FAQ - Frequently Asked Questions
Me and my webpage
Who are you?
Why are your papers so boring?
What is the copyright status of your papers?
What software do you use to draw your graphics?
What software do you use to draw your commutative diagrams?
What are PS files and what am I supposed to do with them?
What is the QEDMO?
Tell me of some good online sources for elementary geometry.
Tell me of some good books on geometry.
Tell me of some good online sources for inequalities.
Tell me of some good books on inequalities.
Why are you not active on the MathLinks forum anymore?
Please delete/edit/move/merge some MathLinks post for me!
Please give me the IMO Shortlist [insert year of last IMO here]!
Can you solve the following problem for me?
Who are you?
From 2006 till 2011, I have been studying mathematics and computer science at the Ludwig Maximilian University in Munich. I have finished my diploma thesis in July 2011.
Since September 2011, I am a graduate student at MIT, Cambridge (MA), advised by Alexander Postnikov.
I was born in Moscow in 1988 and have moved to Germany in 1996. I have spent my school years in Münster and Karlsruhe, Germany, participating in mathematical olympiads like the Bundeswettbewerb Mathematik, the Deutsche Mathematik-Olympiade (both German mathematical competitions) and the International Mathematical Olympiad.
Have won first prizes in the 1st Rounds of the Bundeswettbewerb Mathematik 2001-2006, as well as in the 2nd Rounds of the Bundeswettbewerb Mathematik 2003-2005 (where I gained third prizes in 2000 and 2002), and became Bundessieger 2003, 2004, 2005 and 2006. Participated in the Deutsche Mathematik-Olympiade since 2002, and gained a 1st prize in the 41th olympiad 2002 (Hamburg), an honorable mention in the 42th olympiad 2003 (Bremen), a 2nd prize in the 43th olympiad 2004 (Essen) and 1st prizes in the 44th olympiad 2005 (Saarbrücken) and the 45th olympiad 2006 (München). Silver medals in the 45th IMO (International Mathematical Olympiad) 2004 and in the 46th IMO 2005, and gold medal in the 47th IMO 2006.
My current field of interest is algebra, especially constructive algebra, representation theory and combinatorial algebra (or algebraic combinatorics; this includes Hopf algebras). I occasionally still spend some time on olympiad mathematics (mostly combinatorics).
Why are your
papers so boring?
I guess this is either due to the subject or to the length of my papers.
As for the subject: This website (particularly its geometry part) contains a lot of stuff I have written since 2002 (when I was 14). Some of it is pretty much junk, some was posted just in order to answer some people's questions, some other notes were written out of boredom... don't expect to find anything sensational here.
As for the length: I am trying to keep my proofs as detailed as possible - not only in order to make them understandable to less experienced readers (as far as this is possible - some of the proofs still assume a rather advanced background), but also to make maximally sure they have no flaws - mistakes often hide in "trivial" or "left to the reader" clauses. As a consequence, a proof that takes 1 page in someone else's writeup often takes 4 pages in mine... But let me hope that these 4 pages won't take 4 times as much time to read as someone else's 1 page! In fact, if you are experienced in the respective fields, you might be able to speed-read much of my notes anyway.
What also boosts the length of my geometry notes are the many big graphics. I believe that in times of harddisks with terabytes of storage space, some additional 30KB coming from more (vector!) graphics in a geometrical text are not much of a waste.
What is the
copyright status of your papers?
Every file which is
1. hosted on this webpage -- i.e., its URL begins with "http://web.mit.edu/~darij/www/" or with "http://www.cip.ifi.lmu.de/~grinberg/" --, and
2. is hyperlinked from an .html (or .htm) file on this webpage, and
3. the word "[Prop]" does not appear right in front of the hyperlink that links to it
is public domain, i. e. you can use it in whatever way you want without asking me for it.
