The importance of being a problem solver

Nejsou to ještě ani dva dny, co jsem doma (počítáno od příchodu mého batohu), a už se zase balím na novou cestu. Tentokrát je to na matematickou soutěž IMC v bulharském Blagoevgradu. Jaká jsou má očekávání a jaké jsou mé cíle?

It's less than two days that I've been home (counted from the arrival of my baggage) and I am already packing for a new trip. This time it is a mathematical competition IMC in Bulgarian Blagoevgrad. What are my expectations, what are my goals?

Ptáte-li se, co mám společného s problem solvingem a matematickými soutěžemi, musím odpovědět, že ne úplně málo. Ano, i já jsem se (pravda, neúspěšně) pokoušela o matematickou olympiádu, ale to bylo v mých atletických letech, kdy u mne příprava probíhala spíše nárazově, jeden dva dny se u mne nečekaně objevil zájem, ale pak jsem si kdovíkoliv týdnů na žádné příklady ani nevzpomněla.

If you're wondering how I am related to problem solving and all these competitions, I frankly admit that it's not that unrelated. Yes, even I attempted (in all honesty mostly unsuccessfully) mathematical olympiads, but that was in my athletic years, during which I was preparing very irregularly. I would typically get interested for a day or two and then not even think of any problems for many weeks.

Ani korespondenční semináře u mě nevyvolaly snahu připravovat se dlouhodobě. Pro ty, kdož neznáte, u nás působí mnoho skvělých seminářů, které publikují příklady, vy je vyřešíte, do daného termínu odešlete a oni vám je pošlou zpět opravené a ti nejlepší se můžou ulejt ze školy na soustředění, vyhrát zajímavé ceny a setkat se s novýma lidma. Je to skvělý systém a myslím si, že spoustě lidí přinesl opravdu mnoho. Bohužel ve svých atletických letech pro mě týden matematiky uprostřed sezóny nebyla příliš velká motivace. Ani později, když jsem se stala organizátorkou brněnského semináře Brkosu (http://brkos.math.muni.cz/), jsem si k řešení příkladů nevytvořila vztah tak, jak bych byla chtěla.

Not even correspondence seminars fueled the desire in me to prepare consistently. For those of you who do not know this concept, in Czech there are many beautiful seminars posting problems, you solve them and send back the solution before the deadline, get back corrected problems and the best solvers can go to camps, meet awesome people and win interesting prizes. It is a great system and I believe it has given a lot to many people. Unfortunately, in my athletics career a week of not training due to math during the competition season was less of a motivation. Not even when I became an organizer of the math seminar we organize in Brno did I manage to build a relationship with problem solving like the one I wanted.

Ani univerzitní studia mě nepřesvědčily, že bych měla řešit příklady. Většinou vyvolává mírný úděs / úžas, že se u nás rozdávají domácí úkoly pouze výjimečně, na cvikách je málokdy prostředí vhodné k tomu, abych se dokázala soustředit a pracovat samostatně, navíc většina příkladů je mechanických a v lepším případě technických. A tak se velká část mého matematického studia zvrhla k bezhlavému studování teorie. Samozřejmě, je spousta skvělých knih s přehršlí krásných cvičení, ale málokdy se dokážu motivovat natolik, abych u knihy vydržela celou kapitolu a ještě měla sílu a vůli buďto vydržet u deseti stran příkladů či se později vrátit.

Not even the university studies convinced me that I should be solving problems. It usually generated some excitement and horror when I mention that we are hardly ever required to do any homework, tutorial sessions almost always allow me to focus and work on my own and most of the exercises we get are mechanical or technical at best. So the most part of my mathematical studies have become just amassing theory. Of course, there is a great deal of beautiful books with many an interesting problem but I can't really motivate myself to read the whole chapter and still retain the willpower and strength to solve the ten pages of exercises...

Co však s tím? Vždyť matematika je o řešení problémů, narozdíl od těch soutěžních však nevíte předem, že existuje řešení, netušíte, zda už máte prostředky, kterými by váš problém mohl být zdolán. Dala jsem si už spoustu závazků a předsevzetí, ale nikdy jsem nedokázala vydržet u žádného systému (to ovšem souvisí s mou neschopností vydržet u studia déle než pár dní i bez nucení se do frustrujícíh hodin, během kterých vás nic nenapadne a ani po kapitulaci a přečtení si řešení nejste o nic moudřejší pro další příklady).

What should I do then? Math is all about solving problems, even though unlike with the competition ones,  you don't know whether there is a solution, whether you do have he tools to defy your problem. I have had so many resolutions but never managed to keep up any system in the long run (but I have not been able to sustain reliable studying habits even without forcing myself into those frustrating hours during which you can't solve anything and even after surrendering the proofs do not help you anyhow with the next problems).

