Instead of concentrating hard on my summer readings, I have been thinking instead about my other blog. Mainly I have been re-evaluating my original purposes for starting The problemsheet. It has been fun so far. All the problems I have typed have been nice and typing has helped me understand them more. But honeslty it is very time consuming. And I can see this not being as fun all the time.
So I have been thinking, maybe it would be nice instead to post about a random equation every day. That way I can mention some of my favorite equations and at the same time post about other not-so-familiar equations. Now this seems more of a realistic goal! So I guess I am going to get the crane and start demolishing the blog, so I can reconstruct. It is a pity that Blogger does not have any LaTeX support.
Stay tuned for EOW.
24 May 2007
23 May 2007
A random prime
Here is a random 300-digit prime number. Enjoy!
2039568783564019774057658669290345772801939
9331434826309477264645328306272270127763293
6616063144088173312372882677123879538709400
1583065673383282791544996983660719067664400
3707421711780569087279284814911202228633214
4876183376326512083574821647933992961249917
319836219304274280243803104015000563790123
Oh, the mysteries of number theory!
2039568783564019774057658669290345772801939
9331434826309477264645328306272270127763293
6616063144088173312372882677123879538709400
1583065673383282791544996983660719067664400
3707421711780569087279284814911202228633214
4876183376326512083574821647933992961249917
319836219304274280243803104015000563790123
Oh, the mysteries of number theory!
Problem-solving
First I would like to discuss some quotes from Feynman. Here is the first:
I do not think I have the capabilities of ever learning how to solve every problem that has ever been solved. But I guess it is a nice goal to set in life, unrealistic as it is. Is it worth learning all that stuff? Well, one can imagine that if we adopt this task, it will be eternal; new problems are solved everyday. In fact, in mathematics it is customary to re-solve problems with different approaches until the most elegant and simple way of getting the results have been reach. But life is all about learning. One will never know enough. In my opinion this is true, only arrogant will believe that they will know enough one day that they will simply stop learning.
Another quote from Feynman goes like:
I am not saying that one should not try something hard and just comfort on the easy problems, whatever those are. The thing is this too is individual. Some people find some problems easy and others hard and some other people do the opposite, so in the end it also depends on interest. What I am trying to say can be explain better through an example. Say I am a theorist, and I want to calculate something that involves an application of a branch of mathematics I really do not know much about. In this case learning the new math will come as part of the knowledge package that comes during the process of solving the problem. But if I am really bad with that particular branch of mathematics, then depending on the degree of badness one can try and try and someday solve the problem or just be stuck forever on something that simply is not your stuff.
Maybe, just maybe, that quote was also referring to Feynman's view on string theory or quantum gravity in general. Maybe Feynman wants to tell us that there are some questions that really do not matter. Personally I do not think that the problem of quantum gravity does not matter just because it might not be pertinent in life. The truth is that there are also other open questions in modern physics that are more "basic", like understanding turbulence. It is "basic" in the sense that the problem is of classical origin, and has been around for a long time. I recall reading something along the lines of "There are other exiting problems in physics other then quantum gravity, like understanding the flow of water through a pipe". This is true. But I believe that turbulence is not an easy problem so in my case it is not worthwhile ;-).
In the end there are no such things as easy or hard problems; all problems require a consideration of certain ideas and situation that sometimes happen to be the most familiar to the person trying to solve them. For example, in my Quantum Mechanics final exam I could not answer one question about eigenfunctions of the quantum harmonic oscillator. Of course as an undergraduate student I went through all the derivation of the solutions (which apparently I forgot). Was the problem hard? No, I just happened to forgot a particular set of information, namely a set of symbols that represent the energy eigenfunctions for the quantum harmonic oscillator in an arbitrary energy level. It was not just a set of symbols, but I am still bitter about it ;-).
Some time ago I started another blog, The problemsheet. My intentions to start that blog were (1) to share with others solutions to some of the problems I encountered as a graduate student, and (2) to practice my typesetting with LaTeX.
In the back of my head I had some other intentions, like pursuing my own version of Feynman's goal and trying to show "someone" that I can solve problems. Maybe I wanted to be a smart ass like the people who display the solution to famous textbook problems online. I guess most of them do not want to show-off, they are just trying to help other students. That is particularly my first intention, but I know that in the back of my head I also want to show-off the grandness that I sincerely do not have. Nevertheless I comfort myself by thinking that by typing this solutions I am actually going through the problem again from the start, following it and looking for mistakes.
Another point that is also related to teaching is the fact that sometimes it is not easy to present one's results in a clear way without omitting some important steps. When I write down my solutions to assigned problem sets I try to be as clear and explicit as possible. Maybe it is the mathematician in me (who does not help me that much, that bastard...), or maybe it was the product of my undergraduate professors. I notice that fellow graduate students are not as explicit as I am in their solutions. I guess I want to be as clear as possible that (I think) I know the stuff I am talking about and am not fooling anybody. Nevertheless, I have been able to fool myself a couple of times.
Do people really expect students to solve every problem that is thrown at them? Now that I look back, I think my professors did. And I wonder why I was not able to solve every problem from the problem sets. Most of them were easy, in the sense that they involve some application of the stuff that was discussed in class. I do not think I encountered any evil problem during this two semesters, evil in the way that it requires some amount of genius to realize some not-so-obvious pattern or what-have-you. But as a professional, am I supposed to solve all the problems I encounter in life? I am afraid that a negative answer might imply some relying on others or something like that to avoid responsibilities. But after all, are we not working on a community? Well, I guess I tried being independent during this past semesters... but I suppose most people discuss their problems with somebody else.
