Sunday I played a lot of poker, making it very far in a tournament but coming out almost empty handed (won just 75 cents).

The weekly classes were fun getting to the main event of the class, the Central Limit Theorem. What a beautiful theorem. I really enjoy the class very much.

Research is becoming more exciting, some cool things need to be proven.

One of the main events this week was getting pulled over by a cop. On Tuesday, I went to renew things for the car and to renew my driver's license. However the DMV was closed for renovations and I didn't want to drive 40 minutes to Claremont for it. Of course, I had to be stopped by a cop on the next day and while she stopped me for something bogus (claiming I crossed a red light when it was yellow), she had the right for asking for my driver's license which was expired. Hence on Thursday I had to go to Claremont to get a driver's license and next week I'll have to go to Concord to show the state court that now I have a driver's license.

Thursday Night Salsa was fun. Lots of dancing. Tuesday night swing was also fun, I think Yuliia and I dance it well.

I have also been into programming lately, working hours on some projects. I mainly got back into programming things because of the probability class, but now I have my hand on trying to program some number theory things. I love it, it is very fun.

With respect to movies, I watched Funny People yesterday, which was pretty good. It is very long for a comedy, clocking in at 2 hours and 20 minutes, but I guess that is not so unusual with Judd Apatow (Knocked up also reached the 2 hour threshold). I liked the movie. While the main jokes are about farts or penises, the story itself is interesting. I wasn't expecting that. Yuliia didn't like it.

With respect to reading, I read a Spider-man issue and just a few pages of a Neal Stephenson book. I also read some math papers. But what consumed most of my reading time was a manga called Liar Game. It is a manga that is driven by fun puzzle like games. It is really good, the story is kind of addicting. I read 80 issues of the manga during the week. Good stuff, I had never read manga before (although I tried a bit with a manga that Geoff lent me a few months ago). Good stuff.

Life is good.

In the last three days I've spent a lot of time doing math. I worked on writing my results on Burgess. What I wrote was fine except that there's still much more to do. I also gave classes all three days. The class on Tuesday was a special lecture where I covered four cool problems somewhat related to probability but not something covered in the syllabus. I enjoyed the class pretty much, it was fun preparing for it. Probability is a really cool class to give, I have lots of fun with this class.

On Tuesday I went to a swing dance class. It is the third I go to. Yuliia and I are getting good at it. I think our salsa knowledge help us learn the dance quicker than other students, but then again it might just be my ego talking.

On Saturday, I didn't end up going to my uncle`s house because there was such a long line. Instead, Maribel, Yuliia and I went to watch my mom dance. Many groups performed little numbers in the university theater. It was cool for Yuliia to watch the traditional Mexican dances. Besides the folk dances, a group danced belly dance and my mom's group danced`tango.
After that we went home and played many board games. Cuban domino, Nerds, Marrana. Marrana was super funny as we did a "Ratonera" for punishment to the losers. A Ratonera is where a person passes between the legs of everybody and gets spanked (everybody forms in a line to deal the punishment). It was hilarious, Yuliia couldn't stop laughing even though she was the one that lost. We played all night till 4am. Really fun.

On Sunday we woke up late, watched a bit of TV, ate pancakes and then went to my father's house to celebrate Father's Day. He cooked some steaks at the grill. There was tasty potato, Rajas (cheese with jalapeño), nopales and other things. Very tasty, I had a good time. I also learned how to do some card tricks.
At night there was Nerds again and this time I was last place.

Today will be a long day full of activities because it is my last day in Juàrez. Should be fun.

On Monday Yuliia and I moved. It was much harder work that I thought it would be. I started moving things at 3pm and we ended at 10:30pm (although we did take a one hour break). When we finished we rushed off to Applebees to get a pretty awesome dessert called Mile High Cream Pie, which was delicious.

On Tuesday I went to school for the last day of classes and then went shopping with Yulichka (things for the new apartment). Besides that, I did a lot of reading.

On Wednesday, I had my meeting with Carl and talked about the Burgess bound. Good progress has been happening of lately, I am excited about it. The meeting was pretty cool. Again, Yuliia and I did more shopping at night.

