not that bad that Thailand's education system is crappy, it's more relax.
You can quickly gain a kind of "Rain Man" reputation if somebody mentions a date and you instantly mutter "Saturday". But it's just a matter of adding three numbers and taking the remainder modulo 7.
0 Oct, Jan
3 Feb, Mar, Nov
5 Sep, Dec
6 Apr, Jul
Other examples: D-Day, 6 June 1944, was (44+11 == 55 == 6 mod 7 for the year) + 4 (Jun) + 6 == 16 == 2 mod 7 == Tuesday.
The only twist is needing to subtract 1 from the result for dates in Jan and Feb on leap years, since those dates precede the leap day.
This one's my favorite, and I like to combine it with doing all borrows/carries in a separate pass, which means intermediate "digits" are sometimes no longer 0..9.
For example: 78 + 89 = 7+8|8+9 = 15|17 = 1|6|7 = 167
Actually, I believe it just depends on ways which either fits your brain or you gets used to it.
Truth is I don't know how I came up with it, I think I was just lazy.
I don't think of these as "tricks", just "how I do it in my head".
This is awesome book, it teach you all sort of tricks from 3 digits addition to 3 digits multiplication.
I know its written for school teens, but still pretty helpful life skills.
While it's a great story and is very entertainingly written, as is typical of Feynman, I don't think he was being very fair to the merits of the two approaches to mental math -- his own vs that of the soroban.
Feynman clearly hadn't done any research on the merits of the soroban method, he just had this single run in with a random soroban salesman. From this one experience, and without very much thought on the subject, he just kind of dismisses the method almost out of hand. Such offhand dismissals are unfortunately also pretty typical of Feynman regarding subjects he is mostly ignorant of and has little experience with (such as his dismissals of philosophy in other talks).
In the story, the random soroban salesman, who clearly hasn't even very much proficiency with the soroban (as evidenced by his need for a physical soroban, vs soroban-trained practitioners who no longer need the physical device but can apply the soroban methods in their head) is matched against one of the greatest physicists in history, a Physics Nobel Prize winner who has advanced math training. That's really not a fair match.
It would have been great to see how Feynman would have fared against someone like this guy:  or against one of the national soroban competition winners, or against a top mathematician or physicist who was soroban-trained. That would be a fairer match and the results more indicative of the merits of the two approaches.
 - http://www.ee.ryerson.ca/~elf/abacus/feynman.html
 - https://www.youtube.com/watch?v=rPTKZ4PLkMc