Jediné, co na mě zatím zapůsobilo, je kolektiv. A proto zítra odjíždím do Bulharska, potkat se s těmi blázny, co zasvětili svůj život řešení problémů, s těmi normálními blázny, co to prostě jen baví, ale taky s těmi, co jsou na tom podobně jako já. Chtěli by, ale zatím si nenašli cestu. Vždyť mě nad tím taky baví přemýšlet, i když nic nevyřeším. Jen se potřebuji vnitřně nastavit tak, abych si na to vše dokázala najít čas...

The only thing working out of me then is the community. And this is why I am going to Bulgaria tomorrow, to meet the madmen who devoted their lives to solving problems, to meet the normal crazy guys who simply like it, but to also meet the people in a position similar to mine. Those who would like to but have not yet found a way. Because I do thinking about it, despite not solving anything. I only need to find the right state of my mind to free up some time for it...

Můj jediný cíl tedy je: odvézt si trochu toho nadšení ostatních, ať vydrží alespoň pár dní!

Therefore, my only goal is this: bring back home at least a bit of the excitement of the others and keep it up for at least a few days!

 

My mathematical life

Because my boyfriend does not know how to use Google translate, I decided to convert my latest post into English. For the Czech version, see http://mujsvetmojematematika.blogspot.com/2015/07/muj-matematicky-zivot.html

Being too restless to think of new things, I decided to share with the world some of the thoughts I have used elsewhere. For instance, this is a part of my effort to convince young ladies during a mentoring program http://www.zenyaveda.cz/ that doing maths can be nice and interesting.

Disclaimer: in exactly the same way I would support any young guys thinking about pursuing a mathematical career. However, I remember quite well how scared I was of my mathematical life, how convinced I was that there is no real place for women in science and that I will never be good enough as of course, women have a different education, social status, we are simply in a different starting position. But whatever, I do what I do, I enjoy what I do, I don't have to prove anything to anyone. I am as good as how well I work on myself. Some might be more talented, some might be faster learners, but who cares,  I study for myself, not for others. I don't believe anymore that maths is a male-only game, it is all about effort, persistence and strain and that can be found in anyone.

So this is my slightly jovial response to what does it mean to study pure mathematics, what do we do afterwards and how easy it is to start studying math. This account of my studies relies almost exclusively on the experience I have had at Masaryk, Brno.

So what is the difference between pure mathematics and applied? It's mostly different in content and attitude. It certainly is not only for the mathematical geniuses from all the Olympiads, on the contrary, those in particular have to deal with a great shock of suddenly starting to study different maths they might not excel at anymore and actually, some of them burn out completely... About lectures - in Brno the approach is very much definition, theorem, proof, it is difficult from the beginning to get oriented, but you should not be afraid of that, it is enough to be active and if you don't understand, get someone to talk you through it, annoy all the people around you to help you explain things again and again, get them to tell you what to read and what to work on.

Pure mathematics should lead towards the world of research mathematics. Therefore, the concepts are more abstract and it is particularly important to interact with senior mathematicians, be interested in what is happening in the world, the math community, it is not just about what you learn in the lectures. For it to make sense, at some point you will have to step out of the safe zone and become interested in things outside - it might sound scary, but definitely with your thesis you will start studying things outside the standard lectures and you will learn how to ask your own questions and pursue your own answers. It might be frightening, but you will learn how to spend your time on mathematics outside the school. At some point, anyone will find a thing that interests them, some things might be boring, but sooner or later something will capture your attention.

In applied math you learn more practical concepts, but many pure mathematicians leave for commercial sectors anyway and we are well sought for, we might not have as much experience with a specific computational software, but we are used to studying difficult, abstract concepts, solving problems for which you do not know in advance whether they will have any solution at all. I myself am a bit skeptical about applied math: for instance, in statistics, you know what kind of answers you are looking for and try to get them!:)

You will be more than fine with just high school math background, but as anywhere else, you will need some time to get acquainted with the new language, concepts and approach, but this is nothing to worry about. What do they want from us in Brno? Not much. Frankly, if you have some good background from your high school, you don't have to do anything until the exam period and for most of the exams (definitely the bachelor ones) I did not need more than a week to prepare, despite having done very little during the semester and despite being no genius, I do have to work hard to get those things done.

What can  you do with pure maths? The most beautiful option is to stay in research, you can do crypto, where they are really in desperate need for mathematicians, you can learn how to code better and be a programmer, you can do "big data" = "big money", a new and exciting field. But even from applied courses in Brno you can get to Berkeley and I got accepted to Cambridge, so the education we get is good enough for many places. Concerning travelling: to get to summer schools is easy, to get enough funding is... sometimes tricky. But I got to many summer schools this year, two of those were organized by the Institute for Advanced Study that mostly covered my expenses and Brno was generous enough to cover the rest, I got to some that cover some subset of room, board and travel expenses. You can't get everywhere you want but I can pick from (for instance if they cannot offer to give me enough support and it wouldn't make much sense for me to go there then).

