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 are PS files and what am I supposed to do with them?

What is the QEDMO?
Please tell me of some good online sources for geometry.
Please tell me of some good books on geometry.
Please tell me of some good online sources for inequalities.
Please 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?

Since 2006, I am a student of mathematics at the
Ludwig Maximilian University in Munich. 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 and 2005. 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.

Now I am mostly busy with studying university mathematics, with a particular passion for (but alas, not a particularly good understanding of) algebra, especially constructive algebra. This keeps me from updating my website more often, but I still spend some time on olympiad mathematics.

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 contains a lot of stuff I have written since 2002 (when I was 14 years old). Some of it is pretty much junk, some just stands was posted in order to answer some people's questions, some other notes I have written while I was bored... don't expect to find anything sensational.

As for the length: Yes, I am perfectly aware of the fact that a proof that takes half of a page in someone else's writeup often takes two pages in mine. I am trying to keep the 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 use rather advanced background), but also to make maximally sure they have no flaws - mistakes often hide in "trivial" or "left to the reader" clauses. I am sorry for the obvious consequence of the proofs becoming considerably longer this way... If you are experienced in the respective fields, you will be able to speed-read much of my notes anyway.
What also boosts the length of my 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?

All parts of my webpage - this means all files accessible through an URL beginning with
http://www.oocities.org/de/darij_grinberg/ or with http://www.cip.ifi.lmu.de/~grinberg/ and accessible through a hyperlink from another such URL (*) -,
except for the documents listed under "
Eine unvollständige Liste von Lösungen anderer Teilnehmer:" at the German page (these documents are written by other people and may or may not be public domain),
are public domain, i. e. you can use them in whatever way you want without asking me for it,

That said, it remains idiotic to put one's name under others' work, but I believe that not everything that is idiotic must be forbidden.

(*) Why this? Well, sometimes I exchange some data between my home computer and my university account by uploading them on my webspace (without linking to them on this website, naturally). Of course, they are not public domain.

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&quoot; tags);
- attachments to posts (some of these are public domain, some arn't);
- posts on MathLinks beginning with the seentence
"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.

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 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 will actually use GSView to read PS files; Ghostscript is just required for GSView and will run automatically when you use GSView.

Note that GSView can also read most PDF files (more precisely, all PDF files without Adobe gimmicks such as encryption). However, GSView is not capable of antialiasing (or, if it is, Adobe Acrobat Reader is much better at it), so you can use GSView as the default viewer for PDF files instead of Acrobat Reader, but some PDF files (mostly those that have been scanned or use low resolution fonts) will look very ugly in GSView. GSView is not free of bugs, but so is Acrobat Reader, and GSView takes less time to load than Acrobat Reader.

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.

Please tell me of some good online sources for 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!]

Please 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 you say that reading from monitors is bad for your eyes, that you want to train your geometry skills while lying in bed or sitting on a bench and ... Okay, you want books, in the very old-fashioned, offline meaning of this word.

The first choice is obviously
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.

Please 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.
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...

Please 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 on the MathLinks forum anymore?

In fact, I am probably more active than you think, as I rather often do some moderator jobs on MathLinks such as moving topics and deleting spam, but indeed this is not the interesting kind of activity. In fact I would be glad to spend more time solving problems and posting their solutions, but I don't have this time.

Note that I am slightly more active on a younger forum called
Problems in Elementary Number Theory (PEN). If you cannot access this forum because it is offline (what happens sometimes due to the server), you can find the source code of my (relevant) posts here.

Please 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 mmathematical 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 seection, 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 am sometimes getting private messages over webfores with people asking me to solve mathematical problems.

Unfortunately, I mostly do not have the time to reply to such messages. First of all, don't ask me for help with combinatorial geometry, as I have really no experience in this area. Pretty much the same holds for functional equations. I am rather experienced with geometry and inequality, but currently I do not want to pursue these fields any further, so please don't confront me with them any more.

Linear algebra and commutative algebra questions will most likely be answered, as I like these fields. But don't expect me to write full solutions for your homework. I will most likely give hints and answer questions on understanding. I will think about your combinatorics/graph theory questions if I find them interesting, but alas I am not too good in combinatorics.

I am pretty clueless about analysis and topology, so you should not expect much from me.

But actually, rather than telling the problem to me via a private message, you could do the following: Post the problem on
the MathLinks forum and then send me, as a private message, a link to the problem statement. This has the consequence that, if I don't have the time, someone else might help you as well, and the solution posted will be probably of help to other people who also want to see a solution of that problem.

A sidenote: Don't try to cheat on contests by asking others to solve the contest problems for you. People on MathLinks talk with each other and may find out that the problem you asked them for was from a running contest. And moderators on MathLinks can see both your IP and your email addresses, and they can send this information to the contest organizers.

FAQ - Frequently Asked Questions

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Darij Grinberg