I would like to mention something attributed to Gell-mann about Feynman's problem-solving algorithm:
One last thing I would like to address. Solving textbook problems does not make me great. After all, their purpose is to teach and get some ideas across. All this problems have been solved countless times by many others. So me and my little blog about problems does not makes me any better than anybody else. I am eager to start working on research problems, the type of problems that nobody has solved yet. This is what science is about in the first place, to understand the unknown.
Know how to solve every problem that has been solved.What is Feynman trying to say? He means understand the solution to every problem that has be solved so far. Well, to most problems that have been solved. The way I see things so far, physics can be seen in some ways as a collection of canonical problems in different disguises. For example, the linearisation of non-linear equations of motion. Some of them admit solutions that involve harmonic oscillations about a certain point. In this case, the harmonic oscillator is the canonical problem. Even though this approach does not gives us the complete equations of motion, it still gives us some information about this small oscillations. And of course, the importance of the (classical and quantum) harmonic oscillator cannot be overstressed.
I do not think I have the capabilities of ever learning how to solve every problem that has ever been solved. But I guess it is a nice goal to set in life, unrealistic as it is. Is it worth learning all that stuff? Well, one can imagine that if we adopt this task, it will be eternal; new problems are solved everyday. In fact, in mathematics it is customary to re-solve problems with different approaches until the most elegant and simple way of getting the results have been reach. But life is all about learning. One will never know enough. In my opinion this is true, only arrogant will believe that they will know enough one day that they will simply stop learning.
Another quote from Feynman goes like:
The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to.Now Feynman is trying to tell us that some problems are more worthwhile than others, based on their resolvability. I think this is a comment address to individuals. In my opinion it says something like "Know when you have more than you can bite". That is, everybody has their talents and it does not make much sense to approach problems where you will just stare at it silently for long hours with no idea at all. Now I am not talking about classroom-type problems, but in general physical questions. For example it could refer to some sort of experiment that cannot be carried out for some particular reason, or simply a calculation that is really out of ones league.
I am not saying that one should not try something hard and just comfort on the easy problems, whatever those are. The thing is this too is individual. Some people find some problems easy and others hard and some other people do the opposite, so in the end it also depends on interest. What I am trying to say can be explain better through an example. Say I am a theorist, and I want to calculate something that involves an application of a branch of mathematics I really do not know much about. In this case learning the new math will come as part of the knowledge package that comes during the process of solving the problem. But if I am really bad with that particular branch of mathematics, then depending on the degree of badness one can try and try and someday solve the problem or just be stuck forever on something that simply is not your stuff.
Maybe, just maybe, that quote was also referring to Feynman's view on string theory or quantum gravity in general. Maybe Feynman wants to tell us that there are some questions that really do not matter. Personally I do not think that the problem of quantum gravity does not matter just because it might not be pertinent in life. The truth is that there are also other open questions in modern physics that are more "basic", like understanding turbulence. It is "basic" in the sense that the problem is of classical origin, and has been around for a long time. I recall reading something along the lines of "There are other exiting problems in physics other then quantum gravity, like understanding the flow of water through a pipe". This is true. But I believe that turbulence is not an easy problem so in my case it is not worthwhile ;-).
In the end there are no such things as easy or hard problems; all problems require a consideration of certain ideas and situation that sometimes happen to be the most familiar to the person trying to solve them. For example, in my Quantum Mechanics final exam I could not answer one question about eigenfunctions of the quantum harmonic oscillator. Of course as an undergraduate student I went through all the derivation of the solutions (which apparently I forgot). Was the problem hard? No, I just happened to forgot a particular set of information, namely a set of symbols that represent the energy eigenfunctions for the quantum harmonic oscillator in an arbitrary energy level. It was not just a set of symbols, but I am still bitter about it ;-).
Some time ago I started another blog, The problemsheet. My intentions to start that blog were (1) to share with others solutions to some of the problems I encountered as a graduate student, and (2) to practice my typesetting with LaTeX.
In the back of my head I had some other intentions, like pursuing my own version of Feynman's goal and trying to show "someone" that I can solve problems. Maybe I wanted to be a smart ass like the people who display the solution to famous textbook problems online. I guess most of them do not want to show-off, they are just trying to help other students. That is particularly my first intention, but I know that in the back of my head I also want to show-off the grandness that I sincerely do not have. Nevertheless I comfort myself by thinking that by typing this solutions I am actually going through the problem again from the start, following it and looking for mistakes.
Another point that is also related to teaching is the fact that sometimes it is not easy to present one's results in a clear way without omitting some important steps. When I write down my solutions to assigned problem sets I try to be as clear and explicit as possible. Maybe it is the mathematician in me (who does not help me that much, that bastard...), or maybe it was the product of my undergraduate professors. I notice that fellow graduate students are not as explicit as I am in their solutions. I guess I want to be as clear as possible that (I think) I know the stuff I am talking about and am not fooling anybody. Nevertheless, I have been able to fool myself a couple of times.
Do people really expect students to solve every problem that is thrown at them? Now that I look back, I think my professors did. And I wonder why I was not able to solve every problem from the problem sets. Most of them were easy, in the sense that they involve some application of the stuff that was discussed in class. I do not think I encountered any evil problem during this two semesters, evil in the way that it requires some amount of genius to realize some not-so-obvious pattern or what-have-you. But as a professional, am I supposed to solve all the problems I encounter in life? I am afraid that a negative answer might imply some relying on others or something like that to avoid responsibilities. But after all, are we not working on a community? Well, I guess I tried being independent during this past semesters... but I suppose most people discuss their problems with somebody else.