And what do we do at such summer schools? You attend lectures, solve problems, meet people, travel. For instance, now I am in Utah for 3 weeks, we have 2 lectures a day, a problem session and we are supposed to write a 3-5 page investigation of some topic I am pursuing on my own here for 3 weeks. But you can attend more advanced lectures, research seminars. However, I chose to do most of my mathematical interactions here by talking to people about interesting things, mathematical as well as current affairs and problems. There are two Fields medalists, which is always inspiring to be around, but also many mathematicians who transformed or modernized their fields... I have been lucky to meet some of these superstars in my life and it always inspired me immensely.

However, I do not know your attitude towards math. For me it is a hobby I do enjoy a lot, I might not be as smart or good, but there are things I want to learn and enjoy. Sometimes it is frustrating, sometimes it is difficult, but you don't have to work 24/7 in Brno as is the case at other universities. But it is very much about your motivation and dedication. But if you are interested, in Brno, at any course, almost everybody will be happy to talk to you and support you in anything you might be into. It is enough to be a bit active - see how well it works for me! I don't work hard, frankly, I devote the very minimum to math. But I like it.

And if you do stay in pure mathematics, you will travel. Be it some research stays, summer schools, conferences or even going abroad for good, mathematics is about meeting people and spreading the ideas and learning new things from new places. And it is always great to see how things are done elsewhere.

Můj matematický život

For the English version, see http://mujsvetmojematematika.blogspot.com/2015/07/my-mathematical-life.html


Jsa příliš roztěkaná na to, abych vymýšlela nové věci, rozhodla jsem se alespoň podělit s některými svými myšlenkami, které jsem už sdílela jinde. Například tohle byla má snaha, jak přesvědčit moje mentee v rámci mentorinku  http://www.zenyaveda.cz/, že matematika umí být i krásná a zábavná. 

Pro skeptiky: naprosto stejně bych popořila libovolné kluky, ale sama si dobře pamatuju, jaký jsem měla z matematického života strach, jak jsem byla přesvědčená, že holky stejně vědu dělat nemůžou, že možná pak budu učit, ale nikdy nebudu tak dobrá, jako ostatní, protože ženy přece myslí jinak, než muži, máme jiné "vzdělání", společenské postavení, zkrátka jiné startovní podmínky. Ale to přece nevadí, dělám to, co mě baví, co si užívám, nemusím nikomu nic dokazovat, jsem tak dobrá, jak na sobě pracuji, nic víc, nic míň. Někteří možná mají víc talentu, někteří se učí rychleji, ale co na tom, já studuji sama pro sebe. Nevěřím, že by matematika byla jenom pro chlapy, je to celé o píli, úsilí a houževnatosti, a to se dá najít v každém z nás.

Tohle je tedy lehce nekorektní a žoviální odpověd na to, jaké je to studovat obecnou matematiku, co můžeme dělat dál a jak lehké je začít s matematikou studovat.

Jak se liší obecná matematika od aplikované. Především obsahem a přístupem. Opravdu to není jenom pro génie z olympiád, naopak, ti mívají na vysoké problém, protože najednou nejsou ve všem nejlepší, ta matematika je úplně jiná, tak nezanedbatelná část z nich naprosto vyhoří... Co se týče přednášek - v Brně se to dělá hodně definice věta důkaz, takže je těžké se zorientovat ze začátku, ale není čeho se bát, stačí být aktivní a když něčemu nerozumíš, nesmíš se bát se ptát lidí a uhánět je, aby ti to vysvětlili znovu, aby ti poradili, co začít číst, co dělat a tak.

Obecná matematika tě má dovést k matematice na úrovni aktuálního výzkumu, takže děláš víc abstraktnějších věcí, obecně bys měla víc komunikovat s "dospělými" matematiky a zajímat se o to, co se děje ve světě, není to jenom o tom, co tě naučí v předmětech. Aby to mělo smysl, musíš se časem začít zajímat i o věci mimo tvoje předměty - ale neboj, nejpozději s bakalářkou se stejně dostaneš k něčemu, co už ti lidé přestanou servírovat v přednáškách a naučíš se hledat svoje vlastní otázky a odpovědi. Možná je to teď děsivé, ale časem se v matematice naučíš, že to chce strávit i nějaký čas "mimo" školu. Ale toho se vůbec neboj, časem si každý najde to, co ho zajímá, některé věci tě přestanou zajímat, některé tě nechytnou vůbec, ale až se někde najdeš, nebude ti vadit strávit trochu času navíc u něčeho jiného.

