Goodbye Familiar, Hello Unknown...

I write this with deep and utter heart ache.

Not only am I leaving all of you, my readers, but I am leaving a place that has become my home for the past 5 months; a place that has filled a giant hole in my heart.

I know that I have given you the list of things that I will miss, but I think I am going to miss most the attention to detail in my life that this blog made me keep track of during my time here.

I entered this city as a silly girl who was in love with a beautiful subject and who had an open mind to the next chapter of her life. I leave my new home as a young woman in love with a city, in love with herself, and more in love with mathematics than when I started (don’t worry—I didn’t think it was possible either).

Hopefully my parents recognize me when I get off of the airplane. I have changed so much that I barely recognize myself sometimes. I love the person that this place, this experience, this chapter in my life, has shaped me into. I don’t really know what I was expecting Budapest to do for me, but it went far beyond what I ever imagined was possible. I am finally coming into my own.

I have grown only in a positive direction. While I was hurt a lot during these past 5 months, I also have become a better person because of it. I found something here that I will never be able to thank God enough for:

Grace.

Every week I have prayed to God for grace, not fully understanding it and why I needed it. But a few weeks ago, it hit me: grace leads to wonderful love and an extremely happy life. I hope that I continue to grow in grace.



I want to thank everyone for believing in me, and for giving me your love; without you, my life just wouldn’t be the same—nowhere near as beautiful.

It is safe to say that this is just the end of a chapter in my life, not the end of the great, wonderful life that I am supposed to live. I have to say though, this was a good chapter.

Thank you for reading my diary, and being apart of my adventure. It’s such a blessing that I got to share it with you.

I don’t want to say goodbye, because those are always way too sad. Instead, I will say that we shall meet again. Who knows when, and who knows in what form; but I promise you that we will.

Who knows, maybe I’ll write a book :)

So long, Budapest: you will forever hold a very special, spacious place in my heart.

Sziasztok!

Open publication - Free publishing - More mathematics

And remember my secret? Can you tell what it is?

My Last Night at Home...

The apartment is bare and everything is packed.

All the things that made this place home--the objects, the pictures, the bottles, and the tokens that made Caitlin and I call this little space ours--all of that is put away to soon become little, beautiful reminders of a chapter that is drawing to a close.

These things, things which made our whole semester wonderful and unique, are shoved into tiny little spaces in my suitcase.

This place, this little apartment on Margit Korut, this new home of mine, will always be alive in my heart. I will always have the Soviet shower ingrained in my brain. I will never forget cooking for 13 hungry tummys on Fat Tuesday in the world's tiniest kitchen. I will always remember the lice bed. And how could I possibly forget the view?

This post has no change of mood, no switch from sad to happy, because it's sad that this is my last night at home. And it's ok that it's sad. It's impossible to be happy all the time.

So I'm going to be sad. I'm going to say that I will miss this place more than I could ever convey to you with words from this keyboard. And I'm going to cry and not feel bad about it. I can be happy again tomorrow.

Kylee and Ranjan are bringing me to the airport tomorrow. I have no idea how I was blessed with such fantastic friends, but God gave them to me and I'm going to hate saying goodbye to them.

I'm going to go enjoy my last few hours with KyJan and this beautiful city...


Tomorrow is my last blog post, and the last day of Budagirl's adventure...

The Worst Kind of Hugs.

They are leaving, one by one: my new family and my new best friends. They are each off to their little corners of the United States. It feels so surreal that this is ending, that this adventure is coming to a close.

I feel very lucky to be going back to the U.S. and having friends scattered throughout the whole country.

Two days left and I’m kind of getting tired of how quickly life is moving. Wasn’t it just yesterday that I was walking the halls of St. Pius in that hideously wonderful green plaid?

If life is going to keep speeding up like this, then I’m going to need to figure something out, quick, so I can get everything out of it that I want.





I know that all good things must come to an end, but that doesn't mean that the end is easy. It doesn't mean that the end is subtle. And it definitely doesn't mean that the end isn't full of sad hugs goodbye.

The great thing, though, is that when
I get to see all these wonderful people again,
we get to experience the best kind of hugs.

My Family ♥

Episode 11: Series Finale

Last week I gave you these three equations:

1. 2x²-5y²=5z²-1

2. (x²-21)(x²+2)=y⁹

3. a²+b²=11c²

I will solve them now.

1. 2x²-5y²=5z²-1

First, let's rewrite the equation.

2x²-5y²-5z²=-1

Now, let's look at the equation modulo 5.

2x²=-1 (5)

Now, there is this theorem, called Euler Fermat, that says a^(p-1)/n=0,1, or -1 modulo p. Therefore, since 2=(5-1)/2, we see we have three cases.

2(0)=-1 (5) (i)
2(1)=-1 (5) (ii)
2(-1)=-1 (5) (iii)

Now, if we simplify we can see,

0=-1 (5) (i)
2=-1 (5) (ii)
-2=-1 (5) (iii)

Since none of these are true, we can say that there are no solutions to this equation. ♥

2. (x²-21)(x²+2)=y⁹

There is a bit of complicated math in this solution, so I'm just going to show you the end of the solution. Let's look at:

x²-21=y₁⁹
-x²+2=y₂⁹

So we have

23=y₂⁹-y₁⁹

So 23 is the difference of two powers of 9. But let's list the powers of 9:

0, 1, huge

There is no way that 23 is the difference of two powers of 9. Therefore, there are no solutions to this equations. ♥*

3. a²+b²=11c²

There is this great theorem that says that the sum of two square numbers cannot divide a prime of the form 4k-1. We can see that 11 is a prime of the form 4k-1 (where k=3), and (a²+b²) is the sum of two squares. Therefore the left-side cannot divide the right-side and thus there are no nontrivial solutions. (I say nontrivial because a=0, b=0, and c=0 obviously works). ♥

Now, to end this wonderful series, I will share with you one of my favorite theorems and its proof from this semester. Please don't be concerned if you don't understand.

