I'm Spending Holy Week...

...getting as close to Heaven as I can.










I think I got as close as I ever will during my lifetime...

Dear Meteora,
You have become
my favorite place on Earth.
Thank you for existing.
Love Always,
Lydia Ann

I Wish I Had Time...

...to update you about my trip. But I have so much to do!

Here are some pictures to tide you over :)

I really love it here.

Tomorrow: Meteora

Don't Worry About Me...

...Greece is treating me quite nicely.

Episode 4: Ponzi Scheme

*This is a short episode (I'm leaving for Greece in 20 minutes!), but I will continue to talk about this next week!

Do you know this guy, Bernard Madoff? He's in jail for being the operator of one of the largest Ponzi Schemes in history.

What is a Ponzi Scheme, you ask? It's basically making money from nothing.

Imagine you are a point on this graph, and each line is a money transaction from person to person.


If you end up with more money than you started with, then the Ponzi Scheme is successful. However, on a finite graph, it is impossible.

In an infinite world, Madoff wouldn't be in jail. He'd be a smart, rich, free man.

How, you ask? Let's look at an infinite binary tree:




If each person had to pay 1 million dollars to the guy below him, then think about what would happen...You would pay 1$ million and receive 2$ million. You would make a million bucks.

Sounds nice, right?

But will the Ponzi Scheme always work in an infinite world?

What about if the graph is an infinite lattice?

Think about it...


I'll have to tell you more next episode :)

Priceless?

Round trip train ticket to Greece:
33425 Forint

Thrifting for Spring clothes because you were too silly to pack any:
2500 Forint

Coffee to survive deadly, painful midterms:
900 Forint

Suitcase full of Easter Basket goodies for 14:
3345 Forint

"Enough" Túró Rudi for a 23 hour train ride:
1200 Forint


Spending your Spring Break

suit-casing through a beautiful

country with 13 amazing people:

ε-close to priceless :)

A Special Thanks to Mrs. Berg!

My new, fabulous, beautiful quilt.

Thank you so much Mrs. Berg!
I can't wait to start snuggling with it!

Hangtalan Kedd: "Cuban" Cigars Edition...

A Horrid Fear...

Only a handful of people know about this, but I have this horrible, horrible fear that I've just been lucky when it comes to me doing well in mathematics.

It's definitely one of my biggest fears...I mean, it's above clowns!

It's this fear that I'm actually really stupid, but no one has found out yet.

I'm starting to think that if this is true, it has taken me pretty far academically; and I'm beginning to wonder how far it will take me. Will it take me to grad school? And then when I get to grad school will I look like an idiot and fail out? Or will it take me all the way to a PhD? And then when I get in the real world will I get hired somewhere and become a complete failure? Or will it take me all the way through life, with no one ever finding out the huge impostor that I really am!?

For completely selfish reasons, I hope it's the last one...

At times it just feels like I've known the right people, been in the right places, and been exposed to the right situations; but when it comes down to it, I'm not actually smart at all, and my true mental capacity hasn't been exposed to everyone else yet. It's quite a horrible feeling.

The reason I bring this up is because RFM is making me realize that this fear might actually be a reality. At times (ok, like 99.99% of the time) the class seems completely over my head.

The only thing that keeps me going: my love of mathematics.

I mean, I really love math. Even with this impossibly difficult class, I still think it's so beautiful, so pure, and so fascinating. Math makes me happy, and when I'm "learning" it, I have this feeling of contentment; that it's what I'm suppose to be doing (please watch this, it's hilarious!).

So I will continue to read Walter Rudin every night before I go to bed. I will continue to work 4 times as hard in this class than the rest. I will continue to have this horrible fear. And I will continue to love math more and more each day...

Hopefully this thing never catches up with me...

Every.Single.Beautiful.Day.

There have been quite a few people from home who have recently asked me this question:

"Are you really as happy as your blog makes you out to be?"

I hope so?

I've actually been thinking about this a lot lately. And I really think that I am (or at least try to be).

I deserve to be happy, and life is way too short not to be.