V aplikované matematice se naučíš víc praktičtějších věcí, ale spousta lidí z obecné matematiky (nejen u nás) nakonec odchází do komerční sféry a jsme docela cenění - nemáme sice tolik praxe jako aplikovaní (co se týče speciálních softwarů a třeba numerických triků), ale to všechno se dá naučit a lidi nás berou právě proto, že jsme zvyklí učit se těžké, abstraktní věci, řešit složité abstraktní problémy, u kterých předem nevíš, jaké to bude mít řešení, jestli vůbec nějaké. Já osobně se na aplikovanou matematiku dívám trochu skepticky - třeba u statistiky předem víš, jaké odpovědi bys chtěla dostat a snažíš se je dostat :) :)

Bohatě ti postačí znalosti z gymnázia, ale jako kdekoliv jinde, ze začátku si budeš muset zvykat na nový jazyk a nový přístup, ale vážně se není čeho bát. Co se po nás chce v Brně? Nic moc. Pokud máš dobrý základ ze střední, tak nemusíš nic dělat až do zkouškového, reálně jsem na žádnou ze svých zkoušek (alespoň těch bakalářských, jedna mi trvá dýl) nepotřebovala víc než týden, a to jsem v průběhu semestru málokdy co udělala a vážně nejsem žádný génius, musím si to poctivě odpracovat.

Co můžeš dělat dál - můžeš zůstat ve výzkumu, což je krásná věc, můžeš se vrtnout do kryptografie, kde je dost peněž a zoufale potřebují matematiky, nejenom programátory, naučit se líp programovat a být vyloženě programátor, můžeš dělat "big data" = "big money", velmi moderní záležitost, ke které se můžeš snadno dostat. Ale i třeba z modelování a výpočtů se dá od nás dostat na Berkeley, já se z obecné dostala na Trinity na Cambridge, což je matematicky jedno z nejlepších míst na světě... Takže rozhodně se u nás dá získat vzdělání, které ti otevře cestu kamkoliv.

Co se týče cestování - dostat se na letní školy je jednoduché, dostat na to dostatek financí už je těžší, ale třeba letos jsem se dostala na spoustu letních škol, 2 z nich od Institute for Advanced Study (kde působil třeba Einstein a spousta jiných skvělých vědců), které mi pokryly skoro všechno a na zbytek mi přispěla Masarykova univerzita, za což jsem velmi vděčná, jinak většinou dostaneš nějakou kombinaci z možností ubytování, jídlo, cestovné. Dostat se na takovéhle školy není vůbec těžké, samozřejmě, nevezmou mě všude, ale můžu si vybírat. Několik škol jsem odmítla, když mi nemohli přispět tolik, aby to pro mě mělo smysl :)

A co se na takových letních školách děje - chodíš na přednášky, povídáš si s lidma, cestuješ :) třeba teď jsem 3 týdny v Utahu, máme 2 přednášky denně a jedno cvičení, takže většinu dne máš volno, máme napsat 3-5 stránkový text o něčem, co nás zajímá, něco, na čem si pracuješ sama. Ale můžeš chodit na víc přednášek, vědeckých seminářů, já to ale beru trochu jako dovolenou, tak hodně času strávím jenom povídáním si s lidma, ne pokaždé se bavíme o matematice, ale třeba i o politice, obecných otázkách a jiných věcech. Jsou tu 2 Fieldsovy medailisti, což je prestižní cena pro "mladé" matematiky do 40 let, oba jsou úžasní. Ale je tu spousta opravdu skvělých matematiků, kteří zmodernizovali nebo naprosto změnili oblast svého výzkumu... Potkala jsem několik takových matematických superstar a všichni bylo naprosto úžasní a pokaždé mě to nadchlo.

Nicméně, netuším, jaký vztah máš k matematice. Pro mě je to koníček, hodně mě to baví, i když nejsem tak dobrá, je spousta zajimavých věcí, které se chci naučit, kterým chci rozumět. Ale taky mě to prostě baví, občas se naučit něco zajímavého. Místama je to těžké, frustrující, ale tak je to všude a pro všechny, navíc v Brně opravdu nemusíš dřít 24/7 jako na jiných školách, takže máš spoustu času na všechno ostatní. Ale je to hodně o tvém zájmu, dokud budeš mít chuť něco dělat sama, bude to v Brně skvělé na libovolném oboru, téměř kdokoliv z učitelů tě podpoří v čemkoliv. Stačí být trochu aktivní :) Sama vidíš, jak to funguje u mě - matematice věnuji upřímně minimum, spoustu času proflákám, ale baví mě to a můžu dělat zajímavé věci.

A pokud zůstaneš v obecné matematice, do zahraničí se dostaneš :) Ať už na stáže, konference, studijní pobyty či přímo odejít do zahraničí, v matematice je dokonce potřeba cestovat a setkávat se s lidma odjinud. A je skvělé vidět, jak se věci dělají jinde.