Theorem: Prove that a Hilbert space contains an orthonormal basis.

Proof: ZORN! ♥

I hope you have enjoyed reading these
as much as I have enjoyed writing them!!

*The solution is a bit more difficult. It requires knowledge of the Power Product Lemma and Quadratic residues. But the proof basically boils down to that.

The List.

Throughout the semester, I have compiled a list of things that I know I will miss when I leave Budapest. It includes things from both Budapest and BSM.

Seeing as how I have four (I know, right?) days left, I think it's about time I shared it with you...

• Túró Rudi

• My Hungarian professors
• My down comforter…I mean, what’s the point of any other kind of comforter?
• The smell of Moszkva Ter when you get off the metro

• Gyros (I'm sorry there is no picture of this. I always seemed to eat them before I had a chance to take a picture)
  
• Cheap food
• 2$ bottles of wine

• The most delicious ice cream in the world
• Doggies everywhere
• The 4/6 tram

• My keys

• Homework party Tuesdays
• My commute to school
• Kylee’s laugh

• Anna & Anna’s office
• Family dinners
• Sitting in the grass at Deak on a Friday afternoon

• The ride home to Buda when I go out at night
• Margit Hid
• Taking a shower sitting down (yeah…who would have thought, eh?)

• My view.

~The Most Important Lessons Taught
to me by BSM Professors~

1. The most important reason for learning Functional Analysis (and Number Theory, for that matter) is so when a mathematician murderer comes and asks you to prove something (or solve something) with a gun to your head, you can and therefore won't die.
2. 2 is not a prime number.

And......

I'M DONE WITH FINALS!!!

...and I'm not dead? My brain hasn't exploded?!?!?!

I know...who would have thought?!

Now, with less than a week left, there are some things I’ve noticed/realized:

1. I’m so excited to sleep with my 10 pillows when I get home!!
2. Packing 200(ish) Túró Rudi and Gurus into these suitcases might not be feasible.
3. I might be stealing one of these mugs in my apartment...
   
4. I’m going to have to start throwing away more clothes in order to make packing 200(ish) Túró Rudi and Gurus into these suitcases feasible.
5. I definitely have the best parents ever. Definitely.
6. I think I’m going to go through serious culture shock when I get home. Everything is going to seem so expensive; I’m going to actually understand the conversations around me; I can communicate with people without second guessing how I’m suppose to say words (ok, hopefully this is true); AND I’m going from a wanna-be-city, to a wanna-be-surburbia, to a definitely-middle-of-nowhere country town. Awesome.
7. Don’t judge me for 4. Especially if you want some.
   
8. Did I mention that I can’t wait for my 10 pillows?
9. I wonder if I’m going to eat as much cabbage in the rest of my life as I have in the past 5 months.
10. I just found my cell phone. It’s kind of scary, and it flips open, and there is this little circle on the front that “takes pictures”. WEIRD. I can’t believe that I was basically dependent on this thing at one point. I really hope that I don’t go back to that, and my ability to function in society stays mostly cell phone free. Mostly.
11. Why did I bring so many books and notebooks from previous classes? Did I REALLY think they were necessary, or were they more of a comfort thing?
12. I definitely need new headphones. Definitely. I’ve been trying to milk these old ones since April. The sound only seems to come out of this little tiny part of them, so hopefully I am getting new ones almost as soon as I get home. Hopefully they last me this 14 hour flight home...
13. I’m really lucky to be seeing a BSM friend almost as soon as I get home. I think that will make the transition a lot easier. Thank you, Ranjan, for being my date to Katie’s wedding. You will be the best.date.ever. We’re going to have so much fun.

Also, there are things that I’m starting to get really excited about:

1. Tackling my parents at the airport.
2. My ten pillows—just in case you didn’t notice
3. The rest of my clothes and shoes!!!
4. Chipotle…..mmm…
5. Having a beer with my dad :)
6. Kneelers with cushions (seriously, Europe, I think you should reconsider using wooden planks as your kneelers…it’s painful…)
7. A hair cut…goodness gracious that is going to be glorious
8. Watching Luke’s “Tik Tok” performance.
9. Cheeseburgers.....mmm...
   
10. Taking a shower standing up (actually, I think I might kind of miss sit down showers…)
11. Raisin Nut Bran
12. Old Bay
13. Large eggs
    
14. A cup of actual coffee
    
15. Clothes Dryers
    
16. Using my new, wonderful, beautiful, and dying-to-be-cuddled-with quilt.
17. Car rides. Wonderful, glorious, blasting-great-music car rides.
    
18. Seeing my beautiful family
19. Seeing my wonderful friends

It seems that I could continue this list for a very long time. I’m actually very excited to go home. I mean, who wouldn’t be?


It also seems that my flight home has been cancelled (stupid British Airways and their stupid strike). I will probably be spending the next 24 hours figuring this business out.



BUT: I'll leave you with my grades for this semester:

Hungarian Language: A
Theory of Computing: A-
Number Theory: B (I am SO proud of this B--Number Theory is not my thing)
and, last but certainly not least:

Functional Analysis: A (yippie!!)

I'm stinkin' proud of myself. Hardest semester of my life, and I leave with 3 A's and a B? Not too shabby...

Hangtalan Kedd: The Last Edition