I'm not going to get all preachy and tell you how happy I am (because you all apparently know and I don't want to be annoying), but I think that you should know this:

I love my life. I've made some mistakes, I've made some wrong turns, and I'm definitely nowhere near perfect; but when it comes down to it, I know that I have an amazing thing going for me, and I'm just grateful for every day that I get to live this wonderful, beautiful life.

Every.Single.Beautiful.Day.

You should be too.

I'm Feeling Rough, I'm Feeling Raw,

I'm in the prime of my life...


I'm feeling a deep need to update you all on my life (that's what this is for, right?). So here goes!

Wednesday, as you all know, was St. Patty's Day (as well as my Dad's birthday!). Wednesday night was the first night, probably in my whole entire life, where I chose to go out and have fun instead of staying in and having fun by finishing my homework. Ok, you have to understand something: I worked really hard for the whole week before that to get all my work done so I could go out and celebrate St. Patrick's Day with all my friends.

It's just RFM. RFM is killing me. Slowly and subtly. It is so hard. I don't even know what to do about it. I mean I read the book every night before I go to bed to try and learn something from it, but it really doesn't seem to be helping much. We have 4 RFM problems due every Thursday, and I tried so very hard to get them all done before Wednesday night. I finished 2 1/2 of them by Monday. I literally stared at my paper and book for 3 hours on Tuesday to see if I could do the other 1 1/2 problems. No luck. So, I decided to go out Wednesday night, instead of wasting the night not being able to do the homework.

Probably one of the best ideas I've had since I've been here. I had an absolutely fantastic time that night. I even lost my voice (and now consequently sound like a man) and I stayed out with friends until 4 in the morning (did I mention I have class on Thursday from 8-4?). It was awesome.




Thursday was nothing special really, but Friday was pretty great. Caitlin, Kylee, Tall David, and I went to this Hungarian restaurant for dinner. Are you ready for the name of this place? It's kind of ridiculous:

Márványmenyassony Étterem

Pretty awesome, right? Well the dinner experience was even more awesome and was something I know I'm going to remember about Hungary. The four of us arrive, and there are only two other tables that have people sitting at them. It was nice and relaxed, and we sat down and ordered (in broken Hungarian). Then, while we were eating, a gypsy band started playing and these three large parties come into the restaurant. We were guessing, "Wedding?", "Birthday?"...We never actually found out, but right before our food came, a man came up to us and said, "Where are you guys from?" I said, "United States." He replied, "Don't worry, you'll find out later why I asked..."

We all looked and each other and didn't know whether to be scared, creeped out, or excited. I think it was a little of all three. So we ate, and the other parties (mostly older people) were smoking, dancing, and taking shots of Palinka like it was their job. They were definitely enjoying themselves. Then, all of a sudden the man who asked us where we were from had a microphone in his hand. We started getting nervous.

He began to welcomed each of the dinner parties, there was a couple from Hungary (of course), one party was from Greece, one was from Italy, one was from Serbia, and one was from the United States (that was us!!). Then he continued to sing a song to each party, in each of their respective languages (he was pretty impressive).

He sang a Greek song, an Italian song, a Serbian song, and an English song--"I Left My Heart In San Fransicso", to be exact (which is funny because Caitlin and Tall David are from Cali and they got a huge kick out of that). Then, two men and two women came out and started dancing (with multiple costume changes). They danced with bottles of booze on their heads, and even had a whip with one costume change. It was ridiculous. We felt welcomed and included, and it was really awesome...

Not to mention, the food was wonderful. I can't wait to go back after Easter so I can have a dish with meat in it!


Today, it's over 60 degrees outside. It's absolutely, amazingly beautiful.





BY THE WAY:
In 7 days, I'm going to be in Greece for my Spring Break! EEK!!! I'm so excited!!!!

Episode 3: 1=2?

As my Functional Analysis professor says,

"Math is full of really cool things.
The only problem is you need some knowledge
to understand what's going on."

I hope that I can find enough things that are easily understandable to make these Math Episodes interesting. I hope that I don't completely lose all of you with what I say. Well, here's hoping!