Grónsko

Dnes jsem absolvovala nejkrásnější let v mém životě. Nádherné počasí, dechberoucí výhledy. Snad i díky tomu mi po 10 hodinách v jednom letadle nehráblo. Ale popořádku.

Today was the most beautiful flight in my life. Beautiful weather, breathtaking views. Perhaps even thanks to that I have not gone crazy during those 10 hours in one plane. But first things first.

Můj let L začal v Amsterdamu. Tam teda žádné pěkné počasí nebylo. Pouze šeď, šedošedá šeď. A to žádná módní vojenská, ale zastaralá ocelová šeď. Nad Islandem (díky bohu) ještě bylo zataženo, tak jsem se vyhnula zbytečnému sentimentu. Jenže Grónsko mě dostalo. A to i přes to špinavé okno.

My flight F strarted in Amsterdam. But you can't expect any good weather in Amsterdam. It was just grey, greyish grey. And no modern Military grey, plane outdated Ocean grey. It was still overcast over Iceland (thanks god) so I avoided unnecessary sentiment. But Greenland got me. Despite the dirty window.

Na začátku jsem dlouho jsem přemýšlela, jestli jsou to ještě mraky, když jsem konečně zaostřila na pevninu v pozadí
In the beginning I was wondering for long whether those are still clouds, when I finally focused on the land in the background

a nevěřila svým očím, až jsme konečně přiletěli blíž, jak se na droboulinké střepiny rozlámal led,
and couldn't believe my eyes, when we finally came closer, how all the ice broke into tiny slivers,

a když jsme přeletěli nad skalnatá pobřeží, pokrytá sněhem a ledem, modrá si vytvořila své cesty, kterým vzdorovaly jenom kusy ledu,
and when we flew above the rocky coast, covered in snow and ice, blue paved its way, defied only by the bits of ice,

aby je přece jen ledovec přemohl mocným pokusem o hladkou bílou pustinu, čemuž se moře urputně bránilo,
and yet be overcome at last by the mighty iceberg's attempt to create a smooth white wasteland, to which the sea fought back fiercely,

a po lítém boji, jehož rozměry plní člověka jak úžasem, tak hrůzou,
and after the savage battle, the scope of which inspires both awe and dread,

 

vytvořil sníh a led v moři něco, co patří spíše jako snímek do elektronových mikroskopů,

the snow and ice created something seems rather like a picture from an electron microscope

než do arktické pustiny.
than arctic wastelands.

Stále jsem plna až posvátého obdivu k přírodě, která mi dnes ukázala svou krásu v celé své šíři. Hodinový přelet nad Grónskem rozhodně patří k mým nejkrásnějším zážitkům v životě!

I am still full of astonishment by the wonders of the nature that revealed so vastly for me today. One hour flight over Greenland certainly belongs to the most beautiful experiences in my life!

Closing thoughts and thunderstorms

So my stay in Leiden is... over? I don't know if that is the right word for that, as I will be coming back to Leiden soon, I will go back there as an Algant master student and I have fallen in love with the place so much that I will definitely want to come back as often as I can. So I can't say that this is over, as I will make sure my bonds with Leiden will continue. 

But my Erasmus exchange is almost over. Unfortunately, these kind of matters always bring along a lot of bureaucracy and administrative issues, so this together with my exams and general exhaustion from all the travelling and arranging matters and most importantly the beautiful weather begging me to be outside and meet people and talk in the sun render finding the mindset for writing for me impossible. And also, I had to somehow cram a whole semester of a tricky course for me into one week, as I had been so overly diligent with my duties this semester...

Anyway, how was my stay in Leiden?

Great. 

Well, it wasn't a very good semester for me, for obvious reasons I could not study as much as I wanted, so frankly, I didn't get that much out of being at such an awesome place as Leiden. I refused to commute for courses so I missed some amazing opportunities to learn new stuff, but I think I still have some time to learn all that. But honestly, had I taken on more courses, it would have been too much for me in the end. So it was a good decision. And I know best how exhausted all the travelling (even commuting) makes me feel.

Also, I couldn't see as much from Holland as I would have loved to see, but again, this was neither my first nor last time in the Netherlands, so I am sure I will get to see all the places I want to visit. And all the lazy days on the beach and biking through the dunes and lovely strolls with my friends or my beloved one in Leiden, that was well worth skipping more famous and touristy places. And I did my fair share of sightseeing in my life, so I don't mind either.

I could have spoken more Dutch, but I learnt enough, I was able to conduct nearly-decent conversations occasionally, so that was not so bad. And considering the amount of stuff I had to learn learn with higher priority, for instance I finally learnt some class field theory I had been fantasizing about learning for several years now <3, I think I did enough.