I would like to mention something attributed to Gell-mann about Feynman's problem-solving algorithm:
- write down the problem;
- think very hard;
- write down the answer.
One last thing I would like to address. Solving textbook problems does not make me great. After all, their purpose is to teach and get some ideas across. All this problems have been solved countless times by many others. So me and my little blog about problems does not makes me any better than anybody else. I am eager to start working on research problems, the type of problems that nobody has solved yet. This is what science is about in the first place, to understand the unknown.
22 May 2007
Where is the quanta in this blog?
I have been reading the first few chapters of Srednicki's QFT. I feel like I have been moving slowly, I am still struggling with chapter 2 on Lorentz Invariance. I just want to make sure I understand how to work out all the derivations that are part of the end-of-the-chapter problems. Most of the problems are finding the commutator of a scalar field with the Lorentz generators and other stuff. More progress has been made in the next chapter on canonical quantization. I think I was successful in quantizing the complex (non-hermitian) scalar field. I was able to show that the field and its hermitian conjugate ( h.c.) obey the Klein-Gordon equation, I found that the conjugate momenta of a field are really the time-derivative of the h.c. field (i.e. for the field the conjugate momenta is the h.c. of the field-dotted) and wrote everything in terms of a mode expansion. Then I tried my hand at writing the commutators for the coefficients and their h.c., but I had a bit of a hard time understanding the motivation behind some of these commutators. Anyways, I think I wrote down the Hamiltonian density and integrated to obtain the Hamiltonian. I am going to try my hand now at the LSZ reduction formula for the complex scalar field.
I also found some nice material on Ryder's book on QFT about Lorentz invariance and the generators. Might take a look at that later in the evening.
I also found some nice material on Ryder's book on QFT about Lorentz invariance and the generators. Might take a look at that later in the evening.
19 May 2007
Lorentz generators
Today I spent the day reading about the Lorentz generators. Just like spatial rotations, one can find generators that describe boosts. These have the same form as rotations, with the "angle" being the rapidity and instead of having trigonometric functions one has hyperbolic ones.
Basically I just went through some of the steps that Srednicki skips in deriving the commutation relations for the Lorentz generators. I have been slow, if I want to cover a lot of material during the summer I must move faster through the book. At least I am able to reproduce the calculations, which makes me feel not so stupid.
Basically I just went through some of the steps that Srednicki skips in deriving the commutation relations for the Lorentz generators. I have been slow, if I want to cover a lot of material during the summer I must move faster through the book. At least I am able to reproduce the calculations, which makes me feel not so stupid.
18 May 2007
Where to start?
I want to do a lot of readings during the summer. My list includes Srednicki's Quantum Field Theory, Zwiebach's A first course in String Theory and Nakahara's Geometry, Topology and Physics.
The thing is, I do not know where to start... I was reading the first few chapters of Zwiebach's. It is alright, but I kind of want something more pertinent. The first few chapters are just building up to the relativistic quantum open and close string on chapters 12 and 13. I do not want to skip anything, but at the same time I feel a bit desperate. Anyways, I think I am going to try now Srednicki's book. Maybe I will be able to get through the first part on spin 0. I have to start with the math at some point too...
The thing is, I do not know where to start... I was reading the first few chapters of Zwiebach's. It is alright, but I kind of want something more pertinent. The first few chapters are just building up to the relativistic quantum open and close string on chapters 12 and 13. I do not want to skip anything, but at the same time I feel a bit desperate. Anyways, I think I am going to try now Srednicki's book. Maybe I will be able to get through the first part on spin 0. I have to start with the math at some point too...
17 May 2007
Spring grades are up!
I am sad to inform that I got B+ in most of my classes on this spring semester, compare to last semester's two B+ and one A-. I even got an A- in seminar, last semester I got an A!
I have mixed feelings about this. On one side I am still thinking like an undergrad, saying to myself that I could have done better, that I need to be on the top of my class, that nobody would like to work with a mediocre students with all B+s. On the other side I just do not care, and I feel like grades are not important. I have learned a lot, and sometimes I have been a bastard (like with Quantum Mechanics, which ironically was my favorite topic). I did a bit poorly on some homeworks because I did not had an idea on how to start some of the problems. The only thing that makes me feel better was that I did not copy solutions from websites or other students.
So I guess in the end all this grades make me feel more human. I am not a "perfect, know-it-all" student. I cannot solve every problem that is aimed at me. I will try them, and maybe I did not tried hard enough sometimes... but I did tried. Hopefully somebody will still want to work with me next year...
I have mixed feelings about this. On one side I am still thinking like an undergrad, saying to myself that I could have done better, that I need to be on the top of my class, that nobody would like to work with a mediocre students with all B+s. On the other side I just do not care, and I feel like grades are not important. I have learned a lot, and sometimes I have been a bastard (like with Quantum Mechanics, which ironically was my favorite topic). I did a bit poorly on some homeworks because I did not had an idea on how to start some of the problems. The only thing that makes me feel better was that I did not copy solutions from websites or other students.
So I guess in the end all this grades make me feel more human. I am not a "perfect, know-it-all" student. I cannot solve every problem that is aimed at me. I will try them, and maybe I did not tried hard enough sometimes... but I did tried. Hopefully somebody will still want to work with me next year...
15 May 2007
Pi time!
Quantum crops like to celebrate pi time, instead of the British tradition of tea time.
[Edit: I have just realized that pi time should be taken to be 3:14 AM not PM... Oh well!]
[Edit: I have just realized that pi time should be taken to be 3:14 AM not PM... Oh well!]
One year down...
... and so many to go. Today I had my last final examination of the spring semester, on Quantum Mechanics.