I am going to prove to you that 1=2. Now, I know what you are probably thinking, "That's impossible!" But I'm going to do it! And completely blow your mind.*

Let's let a=1 and b=1. So, since a and b are equal

b²=ab.

We can also see that

a²=a².

Now, if we subtract the first equation from the second one, we see

b²-a²=ab-a².

Now, if we factor both sides of the equation, we see

(a-b)(a+b)=a(a-b).

So now, divide both sides by (a-b),

(a+b)=a.

But we know that a=1 and b=1, so if we plug in, we see

(1+1)=1

2=1!

I think the world just exploded.




*Note: If you see where this proof fails, please let me know! Otherwise, I'll tell you all on next week's episode!





<+><+><+><+><+><+><+><+><+><+><+><+><+><+>



Solution to Cannibal Island:

Ok, I'm not going to just give you the answer, that wouldn't be any fun. But, I will walk you through it and try and show you how to get there!

Now, some people (trust me, not too many) can see pretty quickly that you can save at least half of the suckers on the island. How so, you ask?

The first guy, Steve, says the color of the second guy, Doug's, hat, "Blue!". Then Doug thinks to himself, "Oh ok, that's my hat color," and says, "Blue!" too. Then the third guy tells the fourth guy his hat color, and the fourth guys shouts his out. This continues on so that every other person doesn't get eaten by the cannibals.

But that's only half of the people saved! Can we do better?

In fact, we can. A lot better.

Remember how there was an initial strategy session in the cage before the game began? Well everyone got to thinking, and their mathematical skills came out (I mean, wouldn't yours if you were about to get eaten by Cannibals?) They decided on a strategy and then pulled straws (do Cannibals have straws?) to see who went first. Poor Steve.

So the first guy, Steve, counts all the blue hats in front of him. One-by-one, all 999 of them. If there is an even number of blue hats, he says, "Blue." If there is an odd number of blue hats, he says, "Red." Then he gets eaten (the Cannibals knew the strategy, so they would just put the opposite on his head).

But he did a great deed to the rest of the mathematicians (oh yeah, everyone's a mathematician; wouldn't you want to be one right before you die? It sounds so cool: Mathematician.) The second guy, Doug, now counts all the blue hats in front of him. He has all the information he needs from Steve. If the number of blue hats is still even, then he must have a red hat on his head, and thus says "Red". If the number of blue hats is now odd, then he must have a blue hat, and thus says "Blue". Doug is one lucky guy.

But this goes on and on. Everyone can hear the people behind them guessing, and everyone knew what Steve's guess was. They just keep calculating and keep realizing that they must either have a red hat or a blue hat.

All 999 people can be saved.

Isn't that pretty cool?

Silly cannibals :)

To My Leading Man...

...this post was made, with lots and lots of love,
especially for you:

Happy 57th birthday! You are 57!
Would you consider yourself old yet? :)

Growing up with you as my father is something that I cannot even begin to explain. While we are completely different people, our similarities are scary at times, and I think that’s why we butted-heads so often…

“My father was often angry when I was most like him.”

That sounds about right, doesn’t it?




Despite our disputes, and our arguments, I am so grateful for our relationship. You are an amazing father, and I am thankful for everything you have done for me. Without you (and Mom) I wouldn't be where I am right now. You two brighten my life, and I'm pretty lucky to have such wonderful parents.



I'm not sure if you know this, but I feel this constant pressure (more of a need) to impress you, to make you interested in what I’m doing. I don’t know where it comes from and it definitely isn’t something that you put on me, but it drives me. You have always been my toughest critic and I guess I feel like if I impress you, then others will be interested too.




When it comes down to it, you and our family mean the world to me, and I wouldn't change a single thing about us. We're quirky, we're loud, we're emotional, and we're García's.





The fact that I share my last name with you, and what it means to me, has become a huge part of who I am. I think I speak for both Lina and myself when I say that our Cuban roots kick major butt. The food, the traditions, the culture, and the amazing trips to Key West to visit family are some of my favorite things in life. Not to mention, I think that I see you happiest when you are experiencing those parts of yourself as well. Thank you for sharing that with our family, and not keeping the Moho and Picadilla secret :)





I look forward to our growing relationship. I look forward to more of our "life" talks. I look forward to all the cool math that I am going to teach you. I look forward to telling you all about my life, my accomplishments, and my failures. But, I look forward most to becoming more like (the good parts) of you :)

I love you, Dad, and I hope you have a great birthday :)



Love Always,
Lydia (your favorite daughter ♥ )

Hangtalan Kedd: Delicious Pi Edition

Happy Π-Day!!!

