I'm trying to improve my knowledge of Math by getting better at Discrete Math, Linear Algebra, and Calculus. I'm putting extra focus on Discrete Math since I believe that is most useful for programming contests.
Everyone knows that Russians excel at Mathematics, so my question is, how do you guys learn Math? I know that Russian schools have a pretty rigorous Math curriculum, but besides that, do you solve hundreds of Math exercises or what is your secret? :)
Edit: Of course, this question also applies to countries that were part of the Soviet Union.
I'm not Russian, but as Finland is practically a part of Russia (at least in the near future) I think I can help you a bit. Not all Russian schools have excellent math students, nor do all Russians excel at mathematics. The trick is to enable those who are gifted to concentrate at maths, one doesn't simply learn mathematics without working hard.
That's interesting, I'm from Mexico and 90% of gifted kids don't recieve proper education/get encouraged, most are even put down "You shouldn't move faster than everyone else". I think we should learn something from you guys :)
Well, then I guess Mexico should become a part of Russia as well :D
Winter weather is a joke in Mexico, we don't know what snow is and 10-15°C is considered very "cold" here. Not sure if Russians would like that.
Don't worry, you'd get used to cold weather :D
Ramanujan didn't get used to much warmer climate of Britain...
BTW, a large fraction of Russians say they'd wish to move into milder climate. My father is a good example.
That is quite true! I believe the percent of math-talented here is not significantly greater than in any other part of the world.
I myself love math, but math does not love me!
Some schools really give basics of calculus before universities etc, but that is not the rule. And of course not pupils are glad to learn all they are being taught to.
So concluding — with math and programming and everything it is quite important what you yourself can learn, not what anyone else could potentially teach you. Though of course having a good teacher is an advantage. Luckily now we have internet which is if not a teacher, but at least an assistant and great library.
Do you think copying Russian society customs e.g. to sub-Saharan African country would produce the same performance in programming contests?
I don't see how Finland could become part of Russia. Russia is better at programming contests, but seems to decay anyway. It's more likely that China will come as world's leading power.
If you're talking about high achievements — the secret is just in early beginnig. And another reason is that we have many books of famous authors from our Soviet past, so it shouldn't be a problem to learn something by yourself (but it was a problem for me). I don't have an idea of who is the next generation of our education. As it seems for me — we don't have them, but I may be wrong (I hope)... Time will show. And of course, our most important secret, you won't believe — vodka vodka, boris eltsin, balalayka!
In times of Soviet Union there were a period of time when pupils go to school 6 days a week. And there were big amount of lessons of fundamental sciences (math, geometry, physics). And the status of discipline were higher than now: it means that atmosphere were better for child and pupils who wanted to learn. Comparing to later times and to nowadays there are less discipline during a lessons so they are less productive. I mean "discipline" is: when teacher controls the process of participants in class, and use force or other methods (earlier — they were legal, nowadays — some — illegal). If there are some pupils who troll or often disrupt ether, motivation of teacher usually falls down, and that lessons become unproductive.
In Soviet times some schools were strengthened on maths/physics, so it was a good opportunity to choose stronger teaching environment. In nowadays (I will talk about Lithuania) there are schools and gymnasiums (starting from grade 8 / ~15 years). Gymnasiums usually have stronger teachers and stricter discipline with rules of behavior, and pupils who are stronger and more motivated to learn — they take exams to join to gymnasium. The trade-off of this good opportunity sometimes is that someone must wake up earlier to reach that gymnasium in distance.
There are some activities which can improve love to math: olympiads of mathematics (each school can participate), additional "school" for pupils interested in maths (they register to school, get pdf material and problems, solve them and send to mentors), popular math competitions ("Kangaroo" once a year).
From Soviet times till now there are no big differences in school-books of math: (nowadays there are less math), there are some theory and big lists of problems, which you solve at classroom and at home as homework. That mean that you had (and have) to practice a lot. And when I was going to school (decade ago) we usually had about 5-6 academic hours of math a week. Not using calculators also, however no extensive practice on mental calculating. Our physics and chemistry problems also contained some math — so if you were in love to chemistry, you liked to understand math.
It the times of Soviet union there were popular books for children and pupils and students, which could increase love to fundamental sciences (for example: Kvant, Attractive smth series, ... ; In independent Lithuania there was "Alpha & omega")
In Soviet union pupils were learning derivatives being at about 1-4 years younger than nowadays. Nowadays it seems that average level of maths are long time decreasing in Lithuania. But the best pupils can have some awards, go to international olympiads, and have nice teaching environment in best gymnasiums.
I think that secret was consisted of: culture of math (how your math skills are accepted by others), culture of passion of being more clever and understand more, good school discipline and environment, going to school culture (instead of early going to work), much time trying understand theory and many practice of solving problems, maybe patriotism.
But I believe that you can invent math by own and become in love with it without any background.
"And when I was going to school (decade ago) we usually had about 5-6 academic hours of math a week. Not using calculators also, however no extensive practice on mental calculating. Our physics and chemistry problems also contained some math — so if you were in love to chemistry, you liked to understand math. It the times of Soviet union there were popular books for children and pupils and students (...)"
I guess many people could get confused by your post:) If you went to school a decade ago, this was already far far from the soviet times, actually we were already a EU member in 2004. So I hope you won't mind me jumping in, as I have actual experience of attending the school in soviet era.
And one additional fact that I must mention is, that as kids, we didn't have much to do. There were just 3 TV channels, only one of them broadcasting in our language. 30 minutes of domestic cartoons were shown each day, from a limited set which was rotated on a few month basis. Most of the remaining stuff broadcasted was basically some propaganda (which was also included in some of those cartoons).
Of course, in late eghties the internet was not widespread globally yet, but even if it had been, it would have surely been severely restricted by the soviet regime.
So, the kids spent lots of time outside (during the good weather), or they had plenty of time for some kind of sports, or for studying something with great dedication. Also, I have to admit that the education system was really supportive in all of this stuff.
My point (taking it a bit to an extreme) is that if you are in jail, and if you are a bright and motivated person, you really have plenty of time to become proficient in your area of choice.
Contrasting to these days, kids now have unlimited options to spend their time in an undemanding ways: brain overwhelming sources of media, infinite "asocial" networks, life destroying online games, finding friends around the world, etc. It must be really challenging to filter out through all this noise and to focus on some single demanding area.
This is probably the other, opposite end of extremity. If you have freedom, you are responsive for yourself and you must control the choices that you make. Because no one else is going to do control you.
Given all these off topic thoughts, I would really not choose to go back to that kind of jail, ever.
> implying we don't live in a jail right now (1984)
Education has been going down the drain for quite some time, so I don't find it surprising if a lot of Soviet practice was still left 10 years ago and has almost completely declined since.
Good
Yes, those who excelled in math, has solved hundreds of problems. You can find examples here: https://translate.google.com/translate?hl=ru&sl=ru&tl=en&u=http%3A%2F%2Fmmmf.msu.ru%2Fcircles%2Fz5%2F
It doesn't work this way. You should have been eating more buckwheat where you were a kid. Russia wins in programmers contests, why? Russia is World No. 1 in buckwheat production. Ukraine, Poland, China are major buckwheat consumers too, and buckwheat pasta (soba) is Japan's national dish. Average Mexican suffers quality malnutrition and eats too many corn, that's "empty calories".
I, personally, do not consider corn to be even worthy of feeding cows.
I don't get it. Why my comment has been upvoted?