Overall it was a fair examination. I think some of the problems involved a significant amount of tedious algebra. I finished 15 minutes early, but I did not worked on the last problem, and I deserved it. The first problem was a harmonic potential along the z- axis define on a square region of the x-y plane, outside this region an infinite potential in the x and y directions. We were asked to find the energy eigenvalues and normalized eigenfunctions, but I could not recall the functional form of the harmonic oscillator eigenfunctions. I learned them at some point and I got used to reading them from textbooks, so I could not remember from the top of my head. Oh well. This makes me a tad annoyed, since the professor did not allowed a formula sheet. If I were stranded on a deserted island with no books or any food, I think the first thing on my mind will be to get something to eat, not doing any physics. But maybe that would be the fundamental difference between me and "the good students"; they choose physics above personal satisfaction.
Anyways, the second problem was about time-dependent perturbation theory. We had a potential that was turned on and was cubic in x and decayed exponentially in time. The system was a harmonic oscillator. We were asked to find the probability to have transitions to any state starting in the ground state. It took me a while to remember the expression for the first order correction, but at the end I think I got it. I was happy with my self, since I was able to write the cubic x term in terms of the creation and annihilation operators and the number operators and this time I got something that was really easy to finish. I remember one homework we had a cubic term and I did not simplified it enough. But thankfully I had the idea to write everything in terms of the number operator and the made it easy to realized only two terms survived. The third problem was two identical fermions in an infinite well potential and we were asked to consider the spatial wavefunction for the triplet and singlet spin states. Finally, the last problems were about a constant potential radial barrier, and we had to answer some questions about phase shifts. I knew this question was coming and guess what? I did not study for it. The last week of classes were really hard on my sleeping, so I was half awake during class; and I just thought it was a complicated topic for an exam. Wrong! None of those is a real reason not to studied. I never learn my lesson, it is a good thing that I could not answer that last question, because I did not deserved to done well.
All is done, I passed Statistical Mechanics with a B+. I finished my finals. I can relax. Meri is coming tomorrow and we might go to New Haven for some exploring. Today I will try to start with my summer self study: Quantum Field Theory, basic String Theory and a big load of Mathematics!
Overall it was a fair examination. I think some of the problems involved a significant amount of tedious algebra. I finished 15 minutes early, but I did not worked on the last problem, and I deserved it. The first problem was a harmonic potential along the z- axis define on a square region of the x-y plane, outside this region an infinite potential in the x and y directions. We were asked to find the energy eigenvalues and normalized eigenfunctions, but I could not recall the functional form of the harmonic oscillator eigenfunctions. I learned them at some point and I got used to reading them from textbooks, so I could not remember from the top of my head. Oh well. This makes me a tad annoyed, since the professor did not allowed a formula sheet. If I were stranded on a deserted island with no books or any food, I think the first thing on my mind will be to get something to eat, not doing any physics. But maybe that would be the fundamental difference between me and "the good students"; they choose physics above personal satisfaction.
Anyways, the second problem was about time-dependent perturbation theory. We had a potential that was turned on and was cubic in x and decayed exponentially in time. The system was a harmonic oscillator. We were asked to find the probability to have transitions to any state starting in the ground state. It took me a while to remember the expression for the first order correction, but at the end I think I got it. I was happy with my self, since I was able to write the cubic x term in terms of the creation and annihilation operators and the number operators and this time I got something that was really easy to finish. I remember one homework we had a cubic term and I did not simplified it enough. But thankfully I had the idea to write everything in terms of the number operator and the made it easy to realized only two terms survived. The third problem was two identical fermions in an infinite well potential and we were asked to consider the spatial wavefunction for the triplet and singlet spin states. Finally, the last problems were about a constant potential radial barrier, and we had to answer some questions about phase shifts. I knew this question was coming and guess what? I did not study for it. The last week of classes were really hard on my sleeping, so I was half awake during class; and I just thought it was a complicated topic for an exam. Wrong! None of those is a real reason not to studied. I never learn my lesson, it is a good thing that I could not answer that last question, because I did not deserved to done well.
All is done, I passed Statistical Mechanics with a B+. I finished my finals. I can relax. Meri is coming tomorrow and we might go to New Haven for some exploring. Today I will try to start with my summer self study: Quantum Field Theory, basic String Theory and a big load of Mathematics!
12 May 2007
Graduate Food
Now that I am finishing with my first year of graduate school, I think I should start writing about my impressions and experiences. I decided to comment first on the food ;-). You see, when you are so busy sometimes you can forget that you need to eat food at least twice a day. I tried having three meals a day. Since there is so little time to cook, I thought of sharing my usual meals and some recipes.
Breakfast
The easiest breakfast by far is cereal. I fluctuated between Frosted Flakes, Honey Nut Cheerios and regular Cheerios; most of the time buying the generic brand. I know, all this are not very healthy. In fact I do not eat that healthy. But I try! Anyway, some mornings I had late classes (10:40 AM), and since I tried waking up everyday at 8 AM, I had some extra time. These days I made scramble eggs with toast, or pancakes.
I am particularly fond of pancakes, they were the cheer-up meal. Usually I just followed the recipe in the box. But of course, one gets pretty tired of things, so I started experimenting. I remember that my father use to add cinnamon to the batter. I also had some oatmeal pancakes during last summer. Combining these with bananas and some vanilla, I came up with banana-oatmeal pancakes. Just prepare the usual pancake batter. Then add two drops of vanilla, a sprinkle of ground cinnamon, and a mashed banana. These were mostly prepared during the weekends, to my loving girlfriend who also loves them ;-).