Last night was our weekly family dinner! And it was our first Collaboration Dinner--both me and my son, Jared, cooked :) It was wonderful and is going to be happening much more often!

Kylee is becoming a pro at making the garlic-bread

mmm...

We made real Macaroni & Cheese (4 different kinds :] ). It was quite delicious.




After dinner and a really long WHOLE game of Spanish Monopoly, we decided to watch Saw.


Yeah...I don't know why/who decided that....



But today, our wonderful friend (and my cousin in the family) Lucas, is making two delicious Caramel Apple Pies (for Π-Day!!)!! We are going to have a homework party and the pies are being made in OUR apartment (so it is going to smell amazing).


I'm excited. And you should all go make a pie today to celebrate this wonderful holiday :)

My Childhood Dream...

has finally come true!!!!



Last night we had a "No Pants Party" where everyone had to drop trough at the door. It's a tradition at Greg's school, and we are all about carrying over traditions.

Two (out of my three) sons ♥

So, seeing as how we three girls were not about to wear our "panties" to this thing, we decided to buy some boys boxers. So, I bought my childhood dream: Star Wars Undies :)


It was marvelous :)

My son, my uncle, me, and Gramps ♥

Episode 2: Cannibal Island

This Week: Puzzle!!

So, imagine you and 999 of your closest friends (or good friends--ok, just you and 999 other unfortunate souls) are trapped on Cannibal Island.

You are all shoved in a cage in the middle of all the Cannibal Tipis (you know, because cannibals live in tipis). The cannibals are hungry, but they are in a strange mood; they want to play with their food (hehe). They come up with a "fun" game:

They will line everyone up and put either a blue hat or a red hat on each head. You cannot see what color hat you have on your head or the hats of the people behind you in line, just the hats of the people in front of you. Starting from the first person in line, each person must guess the color of their own hat, and if you guess it correctly: you don't get eaten for dinner.

Note: No communication of any sort is allowed, except for an initial strategy session in the cage before the game begins (and the Cannibals are all-knowing--aka they know what your strategy is).



So the big question?

How many people can be saved?


(if nobody gets it, I'll post the solution next Friday)

Happy One Year Anniversary!

One year ago today, my knees lost symmetry.

How I'm celebrating this fantastic day:
A beautiful (almost) 5AM run in the (snowy) hills of Buda :)

Have a marvelous day!

Hangtalan Kedd: Diversity of "Gifts" Edition

On Happiness and Poop...

The last 48 hours have been completely mind opening.


Absolutely, completely.


~ I am exactly where I am supposed to be, doing exactly what I am supposed to be doing, and surrounded by exactly who I am supposed to be surrounded by. Everything happens for a reason, and my current situation is no exception. God knows me and loves me and I would not be going through what I am going through if I couldn't come out on the other side stronger, wiser, and more like the wonderful, beautiful Lydia that I am going to be for the rest of my life. In the great words of Michael Buble, "Somehow I know that it will all turn out..."




~ Sunday morning I was awoken to probably the last thing anyone wants to be awoken to,

"Lydia, we have to clean up a homeless man's poop.."

Umm...

Our Land Lady called and woke Caitlin up to tell her some unfortunate news. Caitlin began to explain the situation to me:

"The neighbors complained about a party that we had and said that whoever out of our friends that left last didn't close the front door to the apartment building all the way and a homeless man came in and slept in the front passage way and decided to take a bowel movement. Because it was our friends, and therefore our fault, we have to clean it up."

I looked at Caitlin and said, "Party?" You mean the people that we had over on Tuesday to do homework? Caitlin shrugged and said, "I guess.."

I was beyond confused. We had people over Tuesday, and a man pooped in the hallway, and no one is noticing it until now?