Of course, I could have talked to people more. But those who know me and understand my shyness and the embarrassment I feel whenever I talk to someone smart (and there are many smart people in Leiden for sure), I am happy I managed to talk to several people I have dreamt about talking to. Surely many more will come, as I will become more relaxed and as I am resolute about doing maths more than twice a week and thus perhaps not forgetting everything before I get back to my studies. Childish naivety, you might object. But I believe in myself, I know that this time things will work out.

So, what next? My plan for the summer is simple: enjoy my well-earned holidays in July, that is, PCMI Summer Session in Utah and IMC in Blagoevgrad and, in August, finally revise my notes from this year and learn properly the things I was so discontinuously trying to study. Now that is naïve.

But I promised a thunderstorm in my title. So here is a video of the most beautiful thunderstorm I have ever seen, descending slowly on my home town Blansko this Monday, June 22nd 2015:

https://goo.gl/photos/XPaDYkfhTF2HeSJRA

Travel guide

I travel a lot. Too much, to be honest. I have seen many places on my own, traveled to a different continent completely on my own (though needless to say, New York City is not a wilderness). But my traveling experiences are usually very stressful to everyone around me. I excel in planning my trips way ahead and everything goes indeed very smoothly.

The motivation behind this post is of course my recent very successful booking of my tickets to Salt Lake City. Nevertheless, two weeks later (and two weeks before my departure, ehm) I finally have my tickets. But first things first, here is a list of my favourite traveling adventures that will make your trip unforgettable for everyone:

Nonexistent connections

Undoubtedly the greatest delight from my traveling for my family!

Ideal conditions: Small town with last connection sufficiently early in the evening, ideally after a long and exhausting week.

What to do: Forget that a certain early morning train doesn't go on Saturdays.

How to react: Wake up your family in the middle of the night asking them to drive you somewhere.

Expected results: Harmonious family relationships.

Failure to book I: the plane

This is undoubtedly my specialty.

Ideal conditions: Booking a transatlantic flight last minute.

What to do: Use a technical glitch to interrupt / cancel your reservation just when you submit the details of your credit card.

How to react: Spend several days waiting for customer care to get back to you via email, panicking, as you cannot provide enough information (e.g. no reservation number as technically, that has not happened) for the airline to help you efficiently.

Expected results: Large sum of money frozen on your bank account for a few days, acquisition of the ticket varies with the airline (Delta yes, US Airways no).

Failure to book II: the bus

A more modest but more pressing variant of the previous trick.

Ideal conditions: Booking last minute a bus connection you need to take due to your obligations / arrangements.

What to do: Reserve a ticket but forget to check that it has been successfully paid.

How to react: As before, wake up your family in the middle of the night asking them to drive you somewhere. Alternatively, run for your life to catch the train.

Expected results: Increase in your stamina by taking way less comfortable connections.

Packing frenzy

Especially effective with an early morning departure.

Ideal conditions: 30 minutes before the departure.

What to do: Check the list of things you wanted to pack and realise that your bag contains a mere half with at least 5 items easily procured anytime except for that moment.

How to react: Run around the house / apartment frantically looking for substitutes, rendering your place uninhabitable with all the junk you assess. Especially efficient in tight places with many doors and stairs. Issue search instructions and commands to anyone around, moving quickly to avoid any resistance.

Expected results: First hours after arrival to your destination will be devoted to sorting out your supplies and getting the missing essentials. 

Please bear in mind that to perform these tricks successfully, you need to repeat them roughly every two weeks or so.

I hope this will be a nice piece of inspiration for your upcoming travels!

 

Horrified I await how will my moving out look like.

 

Thesis: A bit of nostalgia...

So my thesis is printed and submitted already, even though I shall wait a bit for my defense. So, the result is here:

Tak, moje bakalářka už je vytištěná a odevzdaná, i když na obhajobu si ještě chvíli počkám. Výsledek je zde:

https://www.dropbox.com/s/l89hcsw0yl3263m/thesis.pdf?dl=0

Pretty, isn't it? I am quite happy about my thesis, I think I managed to include a lot of interesting things, most of which are true, I learnt a lot while reading upon several topics that piqued my interest and I think my thesis fulfilled the expectations I had for it.

Pěkné, co myslíte? Jsem se svou prací docela spokojená, myslím, že jsem tam vecpala spoustu zajímavých věcí, většina z nich je dokonce pravdivých, naučila jsem se spoustu během toho, když jsem se zajímala o témata, na které jsem během psaní narazila. A myslím, že moje práce splnila má očekávání.

Frankly, my goals were simply to write a coherent text, possibly including some interesting mathematics, but with a feeling that I added something. I am not sure how well I succeeded, but I feel that there are some pretty things I figured out for myself and I am satisfied with the way I look at certain little things in my thesis. Most importantly, I managed to get rid of my fear of many things - such as localisations and discrete valuation rings, so I hope that my thesis is a celebration of this progress of mine.