This is not an invitation to plagiarize, but plagiarism is not about copyright anyway. The reason for condition 2. above is to exclude "secret" files which are (usually temporarily) hosted on my website (e.g. to exchange them between my different machines). Condition 3. is mainly meant to deal with joint papers which have not been fully written by myself. I am a friend of GPL, LGPL, CC and the likes, but I think they are overkill when applied to mathematical writing.
My posts on the MathLinks forum, the PEN forum, the Hyacinthos newsgroup and in other internet resources are public domain as well,
with the exception of:
- quoted text (text inside "Quote" tags);
- attachments to posts (some of these are public domain, some aren't);
- posts on MathLinks beginning with the sentence "The author of this posting is:" (in fact, these are posts made by others which were lost during a hacker attack on MathLinks, and which I reposted because I happened to have backups of them).
What software do you use to
draw your graphics?
I got asked this several times. Unfortunately, the answer is unlikely to help anyone.
(Note - As of 2011, this answer won't be of help even to myself, as I don't have MS Word anymore. But as I am not doing geometry anymore, I don't care.)
First, my notes are written with Scientific Workplace (SWP) - a (commercial, and, for its quality, way overpriced) graphical LaTeX user interface. It generates somewhat messy LaTeX code, with a few additional features - the one I use is the ability to include WMF vector graphics.
The graphics are drawn with the dynamic geometry software Euklid DynaGeo by Roland Mechling. As far as I know, this software is distributed in German only (and being written for school use mainly, it is not even the best choice). Then, through the Windows clipboard, these graphics are either directly exported into SWP as WMF, or first edited in MS Word and then exported into SWP as WMF.
As you could have guessed, this way of handling graphics is very prone to bugs, and I would not recommend this to anyone, even in the unlikely case you have both SWP and Euklid DynaGeo installed on your computer. I would sincerely like to know a better way to get geometric sketches embedded into TeX files in a vector format (please don't tell me about bitmap-based solutions, I don't like pixeled lines).
What software do you use to
draw your commutative diagrams?
I just use the (rather standard) Xy-pic package. See a short introduction on wikibooks and J. S. Milne's tutorial.
If you find its syntax somewhat too spartan, you can try also try out Michael Barr's diagxy package, which provides a kind of UI for the \xymatrix command.
See also J. S. Milne's page for a list of other diagram packages.
What are PS files and
what am I supposed to do with them?
Some papers on this site are downloadable in PS (= PostScript) format only. These are notes I have written some years ago when I wasn't able to convert from TeX to PDF yet. You can view PS files under Windows by installing the following two programs (in this order): -- Being not experienced, I can only hope that the below instructions will work. --
You won't ever have to run Ghostscript (it just needs to be
will open PS files in either GSView or SumatraPDF.
Note that SumatraPDF can also read most PDF files (I haven't seen a mathematical paper that SumatraPDF couldn't read) and is pretty fast at that (I personally use SumatraPDF as the default viewer for both PDF and PS). GSView can also read PDF, but it misses a lot of features like antialiasing.
What is the QEDMO?
QEDMO stands for QED Mathematical Olympiad. The QED is an organization of German mathematical olympiad participants based in Bavaria who organize meetings and seminars for each other. From late 2005 on, some of these meetings feature a math fight (an oral mathematical contest, with two teams solving questions and debating the solutions in front of the blackboard) called the QEDMO. The problems are of varying difficulty (some very basic problems occur on every QEDMO, but a few of the problems have the level of an IMO problem 3). These math fights are usually organized by Daniel Harrer and me, with problems partly taken from different sources, partly invented by ourselves (Peter Scholze has also done some work here).
Until now (June 2007), four QEDMO's have been performed. Proposed solutions for the number theory and combinatorics problems are usually written by Daniel Harrer, and those for the geometry and algebra problems are written by me. The former will be avaliable as soon as the QEDMO gets an official website; the latter are, upon completion, downloadable from the QEDMO section of my website. However, all of these solutions are in German. If you are searching for solutions in English, you can try searching for the problems on the MathLinks forum.
However, you can download the statements of the problems in English. I have tried to retrace the sources of the non-original problems, but this turned out more difficult than I expected.