Ummm.....

I took the phone and called the Land Lady. She said, "No, the party you had last night..."

Ummmm.............

We weren't in the apartment on Saturday night--or Friday night for that matter--and therefore, neither were any of our friends...

The Land Lady was confused and said that maybe it was from Tuesday, but it seemed unlikely. However, we still had to clean it up.

I'm not going to go into the disgusting, absolutely horrible, life changing details; just know that I cleaned up a homeless man's massive dump for no reason. ::shutters::

On the upside, I laughed more yesterday than I have in a really long time. My abs are kind of hurting :)




~On Saturday night a group of us went to a bar about 5 stories above a grocery store. Weird, huh? It was a dance club with Techno music. I was definitely thrown off a little (Techno music? How do you even dance to that?). I was told (very nicely) that I just needed to loosen up a little. It kind of hit me hard and I instantly realized something about myself: I'm really uptight when it comes to certain social situations. I guess I'm just not used to this whole being single thing. I need to be more comfortable in my own skin and just relax. I really do need to "loosen up". Needless to say, I decided to just relax a little bit and I ended up having an amazing time that night with some of my favorite people. Who would have thought? :)





~Yeah, we cleaned up poop. A homeless man's poop. That actually happened.





~While I was on the Tram yesterday, listening to my Study Playlist, The Weepies song Happiness came on. I couldn't help but smile:

"You can't steal happiness..."

And boy, are they right. A person's happiness should never depend on anyone else, and no one person should ever be able to take your happiness away. People are to aid in your happiness, not create it or destroy it. I was confused about this for too long of a time. I am a very happy, smiley person and I enjoy being that way. No one can steal that away from me. :)





~ Caitlin and I decided we are extremely grateful for toilets...

Episode 1: The Continuum

Starting this week, I am going to try and do a “Math Post” every Friday. That is, I’m going to share with all of you something really cool that I’m learning about or that I have learned in the past. I think that this will be a great way for you to understand why I love math so much. Plus, you get to learn really cool things!


If you’re a math person and you’re reading this, then it will be a nice little refresher (or you can just stop reading). If you don’t consider yourself a math person, you’re in for a real treat (hopefully, if I don’t confuse you too much)! Enjoy!





Episode 1: The Continuum


So whether you want to believe it or not, everyone knows what a set is, and everyone has some sort of set. You have a set of socks, you have a set of shirts, and you probably have sets of silverware. This is how it works for numbers too. You take a group of numbers, and you basically have a set.

So for example, {1, 2, 3} is a set. We consider {1} to be a subset of {1, 2, 3}. We call the set which contains all possible subsets of a set the Power Set. So, the Power Set of {1, 2, 3} is

{ { }, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} }

In fact, a set of n elements (in our case, n=3) has a Power Set of 2^n elements (in our case 8).

Cool, right? But what if our set looks something like the Natural Numbers,

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 …}

Or, maybe even scarier, the Integers,

{ …, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, …}

Or, maybe even worse, the Rational Numbers,

{ 0, 1, 1/2, -1, 2, -1/2, 1/3, 1/4, -1/3, -2, 3, 2/3, -1/4, 1/5, ...}

How can we tell how big these sets are? They look like they go on forever (infinite). But is that it? Do we just label them as infinite sets and move on?

Actually, amazingly enough, all of these sets are smaller kinds of infinity. We call these sets Countably infinite. Meaning, we can make a list of everything in the set. Yes, all three of those sets are the same size of infinity. Doesn’t that seem strange?

Are you thinking it couldn’t get weirder?


Pshh, you haven’t seen anything yet :)

What about π? You know that number, right? The one everyone knows the first 3 digits to: three point one four something something? OR, what about √2?! Or √287?

These numbers, along with the Natural Numbers, the Integers, and the Rational Numbers, and a whole bunch of others (the Irrational Numbers), belong to what we call the Real Numbers.

All the Real Numbers live on the Real Line, which is called the continuum. Any number you can think of (as long as it isn’t imaginary) is a Real Number.

“A continuum is something every part of which has parts.”