Thursday was a pretty awesome day. I went to teach a class to Hartford High School. The math teacher invited Dartmouth to send a grad student to give a class and I volunteered. It was very fun. I started out by showing Pascal's identity in two ways, algebraically and combinatorially. Then showing that the sum of the n-th row of Pascal's triangle is 2^n by using the Binomial theorem, but also giving a combinatorial argument. They seemed to enjoy it. Then I gave them some examples of counting things and gave them the task of counting the different poker hands. They really got into the project and were very enthusiastic. The class was a success, I was very happy. Yuliia took some cool pictures (Dartmouth asked me to take pictures).
After the class, the apartment manager helped me pick up a kitchen table (as I don't have a truck) and then Yuliia and I built it. It took two hours, much more than I thought it would. At night, Yuliia and I went dancing and I enjoyed it very much.

Today (Friday), I had another meeting with Carl and it was cool. We finally figured out why Booker used something to range through primes when it seemed unnecessary. Also, I was happy to understand Weil's bound better. In the afternoon I ate a really good meal that Yuliia cooked (chicken with a mushroom sauce) and then we went to watch Hangover which is absolutely hilarious. Yuliia and I couldn't stop laughing, it is really good.

On Wednesday, I woke up early to work on math. In number theory class we proved Bertrand's postulate. I find it much easier to learn things in classes than on my own, as when I see a proof on the board, I can recreate it, while when I see it in the book I need to read it many times before I can start recreating it. I wonder why?

My mom cooked chicken in curry sauce and some very tasty potatoes, they were delicious.

At night I went to play soccer. We won 4-2, the game was pretty tight, for a long time the score was 3-2. I had some good saves and overall a good game but for some reason I don't feel like I played that great.

After soccer my mom and I watched some TV like the old days.

Thursday was math day. Class from 10-12, seminar from 12-1, seminar from 1:30-2:30, seminar from 2:30-3:30 and colloquium from 4-5. The class was pretty fun, seeing a proof of the Marriage problem which permitted us to prove a pretty strong lowerbound for latin squares. The first seminar was the graduate student seminar and it was a sort of introduction to K-theory. Matt is very good at giving a talk. After that talk, it was combinatorics seminar where Sergi showed a combinatorial proof of a sum that shows the (n+1)-derangements = sum of k*a_n,k where a_n,k is the number of times k is the biggest fixed point in a permutation. It was a pretty good talk.

The number theory seminar was given by my friend Paul Pollack and he gave a really nice talk about sigma(n) (sum of the divisors of n). And proved that the gcd of (n,sigma(n)) is large very few times, therefore giving another proof that the perfect numbers are o(x) (density 0).

Colloquium was from 4-5 and Kevin Ford gave a talk on Pratt trees which were used earlier to show that to verify that a number was prime, you could do it in O((logp)^3+epsilon). It is interesting then to analyze the size of a Pratt tree to be able to reduce the time to verify the prime. If you improve the Pratt stuff as much as you can you get O((logp)^2+epsilon) which is already known by another method (due to Carl Pomerance), but studying the Pratt trees are fun in their own regard as funky things happen, with the distribution of H(p) (height of the Pratt tree).

At 6:30 I went to dinner with the number theory crowd, to spend some time with Paul. It was quite fun and quite tasty.

After dinner I went salsa dancing with my mom. It was very fun. I also danced with other girls that really enjoyed dancing. Always fun to salsa.

Classes started last week. Carl, my advisor, is teaching a grad level course on number theory. I have enjoyed that class very much this week, specially the homework assignment which consisted of seven problems. I brute forced my way through one of them, but usually I would find pretty solutions. My favorite was proving that the set {p/q: p, q prime} is dense in the positive reals. I also enjoyed using a theorem from class to give a correct proof for what I call Enrique's theorem (For b >= 3, for all n a natural number, there exists an n-th digit number base b that is a multiple of 1,2,3,...,n). I had proven it for large enough n, but now I can do it for any n.

Besides the class, my weekly meeting with Carl was fun. We talked about highly factorable numbers and it was nice to see a big simplification by Carl once I presented a proof I read in a paper. I have a project for this week and it looks fun.