Tell me of
some good online sources for elementary geometry.
Please visit the links section of this website.
[I will be glad to know if you have good links that can be added to this section!]
Tell me of
some good books on geometry.
I hope you mean elementary geometry (as opposed to topology, differential or integral geometry which are absolutely different fields of mathematics).
First, please visit the links section of this website to find some online literature. It has the advantage that it is free and doesn't take time to ship. You can learn a lot from the Cut-the-Knot website and from Kedlaya's Geometry Unbound. Leites' translations of books by Victor Prasolov are invaluable to a problem solver who wants to get better in geometry.
Now, if you really want
books in the classical meaning of this word (as in: these things
printed on paper, offline, without hyperlinks...), the first choice is
H. S. M. Coxeter, Samuel L. Greitzer, Geometry Revisited
(this one has been printed several times, and as far as I know, the editions only differ in the solutions to the exercises - the newer ones have partly better solutions). The first three chapters of this book contain some real common knowledge on triangle geometry and radical axes theory. However, the "introduction into projective geometry" chapter is anything but an introduction into projective geometry, and the way inversion is introduced is far from complete.
The next textbook is
Nathan Altshiller-Court, College Geometry.
This has been reprinted in 2007 after having been elusive for a long time. It contains nearly all plane geometry you might need on contests.
Along with this book,
Roger A. Johnson, Advanced Euclidean Geometry
has also been reprinted. While I would not recommend this for olympiad training, it can be helpful for a more serious study since it contains a number of lesser known results.
Then, there is
Ross Honsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry.
This one is really fun to read if you are into elementary geometry. Much of the content can help you in mathematical olympiads as well - though, for an IMO gold medaillist with focus on geometry, this one will be rather like a collection of simple exercises (which can still be of use).
I have now put up a page for errata in these three books (some other books may also be included).
Unfortunately, this is pretty much all books I can recommend - apart from the (also rather few) German and Russian ones I won't itemize.
Tell me of
some good online sources for inequalities.
Here is some random stuff I found useful. In fact, I have never learnt inequalities systematically in online sources - most of my basic knowledge comes from the German IMO training, and the rest is experience from solving MathLinks problems and reading others' solutions.
Thomas Mildorf has a nice script on inequalities. (A newer version used to be at Mildorf's MIT home page, but that is now offline.)
Hojoo Lee is rather known for his "Topics in Inequalities".
Kiran Kedlaya has another text similar to the two above.
This MathLinks topic is partly of interest, and the whole Inequalities Theorems&Formulas section has a number of interesting discussions, along with tons of spam.
If you read German, Robert Geretschläger has his script as well.
Anyone knows more sources? Just tell me...
of some good books on inequalities.
There are several books by the (Romanian) GIL publishing house on olympiad-style inequalities. Two of them are in English. Please don't ask me how to order books published by GIL from outside Romania - apparently this has not been organized smoothly yet :( . Let me make some words about these two books:
Vasile Cîrtoaje, Algebraic Inequalities - Old and New Methods, Gil: Zalau 2006.
This one is 480 pages long and features many interesting tactics and examples on solving inequalities. Unfortunately, you are not likely to enjoy all these 480 pages, because many of the modern methods for solving inequalities include applications of calculus and involved computations. However, a lot was done to keep these ugly parts at a minimum while keeping the whole power of the new methods.
The RCF ("right convex function"), LCF (guess what this means) and EV (equal variables) theorems as well as the AC (arithmetic compensation) and GC (geometric compensation) methods provide a means to solve >95% of olympiad inequalities using rather straightforward - not nice, but doable - computations. All of these methods are extensively presented with numerous examples. A short chapter underlines applications of the (underrated) generalized Popoviciu inequality. Finally, and - in my opinion - most importantly, a lot of exercises with solutions are given which don't require any strong new methods, but just creative ideas and clever manipulations.
Pham Kim Hung, Secrets in Inequalities (volume 1), Gil: Zalau 2007.
