[HN Gopher] The math exams of my life
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The math exams of my life
Author : lordnacho
Score : 40 points
Date : 2024-01-21 19:19 UTC (3 hours ago)
(HTM) web link (www.andreinc.net)
(TXT) w3m dump (www.andreinc.net)
| ykonstant wrote:
| The topics and problems presented, particularly the Bacalaureat,
| are very similar to older Greek national exams problems for high
| school students (up until the late 2000s I think). Nowadays the
| mathematics problems for the Greek national exams are much
| easier. However, we still insist on rigor and proofs (e.g. proofs
| of continuity, differentiability etc.).
| redrove wrote:
| The fact that I could figure out the writer was a fellow
| countryman just by reading the title of the HN post alone speaks
| volumes about this country's obsession with math.
|
| I went through something very similar to the author (went to the
| best high school and yadda yadda), I then went on to get dragged
| through even more math in Comp Sci. I was fairly good and I loved
| the way of thinking math makes you discover, but I hated the
| grind and my grades suffered as as result, started dropping below
| a 9 at the end of HS and barely got passing grades in Uni.
|
| IMO this system is thoroughly fucked due to how disconnected it
| is from teaching students something that's actually relevant and
| applicable in every day life.
| paganel wrote:
| It depends on the maths teacher on how good or bad one can be
| at maths (I used to be bad at maths before HS because of a
| teacher, I was actually good at maths in HS also because of a
| teacher), even though I agree with you that we have an
| obsession with it, and especially about those Olympics that are
| of no use (I always like to point to people that no matter how
| many "gold" medals we got at those olympics we've never had a
| Fields medalist until now).
|
| What's not told to students, or not instilled into their heads,
| is that, first, maths as taught in uni has no connection to how
| maths is taught in HS, and that's a good thing (there are a few
| exceptions that confirm the rule, meaning HS math teachers that
| "approach" the philosophy of how maths is taught at uni but,
| again, they're very few and far between), and second, the first
| two years of uni are some of the most important years in one's
| education when it comes to his/her future professional life.
| Later on during uni you're sort of specialising, but during
| those first two years you should construct the theoretical base
| for your future career in any field related to maths (which
| covers a lot of today's tech).
|
| You mentioned teaching students stuff that is not relevant, and
| of course that many of my colleagues at uni (Comp Sci at
| Bucharest Politehnica) at the end of the '90s - the start of
| the 2000s had the same opinion, that's why the class that was
| teaching Object Orientated programming applied to Java was
| almost always full (or as full as a Politehnica class could
| have been back then), while the _Matematici Speciale I + II_
| class (I think the Americans call it Algebra I and II, not
| sure, never been there) was attended at some point only by
| 15-20 students out of a total of 100-120. It turns out that
| nowadays matrices and manipulation of matrices (which those
| classes covered quite in detail) is a lot, lot more important
| compared to writing some stupid videos games in Java applets
| (which I think was the subject of a class in like 2002-2003,
| something like that).
|
| Also, because this is an American forum and we're talking about
| how maths is studied in Romania, I'll always remember our first
| year Calculus teacher at Politehnica (mr. Rabanca, a legend in
| his own right if you search for his name on the early Romanian
| web) who was bad-mouthing the American Green Visa Lottery
| system in between talking about some infinite series or what
| have you. Apparently he had won one such visa sometime in the
| mid-'90s, had actually gone to the States only to find out that
| he was unemployable in his field of study there, or at least at
| the beginning, to quote him: "I got there and they asked me to
| mop the floors. Of course I came back". That was a big loss for
| the States, a big win for us.
| nrabulinski wrote:
| > Back in school, I had to remember a few radicals to use them as
| needed. [?]13 was one of them. I have forgotten them by now. We
| also had to learn the algorithm to compute any [?] as needed
|
| That's very interesting. In Poland we also had problems of this
| type, but we were taught to solve them by simply bringing
| everything under the square root and comparing the numbers.
| Definitely resulted in much bigger numbers but meant less
| memorization x)
| georgecmu wrote:
| The comment for that particular problem also caught my eye.
| There's absolutely no need to remember radicals to solve it;
| just square both sides and compare.