My girlfriend and I are also very fond of French toast, but again this is a slightly complicated meal that takes a bit of time. So I guess my final advice for breakfast is cereal. If you really are on a hurry, there is always a bagel or a pair of toasts.
Lunch
My lunch is also not that healthy, but I found it very popular among graduate students. In order to force myself to eat some fiber, I have been eating peanut butter and grape jelly sandwiches on whole wheat bread. This is money friendly, since with less than $10 you can buy lunch for the whole week. In fact, the jelly and butter will last for a few weeks. Sides include a fruit, mostly a banana, apple or an orange; and sometimes white corn chips. All this drown under a litter of water, all important.
Maybe I will try to experiment with salads during the summer...
Dinners
Dinners are also sometimes rushed. I found that it is best to pack something and heat it on the microwave, than to walk back to the apartment or buy something at the student center. I am pretty sure pasta is the most popular food for graduate students, since it is easy to cook. Well, I am convinced now that pasta with marinara sauce does not saves well. Once you save it in the fridge, the next time you heat it it is very dry and nasty. But pesto saves the pasta, maybe because I love pesto. I had never heard of pesto before I came to the US. Two years ago I had my first basil pesto pasta. I liked it, and I am happy to say it saves well, after a couple of days it still tastes fresh. Just buy a big box of pasta and a jar of traditional basil pesto, boil the pasta, then just add the pesto. You will have three days worth of dinner. I found that helpful, cooking on Sunday night and then not bothering until Thursday night.
Another popular thing is the Mexican tortilla. You can make burritos, quesadillas, etc. Quesadillas are easy to make and are a quick meal. But my favorite are the spinach enchiladas. I learned about these two summers ago, but finally tried them last summer while at Stanford. This is the only dish that has any type of vegetable, I feel bad about that... but they are really good! I guess I add lots of cheese, which is not good for your veins... Anyways, here is the recipe:
Spinach Enchiladas
1/3 of a package of frozen chopped spinach, defrosted of course
ricotta cheese
sour cream
Mexican cheese blend
one can of enchilada sauce
flour tortillas
In a big bowl add the spinach, three spoons of ricotta, one small spoon of sour cream, half of the Mexican cheese blend and a drip of sauce. Mix well. Spread over tortillas and roll. Place enchiladas on a baking pan, maybe you want to add a layer of sauce at the bottom. Cover the enchiladas with a layer of sauce and the rest of the cheese blend. Cover with aluminum foil and bake in the oven at 435.927778 Kelvin for about 25 minutes or until the cheese is melted; you might want to uncovered them so they can get a bit golden. This makes about 4 servings.
You can make enchiladas on a Sunday night and have dinner through Thursday! Other things I tried were rice with frozen vegetables, but that never came out fine. There is always delivery. Here in the Stony Brook area so far I have tried Lan Wo, Chinese food that is cheap and they have SUNY student dinner deals. There is always Domino's and I also tried once a nearby Greek place, but that was a visit. There is an Irish pub, but I asked for a Parmesan sandwich and they brought me a chicken Parmesan pasta, which was not bad, but i was sick of pasta. When I visit Merideth in Boston, we always stop by Anna's Taqueria in the MIT campus. Their chicken quesadillas are just amazing.
Another favorite dish is the pita-bread-pizza. Just take a pita bread slice, spread some tomato sauce and add some mozzarella cheese, then bake in the oven for about 15 minutes or you can also try the microwave oven for about 2 minutes. I just love these!
I am not going to say it is very original, but after some time I decided to sprinkle some Italian garlic seasoning to the top layers of a grilled cheese. The result now is pretty tasty, you might want to try it.
There is not much meat in my usual meals. I found that meat takes longer to prepare, and I have grown comfortable with the simplistic attitude in the kitchen. I love my pork, sometimes I made some pork chops with mashed potatoes. But these were very rare.
Desserts!
This might be a surprised, but desserts might be the thing that can keep you happy through a week of exams, homeworks and grading. Mostly I made brownies. Just follow the recipe on the back of any mix box. I also rediscovered pumpkin pie. Again just follow the recipe in the pumpkin can. Pumpkin pie will also be my holiday dish for March 14th (3/14).
All this made me feel hungry...
Breakfast
The easiest breakfast by far is cereal. I fluctuated between Frosted Flakes, Honey Nut Cheerios and regular Cheerios; most of the time buying the generic brand. I know, all this are not very healthy. In fact I do not eat that healthy. But I try! Anyway, some mornings I had late classes (10:40 AM), and since I tried waking up everyday at 8 AM, I had some extra time. These days I made scramble eggs with toast, or pancakes.
I am particularly fond of pancakes, they were the cheer-up meal. Usually I just followed the recipe in the box. But of course, one gets pretty tired of things, so I started experimenting. I remember that my father use to add cinnamon to the batter. I also had some oatmeal pancakes during last summer. Combining these with bananas and some vanilla, I came up with banana-oatmeal pancakes. Just prepare the usual pancake batter. Then add two drops of vanilla, a sprinkle of ground cinnamon, and a mashed banana. These were mostly prepared during the weekends, to my loving girlfriend who also loves them ;-).
My girlfriend and I are also very fond of French toast, but again this is a slightly complicated meal that takes a bit of time. So I guess my final advice for breakfast is cereal. If you really are on a hurry, there is always a bagel or a pair of toasts.
Lunch
My lunch is also not that healthy, but I found it very popular among graduate students. In order to force myself to eat some fiber, I have been eating peanut butter and grape jelly sandwiches on whole wheat bread. This is money friendly, since with less than $10 you can buy lunch for the whole week. In fact, the jelly and butter will last for a few weeks. Sides include a fruit, mostly a banana, apple or an orange; and sometimes white corn chips. All this drown under a litter of water, all important.