The two other cool math things this week were a talk by David Stork using mathematics to discover art history, such as proving that the painters didn't use help of optics in 1425 (there's a big debate about this because a modern painter wrote a book attributing the difference in quality between paintings after 1425 and the ones before 1425 to the use of optic techniques and tracing), proving that Vermeer painted the Girl with the Pearl Earring alone, proving Van Eyck used a real room and not a fictitious one for his Arnolfini painting and much more. Great talk. Another great talk was given by Bart de Simon, explaining the famous abc conjecture, using lots of jokes and giving lots of computational data (I must admit, I am a data junkie).

On Monday and Tuesday Yuliia was getting more and more nervous because of her flight to Ukraine on Wednesday. On Wednesday we left the house at 8:30am driving to New York, to the JFK airport. We got there at 2:30pm and I left the airport at 3pm to go pick up my mom at La Guardia (her plane arrived at 2:50pm) and I got there at 3:40pm due to traffic. After that, I drove all the way back to Grantham, NH for a soccer game that was at 9pm. I was really nervous I wouldn't make it so I only stopped once (to eat), unfortunately, the traffic in New York, New Haven and Hartford prevented me from going fast and then once I got free of traffic it started raining. Hence I arrived at the game at 9:10pm, 5 minutes late (in terms of game time) but we were already down by 2. I played great and it was a fun game but we lost 4-3 (I arrived when we were losing 2-0). It was fun.

On Thursday, after my advisor meeting, I went to watch I Love You Man with my mom. The movie had some very funny moments and a good story, but it wasn't that great a movie, it was just good. In the evening I went to eat pizza with the prospective students and I met some of them, most of the time I spent talking with Yulan, a student from MIT that wants to work with Pete Winkler. Dartmouth seems like a great fit for her. After the pizza thing I went to dance salsa with my mom. It was quite empty, but it was still fun (I love dancing with my mom).

On Friday, I went to the grad student seminar talk which was great. I learned about Markov chains from Giulio and he wrote some beautiful programs, such as generating a random email of a person by analyzing statistically all his other emails. He also wrote a cool decrypter for simple encoding tricks. It would be cool to do something like this with all the data I have from IM conversations, to be able to generate emails that would look like my friends emails.
After the talk I went to other prospective student events including dinner at the Orient, which my mom joined us too. After dinner, my mom went to watch "Monsters vs Aliens" while I went to Game Night where I played a lot of Rockband. I was a little rusty with guitar playing in Expert, but I could still do them in Hard. I had a lot of fun singing too. I love that game.

Saturday I went to play basketball with other grad students. We played 4 on 4. My team won 11-6,11-6, 11-8 and 11-6 (the 11-8 we were down 8-0 and came back). I didn't play very good, but Asa had a great game and it was fun to have two new players: Peter and Brad.

After basketball I went to watch a movie with my mom. We watched Adventureland which was really good. The laughs weren't there all the time, but the overall story was very well done. A funny, interesting movie about summer love.

After the movie, it was the main event, Noche de Primavera, a semiformal dance featuring a live band playing salsa, merengue, bachata and tango. My mom and I helped teaching bachata and walking around helping with the other dances at first (there was an hour class before the actual event). Once the band started playing it became super fun. I danced a lot with my mom and Daisy. I had a lot of fun dancing as all the girls I danced with smiled a lot, it is always fun to feel the pleasure of dance. My mom danced with some very good dancers once they noticed how she dances (at first when I would dance with someone, no one would take her out but later in the night when everyone had noticed how she dances, it was almost impossible for her to remain seated). Really fun. I danced for about five hours. A really long day considering I played two hours of basketball.

On Sunday, it was all about homework for my number theory class. I also went to the Quechee gorge to show my mom. In the evening we went to the Dartmouth movie theater to watch Lola Montes, a 1956 movie about the Spanish dancer that was a lover of many famous men (such as the king of Bavaria and Franz Liszt). I was bored at times, mostly because I had number theory problems in my head, but after the middle, I started enjoying the movie very much. Interesting story and an interesting storytelling technique.