Ok, I know, I know. I might be losing you, but don’t try and think about it too hard. The Real Numbers are uncountably infinite. Meaning, we cannot count the Real Numbers like we did with the other three sets. There is no place to start, and no order we can go in. It’s just crazy to even try to think about it.

BUT, now we are starting to get into the really cool stuff. There are sets of numbers which are BIGGER than the continuum. Crazy, right?!

Remember the Power Set? Imagine the Power Set of the continuum…

Whoa…

A SUBSET of this would be something like this:

{ {π, 1} {π, 2}, {π, 3}, {π, 4}, {π,5},... {π, 1,2}, {π, 1, 3}, {π, 1 , 4}, {π, 1, 5}, {π, 2 , 3}, {π, 2 , 4}, ... {π, 1, 2, 3}, {π, 1, 2, 4}, {π, 1, 2, 5}, ... }

..and that's just a SUBSET!!


What about the Power Set OF the Power Set of the continuum?

Eek!



Can you see now that there are infinitely many types of infinity?


"infinitely many types of infinity"







Doesn’t that just blow your mind?



Maybe a little?







Remember this from yesterday:

"Do you know how many there are? There's continuum many!...
That's not too many, you know!"

It makes more sense now, doesn’t it?




Isn’t math remarkable?

Wise Words from FUN

My Functional Analysis professor, Gábor, says some of the funniest and most profound things. I thought I'd share some of them with you on this terrific Thursday:

"Do you know how many there are? There's continuum many!...
That's not too many, you know!"

"This is Hotel Infinity. There are infinitely many floors with
finitely many rooms on each floor. There is always a path
down, but is there always a path up!? Now, even if this is true
I'm not saying there is a straight road to heaven! NO!"

"The most important technique in Mathematics is massaging."

"There was a book written by him published years after
his death...eh, sometimes it happens..."

"This is the OBTBD for compactness....
Official But Totally Boring Definition"

"Cheating taxes is not only a Hungarian past-time...it's the
Hungarian way of life"

Are you starting to understand why this is my favorite class?

Watch Out, New York!! (and Canada?)

Yesterday I accepted an offer at the SUNY Potsdam REU doing research in Topological Graph Theory for 8 weeks (June 7th-July 31st)!!!!!


Isn't that so exciting?!

Doesn't that sound so cool?!?!

"Topological Graph Theory"
(I mean, you have to admit, it just sounds really cool...)

IF you are interested, here is some background information to some of the stuff I will be doing this summer. I'm not exactly sure what my research question will be, but I'm anxious to find out!

I know this is going to be a really amazing experience; and it will be a nice buffer between my awesome adventure in Budapest and my senior year at the River!!

Gah! Life is full of so many wonderful things, right?

AND, besides the fact that I'll be so close to Canadia that I can hit one of them in the head with a rock (not that I would want to or anything...), I am ONLY three hours away from the Vermont Lonergans. They may or may not be getting a visit from me...

Sziasztok!

Hangtalan Kedd: Three Musketeers Edition

Take a Cue from Hungary, America

Ever since I can remember, there has been a negative connotation to the term PDA.

Well, not in this country. It’s a Hungarian way of life…

Whether you are 25, 87, or 12, the people in this country have no problem showing the world (or the other people on the metro, tram, or bus) how they feel about their significant other: in a very loving way.

I’m not going to lie, at first I was kind of put off by it. I usually thought, “Don’t they realize every one can see?!” or, “Don’t you think that you shouldn’t be holding her butt like that in front of all these people on the tram?!”

But then, oh then, my naiveté soon faded, and I came to some pretty fascinating realizations:

Who am I to judge other people’s expressions of love? Who am I to feel uncomfortable around two people who care about each other? Shouldn’t I just be happy that they have each other? That they actually care about each other?

Now don’t get me wrong, it still makes me slightly uncomfortable to see two 75 year olds making out on the bus, but I’ll get over it with time…I think. If it makes them happy, then who I am to judge?

I think it will be totally and completely wonderful when I find the guy for me who doesn’t care who in the world is around when he wants to show that he loves me...

Who says PDA has to be a bad thing, anyways?