This one has 256 pages, and is remarkable for mostly avoiding computations. Numerous creative ideas can be found here - I was particularly surprised about some of the applications of the Chebyshev and rearrangement inequalities. Besides, a good introduction into the applications of convexity is given. I would recommend this book to olympiad participants who look for challenging problems and intelligent techniques without the aim to be able to kill every inequality.
Why are you not active
As of 2010, I have moved on to advanced mathematics. This doesn't mean I am not doing elementary combinatorics once in a while, but I am not that centered on olympiad problems anymore. You will more likely find me on MathOverflow asking and answering questions. I still do roam MathLinks from time to time, mostly the Linear Algebra and Superior Algebra subforums.
If you are here for my PEN (Problems in Elementary Number Theory) solutions, you can find the source code of my (relevant) posts here.
delete/edit/move/merge some MathLinks post for me!
Okay, give me a link to your post. However, please note that
- I am never going to remove any mathematical content without a very good reason. When you post something on MathLinks, you are giving it away to the community and you should not be able to take it back again. (And experience shows that people who want their mathematical posts deleted often happen to be cheaters who want others to solve an olympiad problem for them and then to have it deleted in order to cover the tracks.)
- I am only a moderator in the Olympiad section (minus Inequalities), the College section and parts of the National Olympiads subforum. This means that, among other things, I can move topics from the Olympiad section into Pre-Olympiad, but I cannot move topics from Pre-Olympiad into the Olympiad section.
Please give me the
IMO Shortlist [insert year of last IMO here]!
Chances are high that I don't even possess the Shortlist.
However, even if I do, I am not entitled to distribute it further.
Most people who ask me about shortlists do know pretty well why these are kept confidential until the next IMO. For anyone else: The Shortlist of year t contains the problems that were "almost" selected for the IMO of year t. There are y (usually y is approximately equal to 30) such problems, and 6 of them are finally selected as the IMO problems. The other y - 6 problems are used by various countries in their team selection tests for the IMO of year t + 1. Therefore, publishing these problems can make team selection in other countries unfair, as some participants will know the selection problems in advance from the internet.
Of course, nowadays everybody discusses everything online, and there are various places where IMO Shortlist problems leak into public access. I, among other training participants, found it fun to hunt down such leaked problems through the internet in my IMO training times - but we were "fair" enough to take them from publically accessible websites only (rather than asking people for them via mail) and to disclose our knowledge to the team leaders (what did not stop us from intentionally creating havoc by doing this as late as 1-2 days before the actual test, so that the whole test had to be rewritten in these 1-2 days... so much for actual fairness). If you are into this kind of games, nothing keeps you from doing your own googling but I won't provide you any undisclosed data.
Wait until IMO t + 1 to find the IMO Shortlist t freely accessible online, most likely with solutions.
Can you solve the
following problem for me?
I sometimes get emails and other messages from people asking me to solve mathematical problems.
Unfortunately, I mostly do not have the time to reply to such messages. If you want a reply, please keep the following things in mind:
- Please post your problem on the MathLinks/AoPS forum (and then send me, by email, a link to the post). This serves three purposes: First, even if I don't reply, somebody else may. Second, the solution (or hints) will be of much more use when posted publicly on the internet. Third, it is the only way I can really be sure that you are not trying to cheat on a contest by letting me solve the problems for you (sorry, but people do try to cheat this way). (Exception: If you want to collaborate with me in writing a research paper, then you can send me the problem via email.)
- My current fields of expertise are linear algebra, Hopf algebras and representation theory. Also I have some knowledge of commutative algebra, combinatorics (enumerative, extremal and graphs; no games) and olympiad-level number theory. I used to be good at elementary geometry (in the plane) and inequalities, but nowadays am not interested in these anymore (exception: inequalities with a combinatorial flavor, e. g. majorization theory). I have pretty much no experience with combinatorial geometry, functional equations, functional analysis, complex analysis, topology (except for algebraic) etc.
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