Popravdě, moje cíle byly pouze napsat souvisý text, pokud možno obsahující zajímavou matematiku, ale s pocitem, že jsem k tomu něco přidala. Nejsem si jistá, jak se mi to podařilo, ale jsou tam drobnosti, které jsem si rozmyslela sama a jsem spokojená s tím, jak se na určité věci dívám. Ale nejdůležitější je, že jsem se přestala bát některých věcí - třeba lokalizací a DVR, tak věřím, že má práce je toho hodnou oslavou.

There are so many things I wish I had included in my thesis, such as some of the estimates for class number, more about Chebotarëv, write in detail, why random polynomials have Galois group $\mathbb{S}_n$, but there simply isn't enough time to do everything. In any case, it is done now.

Ale je tolik věcí, které bych si byla přála do mé práce přidat, jako odhady na class number, víc o Čebotarjovovi, rozepsat se, proč náhodný polynom má Galoisovu grupu $\mathbb{S}_n$, ale na všechno prostě čas není. Nicméně, teď už je to hotové.

So, here some the nostalgic bit - submitting my thesis almost concludes the three years I have been studying here in Brno, some of the time was beautiful, some less, sometimes I felt like I am learning a lot, at times I felt I was not learning enough. Masaryk gave me a lot of freedom and did not interfere with my interests much, but I am not sure it was the right option for me. However, what kind of background I have managed to gain here remains to be seen. I hope I do have a nice starting point now anyway.

Takže teď přichází ta nostalgická část - odevzdáním mé práce jsem téměř završila ty tři roky, co jsem studovala tady v Brně, něco z toho bylo krásné, něco míň krásné, občas jsem si připadala, že se učím spoustu, občas jsem se cítila, že se toho nenaučím dost. Masarykova univerzita mi dala spoustu volnosti a nevměšovala se do mých záležitostí, ale nejsem si jistá, jestli to pro mě bylo to správné. Nicméně se teprve ukáže, jaký základ jsem si zde dokázala vybudovat. Doufám, že budu mít pěknou startovní pozici.

Almost there... / Ještě kousek...

Women and mathematics: the trip

I am still very much overwhelmed by all the beautiful things I've experienced here in the US. So there is just a few notes I want to share, not beautifully structured, with no special aim, but these things deserve not to be mentioned before I forget:

• There are a lot of great women in mathematics. Surely, we are still underrepresented, not every female mathematician is my best friend, but there are a lot of women who are simply awesome. Supportive, understanding. I really enjoyed my two weeks in Princeton because there I didn't have to keep my face, I could ask anyone even about the simplest definitions and silliest problems, there would be always someone to help me out. I am not sure this is a gender-related thing, but I have never experienced this level of understanding and acceptance in predominantly male groups. 

I admit it could have been the spirit of the school, but I hope we will all carry it in us for long.

• It is good to start with easy problems. There is no shame in doing elementary mathematics and revising the things you have learnt before. It could be immense fun, especially if you do it with someone similarly gifted in memory, it is definitely worth it. And again, forgetting things is natural and doesn't make you any less of a mathematician. 
• Neither the US nor Canada is used to pedestrians. I crossed the Peace Bridge between Buffalo and Canada on foot and in addition to having to walk basically twice the distance through all the under- and overpasses that were built for my walking convenience, the officers tended to send me to and fro before they let me in. 
• Also, if the officer at the custom says "How much money are you bringing to the States / Canada?", it is not advisable to react "Ehm, none" or "Next to nothing, I guess, 3 dollars!". But that was the truth and I had my 3 credit cards, none of which seems to work at certain strategical spots like the train stops and the like... But shops and counters are all okay.

Canada looked quite nice.

• I seem to be doing things wrong, eating Chinese, Indian, Italian and French food in the US and Boston burgers in Canada. But I had some tacos (and really sucked at eating that) and a lot of things that I do associate with the American cuisine. Okay, frankly, I ate some bagels. And I ate a lot of strawberries, blueberries, and raspberries, and that was the biggest impression on me here, so the rest hardly matters.
• Everything is so big here. I had a burger yesterday for lunch and I am not really hungry yet (though I've had some chocolate bread today). The streets are wider, the cars are bigger, the buildings are simply huge. Despite these places being so crowded, I still have this nice feeling of space around me, so the cities are energizing, the forests and parks are revitalizing. 
• The more I travel, the more I love my home. It is all so beautiful, but I look forward to being home.

IAS

Yes, this is a fantastic place. No question about it. The maths is great (tough and I am frankly overloaded), people are awesome and the surroundings? Heaven. Paradise. Nirvana. It is simply awesome. I feel happy, after a long time...