Maybe I will try to experiment with salads during the summer...
Dinners
Dinners are also sometimes rushed. I found that it is best to pack something and heat it on the microwave, than to walk back to the apartment or buy something at the student center. I am pretty sure pasta is the most popular food for graduate students, since it is easy to cook. Well, I am convinced now that pasta with marinara sauce does not saves well. Once you save it in the fridge, the next time you heat it it is very dry and nasty. But pesto saves the pasta, maybe because I love pesto. I had never heard of pesto before I came to the US. Two years ago I had my first basil pesto pasta. I liked it, and I am happy to say it saves well, after a couple of days it still tastes fresh. Just buy a big box of pasta and a jar of traditional basil pesto, boil the pasta, then just add the pesto. You will have three days worth of dinner. I found that helpful, cooking on Sunday night and then not bothering until Thursday night.
Another popular thing is the Mexican tortilla. You can make burritos, quesadillas, etc. Quesadillas are easy to make and are a quick meal. But my favorite are the spinach enchiladas. I learned about these two summers ago, but finally tried them last summer while at Stanford. This is the only dish that has any type of vegetable, I feel bad about that... but they are really good! I guess I add lots of cheese, which is not good for your veins... Anyways, here is the recipe:
Spinach Enchiladas
1/3 of a package of frozen chopped spinach, defrosted of course
ricotta cheese
sour cream
Mexican cheese blend
one can of enchilada sauce
flour tortillas
In a big bowl add the spinach, three spoons of ricotta, one small spoon of sour cream, half of the Mexican cheese blend and a drip of sauce. Mix well. Spread over tortillas and roll. Place enchiladas on a baking pan, maybe you want to add a layer of sauce at the bottom. Cover the enchiladas with a layer of sauce and the rest of the cheese blend. Cover with aluminum foil and bake in the oven at 435.927778 Kelvin for about 25 minutes or until the cheese is melted; you might want to uncovered them so they can get a bit golden. This makes about 4 servings.
You can make enchiladas on a Sunday night and have dinner through Thursday! Other things I tried were rice with frozen vegetables, but that never came out fine. There is always delivery. Here in the Stony Brook area so far I have tried Lan Wo, Chinese food that is cheap and they have SUNY student dinner deals. There is always Domino's and I also tried once a nearby Greek place, but that was a visit. There is an Irish pub, but I asked for a Parmesan sandwich and they brought me a chicken Parmesan pasta, which was not bad, but i was sick of pasta. When I visit Merideth in Boston, we always stop by Anna's Taqueria in the MIT campus. Their chicken quesadillas are just amazing.
Another favorite dish is the pita-bread-pizza. Just take a pita bread slice, spread some tomato sauce and add some mozzarella cheese, then bake in the oven for about 15 minutes or you can also try the microwave oven for about 2 minutes. I just love these!
I am not going to say it is very original, but after some time I decided to sprinkle some Italian garlic seasoning to the top layers of a grilled cheese. The result now is pretty tasty, you might want to try it.
There is not much meat in my usual meals. I found that meat takes longer to prepare, and I have grown comfortable with the simplistic attitude in the kitchen. I love my pork, sometimes I made some pork chops with mashed potatoes. But these were very rare.
Desserts!
This might be a surprised, but desserts might be the thing that can keep you happy through a week of exams, homeworks and grading. Mostly I made brownies. Just follow the recipe on the back of any mix box. I also rediscovered pumpkin pie. Again just follow the recipe in the pumpkin can. Pumpkin pie will also be my holiday dish for March 14th (3/14).
All this made me feel hungry...
11 May 2007
Happy Birthday, Mr. Feynman
On this very day, 89 years ago (according to Wikipedia) Richard Phillips Feynman was born. Feynman was natural of Far Rockaway, which is located to the west of Stony Brook, here in Long Island.
Most physicist will tell you that Feynman was one of the best scientist of all time. He was part of the Manhattan Project, where the first atomic bomb was developed. Independent of the final purpose of this weapon, the Manhattan Project was an important and unorthodox scientific project. As a physicist, Feynman contributed to the development of the theory behind Quantum Electrodynamics and developed a diagrammatic approach to calculation that now bears his name. He also had important insights into areas such as elementary particles, computation, nanotechnology and statistical physics.
Last summer I read Feynman's biography by James Gleick. It was a wonderful read. The first thing I did after I finished reading it was to buy the Feynman Lectures. I really admire Feynman, he was really special. But sometimes I wonder whether he was really like that or whether most of his doings were exaggerations by people. In the end I do not care. Once I met somebody that actually had met Feynman. I asked this person how Feynman really was. The person just look to the sky, smiled and said "Oh he really was something...". That was the only thing he said.
Sometimes I feel like it is a bit silly to admire somebody that much. I guess (in general) people think they could be like them, they could attain all the fame and glory that a given famous have had. Well the truth is that there was only one Feynman. Nobody else can be him. And sometimes it is a bit hard to even try to be like them. What I am trying to say is that the best thing that can be done is to be honest with yourself and say: "Hey, Feynman was awesome, but I am not Feynman and should not even pretend to accomplish what he did". I want to say this, because I feel like I tried to accomplish many things that people around me where doing for some time. Maybe I am still doing some of that.