| paganel wrote:
| I'm about seven or eight years older compared to the poster (am
| also Romanian) and most certainly we didn't need to memorise
| [?]13, this is actually the first time I hear about it.
|
| I think (and now that I've checked I'm 100% sure) that we knew
| by heart the first two decimals of square root of 2, meaning
| 1.41, and possibly Euler's number (2.71) too, even though I'm
| not so sure about that anymore (this was 25+ years ago).
| crq-yml wrote:
| That problem can be solved with estimation of the roots on a
| number line. It's not the most precise way of calculating it
| but when visualized you can clearly see that the root of 13
| will have a fractional part above .5, while the root of 2 will
| have a fraction below .5.
| gregsadetsky wrote:
| One of my grandmothers, born about 100 years ago in Romania
| (she's not with us anymore), told me many times she was denied
| from pursuing math education because of then Nazi policies of
| "numerus nulus" i.e. the exclusion of jews from public
| universities.
|
| There's a fascinating wikipedia page on the topic of racial
| academic exclusions -
| https://en.m.wikipedia.org/wiki/Numerus_clausus
|
| And related to math exams, this paper of problems that looked
| easy but were quite difficult (and which were given to jews in
| the USSR) is also quite interesting --
| https://arxiv.org/abs/1110.1556
| nomemory wrote:
| Quite a lot Jewish people were influential in mathematics in
| Romania.
|
| https://en.m.wikipedia.org/wiki/Leon_Birnbaum
|
| https://en.m.wikipedia.org/wiki/David_Emmanuel_(mathematicia...
|
| https://en.m.wikipedia.org/wiki/David_Emmanuel_(mathematicia...
|
| https://en.m.wikipedia.org/wiki/Meinhard_E._Mayer
|
| https://en.m.wikipedia.org/wiki/Isaac_Jacob_Schoenberg
|
| And many others.
|
| My grandfather who become a math teacher eventually had a
| Jewish math teacher. So was my grandmother's brother, he had
| lots of Jewish math teachers.
|
| Unfortunately things become bad during ww2, but before that
| Jews were overly represented into teaching math.
| gregsadetsky wrote:
| Thanks for this. My grandmother came of university age in the
| 40s, so this all makes sense.
| matheist wrote:
| The most interesting math exam of my life was my qualifying exam
| for my PhD. It was an oral exam, and I prepared a syllabus and
| gave it to my three examiners ahead of time. At the actual exam,
| we all showed up and they took turns asking me their questions
| that they had prepared relating to my syllabus.
|
| I was expected to solve the problems at the board. They didn't
| necessarily expect me to solve them immediately, but they wanted
| to hear me think out loud and communicate my ideas. There were
| around 5-10 questions total over the course of I think a few
| hours, ranging in complexity from trivia (i.e. memorized facts)
| to computations to proofs. Some of them I found solutions for and
| some of them I didn't, and they assigned me some to solve later
| as "homework" (though they did pass me without it being
| conditioned on the homework).
|
| In hindsight, it was very similar to white-board coding
| interviews, but I didn't know anything about coding interviews at
| the time. I can't really think of any other place such a format
| would be appropriate as a math exam. When else would a paper math
| exam not be sufficient.
| sdenton4 wrote:
| Yes, my math grad student time ws an excellent preparation for
| coding interviews. In addition to the oral exams, I found
| TA'ing was also an excellent preparation. Students show up with
| lots of questions, which you get to solve on your toes at a
| board...
|
| Classes and competitions also generally have an allowed 'bag of
| tricks' from which you build your solutions. White-board coding
| interviews are the same. If you want to do well, you get to
| know what the 'atomic' operations are in your bag of tricks,
| how they combine into useful tools, and how to spot when they
| might be useful in the 'wild.'
|
| Restating/reworking a problem into a form where some tricks are
| more obviously applicable is also a useful skill. These are
| general problem solving skills, which are pretty independent of
| what's actually in the bag of tricks... Draw a picture, try a
| concrete example, identify the pen-ultimate step, etc.
|
| When I give whiteboard interviews, I have a favorite question
| with about four reasonable stopping points. My general approach
| is to work with the candidate until they get stuck, and then
| see how handle being stuck and getting un-stuck. So, even if
| you have trouble with the 'easiest' part of the problem, I can
| still get a good read on the general problem solving skills.