I had a lot of fun with class this week, although I don't think I did that well a job with the section as my students are clearly confused by some parts of it. I have some plans for next week to fix these confusion, hopefully I'll be able to teach it better so that they can understand it better. This week I had a lot more work than usual with the class as I decided to write some Webwork* problems and it took a while to understand the programming language and "make it work" (-Tim Gunn). I also had to write the homework assignment for the week, which I think I did a good job of, you can find it here.

I also had two classes in my problem solving club where I taught Binomial theorem, Pascal's triangle, combinations, the separating method (for counting), Pompieu's thereom (Geometry) and did easy problems to lead to Putnam problems that use those theorems in their proofs. Next Tuesday we'll go through the proofs of those theorems and then teach some other common problem solving techniques.

The other math included Number Theory Seminar which was a really good talk by Carl proving the Polya-Vinogradov theorem and a cool application (the least non-quadratic residue mod p must be < sqrt{p}logp). There was also a cool Colloquium lecture on trying to measure happiness, that used an experiment from Florida where people rated words as good-bad on a scale from 1 to 10. From those numbers they then computed the average valence of all songs recorded in English in the last 40 years, plus State of the Union addresses and blogs (using the statistics compiled by wefeelfine.org). Really interesting cool stuff, it looks like gender and age does not impact happiness.

Besides math, there was salsa dancing on Thursday which was fun as I love dancing with Yuliia. Our relationship just keeps getting better and better, I am so happy with her.

On Friday night we went to hang out with Andrea and Katy to Claremont. Asa came with us and we watched Taken the action movie starring Liam Neeson. The movie was amazing, this is what action movies are supposed to be like. Full of suspense, good action scenes and a great plot. Best action movie I've seen last summer.

After the movie, we went to a bar and then went to play pool, we played four rounds of pool and it was fun. Yuliia is pretty good at it, I think Asa was the best of the bunch. I had a cool conversation with Asa, it turns out he's also into ping pong and we're planning on playing one of this days. Next week we start a soccer tournament (three month long) where I will be the goalkeeper. It should be very fun because the players seem to be very good, they will probably be much better than me, so I'll have a lot of action trying to stop goals.

Yuliia and I watched another movie together this week, we watched Dumbo. I didn't remember the movie and I was surprised how short it is (65 minutes), but it also was a bit boring although it is a very nice story and the end seems to come a little too fast (just as he starts flying). Good but not great, although definitely nice for kids.


*Webwork is a computer program that has a huge set of all kinds of Calculus problems to give as homework sets where the computer grades on the spot so the student can try again.

Friday night I watched Iron Man with Yuliia. She liked it. I loved the first time I saw it and the movie was still good on a second watching (although a little bit worse). Robert Downey Jr. is awesome and the ending is really good. I am very impressed with superhero movies lately. X-Men, Superman returns, X-Men 2, Spider-Man, Spider-Man 2, Batman Begins, Dark Knight, Hellboy, Hellboy 2 are all really good films.

Saturday was pretty cool. I graded the quizzes for my class and I was very happy with how they performed. Yuliia and I went to a salsa class where I learned some really cool moves, mostly cross handed - cross body leads. After that we went to watch Rachel Getting Married. I liked the movie very much. Yuliia was bored out of her mind. The movie is slow, very character-driven instead of plot-driven. At first I was bummed out by the use of hand-held cameras, but I quickly got used to it. Anne Hathaway's performance is fantastic and I really loved the character of her father, who I cared a lot for during the movie. The dishwashing scene is very memorable. Another movie worth watching.

Sunday was football Sunday. Both games were fun to watch. I was specially happy with the Cardinals winning, I like Kurt Warner a lot, I always root for the underdog and Arizona is actually the closest professional team to my hometown, so I like them for that too. Their first drive and their last drive were gems of good offense. I hope Arizona wins the Super Bowl because I prefer offensive teams winning Super Bowls over defensive teams and mostly because I love underdogs winning (I also happpen to hate the Steelers).