Yes, I am quite excited. I have every right to be. I have been quite lucky in my life to get to such beautiful opportunities to do mathematics, such as this lovely program for women in mathematics:

https://www.math.ias.edu/wam/2015

I think the organizers here are doing tremendous work and this program is running every year, with the topics sort of matching the topics of the special years here at the Institute. So this year, it's some algebraic geometry. What does that entail?

• Lectures: Liz Beazley gave a beautiful, hands on series on Grassmannians and Flag varieties, it was all very concrete, with great examples and intuition to see what was really happening. And we could draw some pictures, that was so nice... Claire Voisin talked about birational invariatns, mostly way beyond my understanding, but I have learnt a lot from the first few days. And did away with my fear of sheaves and bundles and it was all so beautiful. It is good to see some hard maths sometimes, discuss it with others and try to form some sort of a picture. It does feel like jumping right into the middle of the lake and learning how to swim well enough to survive until someone comes and fishes you out. Some faster swimmers reach the dry land, some drown...
• Seminars: intensive talks, some people do some amazing stuff. Really beautiful things. We have talks both on very advanced and complicated research and accessible topics, most of the speakers are so great. It shows how big the mathematical world is, sometimes you discover links that you were not aware of before, some things start making more sense afterwards... And it's fun.
• Socializing. The girls here are quite cool and everyone has an interesting story to tell, be it life, mathematics or all together, most of the people really are fun to be around. One can make great new friends and enjoy lots of beautiful discussions with similarly minded people.
• Sunbathing, coffee breaks and beautiful dinners. Tonight we had some tacos. I must admit that I was a desperate and ridiculously incompetent diner tonight. 

So that's it for now. I am still overwhelmed by all this happening. More to come...

Můj adoptivní domov

No jo, Leiden jsem si pořádně oblíbila. Je to magické místo a měla jsem docela štěstí na příjemné ubytování s milými spolubydlícimi, dokonce i počasí mi vychází naprosto dokonale - na nizozemské poměry tu překvapivě málo prší. I když včera tu byla nádherná bouřka, hučel vítr, tolik energie... Konečně když jsem měla úplně volný den a chtěla vyrazit na pořádný výlet. Tak jsem aspoň psala...

Yep, I have taken to Leiden quite a bit. It is a magic place and I have been lucky with a nice accommodation with cool flatmates, even the weather is so beautiful: for the Dutch standards, it's not raining at all. Even though yesterday we had a marvellous storm, with gusty winds, so much energy in the air... When I finally had a day off and wanted to go for a huge trip. So at least I was writing.

Když nemůžu za tulipány, přijdou tulipány za mnou!

If I can't go see the tulips, the tulips come to see me!

A jak je na tom moje bakalářka? Skvěle! Bohužel, můj vedoucí odhalil několik míst, které jsem doufala, že nebudu muset rozepisovat. Dokonce jsem je ani neuvedla slovy "zřejmě", "jistě" či "snadno", snažila jsem se o psychologický nátlak prostým "protože ...". Avšak byla jsem odhalena a za každou takovou drobnost jsem musela přidat odstavec či dva roztomilých výpočtů, argumentů, samé radosti. No jo, raději to udělat pořádně naproprvé...

And how is my thesis? Brilliant! Unfortunately, my supervisor found several places I hoped I would not have to give much detail about. I even didn't claim they were "obvious", "clear" or "easy", I tried a bit of a psychological pressure with a simple "as...". However, I was exposed and for each such a deceit I had to add a paragraph or two of computations, explanations, so much fun. It's probably better to do things properly on the first try...

Nicméně, po hodinách a hodinách sázení jsem vzala zavděk tužce a papíru. A myslím si, že v ruce to vypadá mnohem líp. Myslím si, že bych dokázala napsat svou bakalářku v ruce, avšak všichni, co po mně kdy něco četli, Vám řeknou, že to není dobrý nápad. Připomíná mi to staré dobré časy, kdy jsme vymysleli šifru založenou pouze na tom, že moje m,n, u a w vypadají prostě jen jako hromada stejných obloučků...

Even though, after hours and hours of typing I settled for my pen and paper. And I think it looks much better in hand. I think I would be able to write my thesis in hand, but everyone who has ever read anything after me, would tell me that it is not a wholly good idea. It reminded me of the good old times when we based a cipher based solely on my m's, n's, u's and w's looking just like a bunch of identical arcs...

vlevo mé poznámky, vpravo již natexováno

Hlasujte!

left my notes, right in LaTeX

Vote!

PS: Pokud to jde vidět snadněji a lépe, tak za to budu jedině ráda ($\mathfrak{O}$ je libovolný order a $\mathfrak{O}_K$ je okruh celých čísel ve stejném číselném tělese).

PS: If you can see it in an easier way, I would be happy to hear it ($\mathfrak{O}$ is an arbitrary order and $\mathfrak{O}_K$ is the ring of integers in the same number field).