| (And if you sail through to the hardest level solution without
| getting stuck, you're probably worth hiring anyway...)
| belter wrote:
| "As a fun fact, the current mayor of Bucharest, Nicusor Dan is a
| two-time Gold Medalist at the International Mathematics
| Olympiad."
| sdenton4 wrote:
| The famous reform mayor of Bogota, Antanas Mockus, also started
| in math! https://en.wikipedia.org/wiki/Antanas_Mockus
| belter wrote:
| Do we have any mayors coding in C, Java or Python?
| smeagull wrote:
| If a school only accepts students capable of attaining high
| grades, in what sense is that school good? That's no proving the
| school teaches well, it's proof that they're trying to avoid
| having to teach.
| koolba wrote:
| > Between a=5[?]2 and b=2[?]13 which one is bigger?
|
| No need to memorize square roots here. Simply square both sides
| and it's clear that 50 < 52.
|
| If x^2 < y^2 then x < y (ignoring negative numbers...).
|
| More generally, these types of "math tricks" are about solving
| for the answer. Not solving for the parts of the question. It's a
| great lessom for life, especially working in software.
| nomemory wrote:
| Author here, it's probably what I did, but i am sure i also had
| to memorize quite a few radicals, and also multiplying numbers
| up to 40X40 + other tricks to multiply fast.
| koolba wrote:
| Memorized non-integer radicals outside of 2, 3, and 5? Those
| at least come up in geometry.
|
| Any idea where I can get more English questions like the ones
| you've listed? They're quite enjoyable! Though some of your
| translations are a bit off:
|
| > A cube has one of its sides 2cm. The total area of the cube
| is ...
|
| Pretty sure you mean "surface area".
| nomemory wrote:
| The sources are scarce at least for everything that's older
| than 2010, but I did started to collect exercises like this
| from various forgotten places.
|
| I plan to put them into a github repo this month.
|
| Sorry for the translations. I will try to check them again,
| and maybe to some corrections.
| ajuc wrote:
| Is it really still this hardcore math meritocracy in Romania?
|
| In Poland it became gradually less hardcore as 80s baby boom
| passed through universities and at the same time private
| universities started to appear everywhere. Now it's pretty laid
| back comparatively.
| dwrodri wrote:
| I didn't experience this, but I was at dinner with someone who
| had recently emigrated from Russia, so I decided to ask, "What is
| it about the education systems in formerly Soviet domains that
| created such a strong passion for computing?" He answered in two
| parts:
|
| 1. Scholars who might've considered studying literature and
| philisophy might have a hard time competing on the global stage,
| as the Soviet state didn't take kindly to the idea of promoting
| anything that could be perceived as anti-Soviet ideals, even if
| it's for the sake of an academic exercise. Not that the Soviet
| Union was alone in this practice, but this practice in particular
| affected their academic community to the extent that many who
| might've considered literature or philosophy changed their minds.
|
| 2. Trade restrictions between the 50s and 60s with large portions
| of the West created a large demand for semiconductor products on
| behalf of the state, as the USSR understood the strategic
| importance of this technology early on. While trade restrictions
| were gradually relaxed in the decades leading up to Perestroika,
| the domestic industry for computer products had been established,
| similar to China's own semiconductor industry and Deng Xiaoping's
| economic reforms which opened the country to global trade.
|
| This is mostly just the verbal account of one person followed by
| my own personal research, so this is by no means an authoritative
| take. If there are others with more knowledge (acquired through
| research or lived experience) I'd love to hear it, as my
| knowledge of the history of computing has a Soviet-sized hole in
| it.
| nextos wrote:
| > If there are others with more knowledge (acquired through
| research or lived experience) I'd love to hear it, as my
| knowledge of the history of computing has a Soviet-sized hole
| in it.
|
| The famous book _Mathematics, its Content, Methods, and
| Meaning_ by Alexandrov, Kolmogorov, et al. has two chapters on
| computing, which is interesting both to take a sneak peak into
| Soviet-era techniques, as well as to understand the importance
| Kolmogorov and friends gave to the topic.
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