2021 O L Maths Paper Answers Pdf Download
Clarabella Doom
Kangourou sans Frontières (KSF) is an independent association, whose purpose is to organise the annual Kangaroo contest with the aim of promoting mathematics among young people around the world. Each year over six million school pupils aged 5 to 18 from more than 50 countries throughout the world take part at various levels. Awards are given to the top scoring students per grade at the national level. We decide to provide here a collections of past papers and solutions for those who wish to practice the math problems.
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How much are editing, revising, updating, adding to, etc., part of the "normal" process of process of drafting math papers? Specifically, papers of moderate (10-15 pages) length. I've noticed I tend to do this for several months, and the thought has occurred to me that perhaps I'm being too "fussy" and that I'm wasting time.
I have published over 2300 pages of technical books, and over 1000 pages of technical papers (conference and journal papers), and if there is one thing I am certain (for me, at least) it is this: writing is editing. Far far more time is spent on editing drafts than initial writing. It is inconceivable that I would or even could write any thing technical from beginning to end and not have to edit it many times.
That being said, it is true that a scholar may get caught up in finicky editing rather than more substantive scholarship and thought, so the question arises when to deem a paper "finished." Often a conference publication deadline dictates the point. Occasionally it is the knowledge that a competitor is about to "scoop" you. Sometimes it is the desire to move to a new topic or new paper that dictates the point.
If you keep revising because you think that it is very important that published papers meet certain standards then it is an ethical choice, in a way. You will have to face consequences (publishing less) which may have an impact on your career. But there is nothing wrong in deciding that your contribution to math will come with a few nicely-written papers rather than with a huge pile of drafty ones.
There is also a possibility that you keep revising because you feel unsure about what others may think of you if you submit a less-than-perfect paper. Which is what often leads to obsessive revising, which doesn't sound as positive, does it?
In this case you should confront yourself on this point. There is a chance that after a number of published papers you'll gain some self-confidence and be more relaxed on this point; but there is also the case that at each submission your level of anxiety will increase and this will in time affect your capability of writing good math.
In any case, personally I've found that after 3-4 rounds of revision it is extremely unlikely that my paper will improve. When it happens that I change the wording of a sentence to a new wording and then I realize it's the one I started with I take it as a sign I have to stop revising.
I don't think that you should be asking about what is "normal." You should instead be asking whether your revisions are improving your paper. If your revisions are improving your paper then it's good to make them. On the other hand, there can come a point where your revisions are actually decreasing the quality of the paper. The most common cause of this is that you add things to the paper that don't really belong in the paper and actually clutter it. If you find yourself doing this then you should train yourself to resist the temptation to try to say or do too much in one paper. But if you are improving the paper then it is unproductive to worry whether what you're doing is "normal." Maybe it's not normal, but if what is normal is not good then why be normal?
Unless you have a need to get the paper published asap, I recommend you put it aside for a month or so instead of looking through it repeatedly. When you next read the paper, many of your preconceptions and assumptions will have been forgotten and you will be much more likely to notice things like missing definitions, logical gaps, and sections of proofs that are going to confuse readers.
If you are building your career and have to follow certain steps to do traditional publishing in journals, then you have deadlines forced upon you (unless you have tenure, in which case your paycheck is not so deadline dependent), and that should factor into your process. I am vaguely aware of different styles my advisors used, but they were different people. I imagine both had several papers in the pipe and protocols for when to tweak and when to let go.
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In general, I think that alphabetical order is very common. However, sometimes this should be alphabetical order in other language, and in english translation this order becomes different. For example, take several papers by Vershik and Kerov - the Russian alphabetical order is VK, but in english this is not alphabetical.
My understanding (as someone who hasn't been in this business very long) is that when pure mathematicians co-author a paper, they form a kind of partnership as equal partners, and all credit for everything in the paper goes to the partnership rather than individuals, regardless of what actually happened behind the scenes. As for why:
Giving academic credit for anything other than a novel intellectual contribution to the content of a paper, for instance for securing funding or having a higher professional status (eg a professor vs a doctoral student) is anathema to most pure mathematicians, in a way that it wouldn't be for other scientists.
The culture of humility is particularly strong in pure mathematics. If a mathematician insists on being 'lead author' on a paper, that's bad for his/her reputation among mathematicians, which cancels out the extra credit that would otherwise accrue to a lead author.
It is always interesting when I meet professors in other sciences, particularly biology, to see their reaction when the issue of author names on papers comes up. The last time this happened, I was speaking to a cancer researcher at Harvard medical school. When I told him that author names in math are universally in alphabetical order his eyes got really, really big. He was amazed because he couldn't imagine how you could figure out by such conventions who did what amount of the work and he then explained to me some intricate rules by which researchers in biology determine the placement of author names. I told him that one plus of this alphabetical convention in math is that we don't need to deal with all the games they play in biology about who goes where at the start of the paper.
Editor's note. In the original manuscript the order of the authors was I. Rivin first, C. D. Hodgson second. This was changed in order to conform with the usual custon, adhered to by Inventiones mathematicae, to have the authors of a paper listed in alphabetical order. We regret to have had this modification made without informing the authors and to have overlooked the fact that it entailed the changes stated above."
In the sciences, it is common to use a convention such as that the first author is the principal investigator for the research while the last author is the leader of the research group. That was not the convention used for a paper published 20 years ago today, W. H. Knox, R. S. Knox, J. F. Hoose, R. N. Zare. "Observation of the 0-fs pulse" Optics and Photonics News, April 1990.
A famous (and rare) counterexample is the Rivest-Shamir-Adleman paper onpublic-key cryptography, which gave us the name RSA cryptosystem. Maybesomeone can tell us the reason for this ordering of authors' names.
It seems to me to be common that if one author (call her author A) contributes significantly less then the others, but still enough to warrant more than an acknowledgement, the paper will be attributed to the other authors (in the normal alphabetical order) with an appendix by author A. This seems to me to be a reasonable way of doing things, since first of all the normal alphabetical order is kept and secondly author A gets credit for her work.
My limited experience agrees with Ryan Williams's answer. As an undergraduate, I wrote a paper with my advisor (last name Mills) and she insisted that my name appear first (my last name is Shelly) so that readers would know that I did most of the work. She was actually being quite generous, and I think really she just wanted the publication to benefit me as much as possible. As she said, if people saw my name second they would assume that I helped out with some trivial aspects of the paper.
Placing the authors out-of-order in a mathematics paper makes a strong statement -- that one author has contributed significantly more than another. There are problems with the alphabetical system, and there are also problems with the ordered-by-contribution system, e.g. when authors contribute comparable amounts to a paper, who comes first?
To be fair, the proportion of papers that have authors out-of-order should be contrasted with the likelihood of a random permutation of those authors' names being out-of-order. So, we should disregard papers with a single author. If there's two authors, then there's a 0.5 probability that "alphabetical order" = "ordered by contribution". Then we need to keep in mind that there's fewer papers with 3 or more authors.
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