The Monday highlight was having fun discussing the movies of the week in Film Society. I also had a delicious breakfast with Yuliia, a class meeting and then TV watching at night. I must also point out I've watched the first four episodes of Season 4 of Project Runway. So far I am not as into it as in the previous seasons, but I am hopeful it will be better as most Runway watchers love this season.

I had a really fun Saturday. Yuliia and I went to the gym and had some fun doing exercise. Although the bad news is that my hip is not yet recovered from the hamstring I got on December 21. After the gym we went to have a nice dinner. I had a Cordon Blue and Yuliia had shrimp and scampi, both were really good.

At night, we went salsa dancing (after watching the great TEN-BAL match). We learned how to samba and we danced quite a bit, we were there for three hours. I had a really nice time.

Sunday, woke up and cooked some breakfast for Yuliia. After watching the NYG-PHI game, Yuliia and I went to play in the snow a bit (it snowed a lot today, more than 6 inches). A housemate had to leave the house and my car blocked him, I helped him shovel and then since the path was cleared I decided to do the shopping. When I came back, my car couldn't go up the driveway because my rear tires are not winter tires. I shoveled a lot more and eventually forcing my motor I got to go up the driveway in the icy conditions. I was super annoyed, but got it done.

Now I am home, preparing my class for tomorrow and writing an essay for Film Society.

The week can be summed up as eating, reading, shopping, dancing and watching movies. I have eaten very tasty stuff, like some tacos, the lamb curry I love from Sinbad, some delicious desserts and a Ukrainian soup. I finished the Christmas shopping. I went to dance salsa with Yuliia and my mom. I also played some American football. I was playing superbly, we were winning 4-2 and I had two touchdowns and three interceptions but I got injured and I continued to play but without being able to run, so we lost 6-4. I feel better already, but it was very frustrating to not be able to run.

The movies I've watched are:
Horton Hears a Who The very cute animated film has a very nice message about acceptance of others and harmony between people. I liked the movie, it was also quite funny.

Rounders A really cool movie about poker. The main thing to take out of this movie is the conversation of Matt Damon's professor where he explains how he is a lawyer in a family of rabbi's. A very good message that one should do what one feels like doing and makes them happy and not what other people tell you to do. The movie is entertaining too.

The Notebook Given that there are many women I know that consider this their favorite movie, it was time to finally see it. I thought the movie was good but not great, I can see why women would love it, but I didn't feel moved by the story. Yuliia loved the movie and cried for half the movie + one hour after the movie ended. A good movie to watch with a girl.

Yes Man The new movie with Jim Carrey. The movie is hilarious and it has a good message too (be open to new things). I loved it. Yuliia, my mom, my sister, her boyfriend and I were laughing almost nonstop. Great comedy.

The book I read:
Tales of Beedle the Bard by J.K Rowling is a book with five fairy tells set in the Harry Potter book. It is supposed to be a very famous book in their universe. The fairy tales were good, specially the Fair Fountain and it was cute to have Dumbledore give a commentary on each fairy tale.

The comics I read:
Daredevil by Frank Miller and Klaus Janson volume 1. The volume consists of 16 issues where Frank Miller was the artist and the last five issues he is both the artist and the writer (he is the co-writer in two more issues). Essentially the volume gets good once Miller is the sole writer. There were one or two issues of those first 11 that are good, but the last five are at a different level. I had read the first half three weeks ago, but I decided to read other stuff because it was a bit boring. I am glad I came back to the comic, because Miller's run was worth reading.

Fables: War and Pieces This book compiles issues 70-75 of Fables and it is essentially what the first 70 issues had been driving too, the war between Fabletown and the Adversary. The story was great. This series might be the best series I have read. It is truly fantastic. The story relates some cool spy stuff involving Cinderella, then the marvelous plan Fabletown had to win the war, which included blasting all the portals to different worlds, sleeping all of Imperial City by getting Sleeping Beauty to pinch her finger, and using Blue to teleport all over the place with the special robe. The plan seemed to work perfectly, but there were some difficulties because of a special arrow that could miss Bigby and a special dragon plan that destroyed the Arabian flying wooden ship. Prince Charming did a wonderful thing to blow the last gate and Bigby fought the Emperor with the help of blue and the super sword. An awesome story.