When I was in high school I remember everybody wanted to be an engineer or a doctor or a lawyer or a psychologist. I did not had an idea what an engineer did, I only knew that it had to do with NASA and space travel. When I was younger I wanted to be an astronaut too, but I think that is more common. Anyways, I remember hearing about the subject "physics", I had to take it during my 11th grade but there was some problem in my school and my class ended up taking biology as the science class. Along that same time line, I remember that I had one of those test about professions and interest. I do not remember what was my result, by I remember reading about all the descriptions for different areas. I had liked the chemistry class, but for some reason I enjoyed more the atoms and electrons part than the whole chemical balance and solutions, etc. Physics was described as something along the lines of "the study of matter and energy and their interactions". For some reason this reminded me of Albert Einstein, I guess because of his most famous equation. So I read on my encyclopedia about Einstein work, and about physics in general and found everything very interesting. And above all nobody else was interested in doing physics. So I felt good about it.
On my 12th grade I finally took my first course in physics, which was a bit disappointing. Around that same time the news of a child prodigy from a nearby town started appearing. At the time he was eleven years old, just finished high school and was going to start college to pursue a degree in physics. I remember that the first thing that came to my mind was hate, I hated him for being ahead of my and for being all smart. Then I realized that there was no real reason for me feeling this way, so I change my attitudes. Still, I continued with my interest in physics and now I wanted to attend the same university the prodigy was attending so I could meet him. It was not until my second year of college that I finally met him. To my surprise I was taking a course with him. And as it turned out, I took mostly all my physics courses with him. During the first few days it was very bad. He was quick and answered most of the professor's questions. Most of the times I did not even had time to consider the question at hand and think of how to answer it. I remember that I concentrated on getting better, just for the sole purpose of beating him. Thankfully it was not to late before I realized I was doing the wrong thing.
Pushing yourself hard just to be better than somebody else is the worst think that one can do. Along the way it makes you act in ways you never thought of behaving. In the end I realized that there was a fundamental difference between the prodigy and I, and that I should not care about his progress but care about my own. It worked well most of the time. We became good friends, just as life should be. I think life should not be about who is the best, but about what individual people accomplish and the importance of everybody's contribution.
In graduate school I found myself monitoring others still. Haven't I learned my lesson? Why is it so hard to disregard other people's progress, and just concentrate on yourself? I guess in the end one wants to success in life, and the fear of not doing so takes over everything else. My ideal state of mind is to fully concentrate on my own progress and flaws, and disregard others. It is not about ignoring, no. I want to have friends and celebrate their own success. But I do not want to compare myself with others. It is just a waste of time and energy (to conjugate variables).
Well, I wanted to talked about Feynman. At the same time I mentioned a bit bout idols and comparing yourself with others. Maybe later I will write some more on this topic.
Two final exams, two silly mistake
Well I feel accomplished! Yesterday night I did my last chunk of grading of the spring semester. I had my Statistical Mechanics final exam yesterday morning too. It went better than I expected, considering the fact that I had been doing pretty bad on the partial exams and on some of the homeworks.
There were three problems. The first problem was to consider an ideal spin-0 boson gas. We were asked to find an expression for the chemical potential, and then decided whether you can achieve Bose-Einstein condensation with that system. It was a straight-forward calculation. In the end I found that there could not be any condensation. The second problem was a two-cite Ising model. We were asked to find the susceptibility and the energy variance. At first I started to freak about about the susceptibility, since I had to calculate the average spin. But then I found an expression for the average spin; it was just the derivative of the free energy, which can be found easily with the partition function. Then I completely forgot that I wanted the susceptibility and carried on to the next part. This was my first silly mistake. I had to provided low and high-temperature behavior of the susceptibility and instead provided the analysis for the average spin. Oh well! The last problem was to consider a weakly damped one-dimensional harmonic oscillator. We had to find the spectral densities for the spatial coordinate and the momentum coordinate. I tried something, but to be honest I never fully understood this last part of the course. Partly because I did not cared (and I should have cared), and partly because It was something new and I felt it was a bit rushed (I know, that is a very lame excuse). Overall, I hope to pass the course, at least with the minimum. I have worst things to think about next semester...
But it was not until today early morning, around 2:12 AM, that I realized my second silly mistake. The Electrodynamics final exam had been on the day before yesterday. Again, three problems. The first was an easy question. My professor is an experimentalist, he works with x-rays at the National Synchrotron Light Source. In day during class he asked us what was the wavelength of one photon with an electronvolt of energy. It turns out that this is related to an expression that involves three fundamental constants: Planck's constant h, the speed of light c , and the elementary charge e. The answer is 1239.8 nm. The second problem was to reproduce the calculation of the electromagnetic fields of a charge particle in motion. The idea was to consider a charge moving with constant velocity along the x-axis and to calculate the field at a fixed point along the y axis by considering the fields in the rest frame of the particle and then Lorentz- transforming to the lab frame. It was straight forward. Finally the last problem was about an electric dipole that was rotating along the x-y plane with a given angular frequency and we were asked to calculate the radiation fields and the angular distribution of the radiated power. This expressions involve a unit vector from the source to the observer. Usually this unit vector is a position vector divided by its magnitude. But no sir, the gentlemen writing to you on this cloudy afternoon decided that the unit vector was just the sum of three unit coordinate vectors. For starters that is not even a unit vector! Everything depended on that unit-vector, so of course everything came out wrong; my power distribution was uniform... I did not realized what my mistake was until after a day. What makes me most angry is the fact that I knew it had to be wrong. But I continued on, lying to myself. It all sucks. Oh well, I had been doing better at E&M, so I expect to pass this class too.
Next Tuesday I have my last final, Quantum Mechanics. I hope I do not have to writ about my third silly mistake.
There were three problems. The first problem was to consider an ideal spin-0 boson gas. We were asked to find an expression for the chemical potential, and then decided whether you can achieve Bose-Einstein condensation with that system. It was a straight-forward calculation. In the end I found that there could not be any condensation. The second problem was a two-cite Ising model. We were asked to find the susceptibility and the energy variance. At first I started to freak about about the susceptibility, since I had to calculate the average spin. But then I found an expression for the average spin; it was just the derivative of the free energy, which can be found easily with the partition function. Then I completely forgot that I wanted the susceptibility and carried on to the next part. This was my first silly mistake. I had to provided low and high-temperature behavior of the susceptibility and instead provided the analysis for the average spin. Oh well! The last problem was to consider a weakly damped one-dimensional harmonic oscillator. We had to find the spectral densities for the spatial coordinate and the momentum coordinate. I tried something, but to be honest I never fully understood this last part of the course. Partly because I did not cared (and I should have cared), and partly because It was something new and I felt it was a bit rushed (I know, that is a very lame excuse). Overall, I hope to pass the course, at least with the minimum. I have worst things to think about next semester...
But it was not until today early morning, around 2:12 AM, that I realized my second silly mistake. The Electrodynamics final exam had been on the day before yesterday. Again, three problems. The first was an easy question. My professor is an experimentalist, he works with x-rays at the National Synchrotron Light Source. In day during class he asked us what was the wavelength of one photon with an electronvolt of energy. It turns out that this is related to an expression that involves three fundamental constants: Planck's constant h, the speed of light c , and the elementary charge e. The answer is 1239.8 nm. The second problem was to reproduce the calculation of the electromagnetic fields of a charge particle in motion. The idea was to consider a charge moving with constant velocity along the x-axis and to calculate the field at a fixed point along the y axis by considering the fields in the rest frame of the particle and then Lorentz- transforming to the lab frame. It was straight forward. Finally the last problem was about an electric dipole that was rotating along the x-y plane with a given angular frequency and we were asked to calculate the radiation fields and the angular distribution of the radiated power. This expressions involve a unit vector from the source to the observer. Usually this unit vector is a position vector divided by its magnitude. But no sir, the gentlemen writing to you on this cloudy afternoon decided that the unit vector was just the sum of three unit coordinate vectors. For starters that is not even a unit vector! Everything depended on that unit-vector, so of course everything came out wrong; my power distribution was uniform... I did not realized what my mistake was until after a day. What makes me most angry is the fact that I knew it had to be wrong. But I continued on, lying to myself. It all sucks. Oh well, I had been doing better at E&M, so I expect to pass this class too.
Next Tuesday I have my last final, Quantum Mechanics. I hope I do not have to writ about my third silly mistake.
02 May 2007
Undergraduate orientation
When I was a freshman (not so long ago... well 4 years) I had a class that was suppose to be an orientation for freshmen. What I recall the most from this class was the professor (who was the head of the department at that time) saying a lot "physics is the science, the rest are details" and claiming that this quote was from Einstein. Anyways, now that I look back, I see all that could have been covered on that class.
Something that needed to be covered was to present physics as the interesting and exciting field that it is. I would have talked about all the interesting work going on at the many national laboratories in the US and around the world. I guess from my point of view, physics sounds interesting. After all it might be a matter of whether the students are not to stubborn. In my year most of the students wanted to change to engineering. They all regarded physics as "hard". To this very day, I still get from people that physics is hard when I tell them about me being a physics graduate student.
I would have mentioned some historical background of important discoveries and advances in physics. For example, the Manhattan project provides a very interesting theme to discuss topics like ethics and working conditions. Other examples would include a small survey of Nobel prizes. The history of Quantum Mechanics would have also been a nice interesting topic, mentioning names like Bohr, Schroedinger, Dirac, Heisemberg and Feynman. Biographical talks would be nice too.
At the freshman level, physics is not that fun. I know some people will disagree with me, but I believe that with no calculus it is hard to go into much details. Still, maybe a survey of the many branches of physics and its topics. An example would be Statistical Mechanics and different species of particles (fermions versus bosons), interacting particles, mention of BECs, importance of the electron gas to Solid State physics, even define what Solid State physics is. A little overview of relativity and the different types of wormholes. Problems in high energy physics. All this maybe to the limitation of just mentioning names and dates... but I think that would be enough to motivate the students to stay in physics and try to go as far as possible.
I good freshman year will give the student the idea that the remaining years in college will be rewarding.
Something that needed to be covered was to present physics as the interesting and exciting field that it is. I would have talked about all the interesting work going on at the many national laboratories in the US and around the world. I guess from my point of view, physics sounds interesting. After all it might be a matter of whether the students are not to stubborn. In my year most of the students wanted to change to engineering. They all regarded physics as "hard". To this very day, I still get from people that physics is hard when I tell them about me being a physics graduate student.
I would have mentioned some historical background of important discoveries and advances in physics. For example, the Manhattan project provides a very interesting theme to discuss topics like ethics and working conditions. Other examples would include a small survey of Nobel prizes. The history of Quantum Mechanics would have also been a nice interesting topic, mentioning names like Bohr, Schroedinger, Dirac, Heisemberg and Feynman. Biographical talks would be nice too.
At the freshman level, physics is not that fun. I know some people will disagree with me, but I believe that with no calculus it is hard to go into much details. Still, maybe a survey of the many branches of physics and its topics. An example would be Statistical Mechanics and different species of particles (fermions versus bosons), interacting particles, mention of BECs, importance of the electron gas to Solid State physics, even define what Solid State physics is. A little overview of relativity and the different types of wormholes. Problems in high energy physics. All this maybe to the limitation of just mentioning names and dates... but I think that would be enough to motivate the students to stay in physics and try to go as far as possible.
I good freshman year will give the student the idea that the remaining years in college will be rewarding.
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