So I am continuing work on the 1985 Putnam, I recently solved problem A4. Unfortunately, like A1, it was not very hard. I have not yet solved any problem of which I am particularly proud. Ah well, I should keep on working.
Define a sequence {ai} by a1 = 3 and ai+1 = 3^ai for i ≥ 1. Which integers
between 00 and 99 inclusive occur as the last two digits in the decimal expansion of
infinitely many ai?
Okay, starting this problem in a clever way is difficult, so I decided to just compute the first few terms of the sequence, and see what happens.
a1=3
a2=27
a3=3^27 (don't know last digits as yet)
I can perform my operations modulo 100 (looking at the remainder of everything when divided by 100), and just get the last digits. However, the other digits matter when taking 3^ai. It would be really nice for me if they didn't matter. (i.e. 3^100=1 mod 100). I know from Euler's theorem 3^40=1 (mod 100). It would be very nice for me if 3^20 was the same thing. I unfortunately just decided to compute it directly.
3^20=(3^4)^5=81^5=81*81*81^3=61*81^3=61*61*81=21*81=1701=1 (mod 100), so 3^20=1, and therefore 3^100=1^5=1)
So a3=3^27=3^7=81*27=2187=87 (mod 100)
a4=3^87 mod 100
=3^7 mod 100=87.
So after a3, all our ai have last digit 87. So our answer is just 87.
Saturday, March 30, 2013
Wednesday, March 27, 2013
Another Short Problem
I was looking at other competitions that I would consider doing in college, and I found out about the International Mathematics Competition for University Students. (http://www.imc-math.org/). I could enter as part of a university team (provided I get chosen for said team), or, failing that, I could go as an individual student. My curiosity piqued, I looked at the problems for the previous year of the competition, available here: http://www.imc-math.org.uk/imc2012/IMC2012-day1-questions.pdf
The first question was pretty trivial, and I got it immediately, I decided to post it here, and then go to bed. (This was a good way to make me feel a bit better about myself after my lack of success with the Putnam questions).
For every positive integer n, let p(n) denote the number of ways to express
n as a sum of positive integers. For instance, p(4) = 5 because
4 = 3 + 1 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1.
Also define p(0) = 1.
Prove that p(n) − p(n − 1) is the number of ways to express n as a sum of integers
each of which is strictly greater than 1.
This means that we have to prove that there are p(n-1) ways to express n as a sum of positive integers, with the restriction that you must include a 1 in the sum.
However, this is obviously true, as take such a sum, and subtract the 1. The remaining integers sum to n-1, and can be anything. And there are precisely p(n-1) ways to get a sum of n-1. So we are done.
The rest of the problems from this contest actually seem really cool, so I will do more of them in the future.
The first question was pretty trivial, and I got it immediately, I decided to post it here, and then go to bed. (This was a good way to make me feel a bit better about myself after my lack of success with the Putnam questions).
For every positive integer n, let p(n) denote the number of ways to express
n as a sum of positive integers. For instance, p(4) = 5 because
4 = 3 + 1 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1.
Also define p(0) = 1.
Prove that p(n) − p(n − 1) is the number of ways to express n as a sum of integers
each of which is strictly greater than 1.
This means that we have to prove that there are p(n-1) ways to express n as a sum of positive integers, with the restriction that you must include a 1 in the sum.
However, this is obviously true, as take such a sum, and subtract the 1. The remaining integers sum to n-1, and can be anything. And there are precisely p(n-1) ways to get a sum of n-1. So we are done.
The rest of the problems from this contest actually seem really cool, so I will do more of them in the future.
Update (March 27th)
So I am working currently on the other problems from that same Putnam exam, and having little success. Under normal circumstances, I would just forget about them and move on. But we can't be having that. If I actually want to get better at this sort of thing, it is important that I finish what I start. (This is applicable to most pursuits actually). I hope to solved at least one of the remaining 12 problems by this weekend.
I really have very little tenacity, it's a pretty big problem. I tend to give up things when they become difficult. If I wish to pursue a career in math, or actually in anything, I need to be able to persevere. This project provides some external motivation for that perseverance, as I need something to document. I am confident that if I pursue this project seriously, I will get some sort of actual improvement. Which is why, despite the fact that my blog entries will not be entertaining for most people and I will have no "interesting" final product, I want to to continue with it.
I really have very little tenacity, it's a pretty big problem. I tend to give up things when they become difficult. If I wish to pursue a career in math, or actually in anything, I need to be able to persevere. This project provides some external motivation for that perseverance, as I need something to document. I am confident that if I pursue this project seriously, I will get some sort of actual improvement. Which is why, despite the fact that my blog entries will not be entertaining for most people and I will have no "interesting" final product, I want to to continue with it.
Tuesday, March 26, 2013
Problem for 3/25
This is the very first problem of the very first Putnam exam. (All Putnam problems are taken from the book The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary, published by the Mathematical Association of America. )
Problem:
Determine, with proof, the number of ordered triples (A1,A2,A3) of sets which
have the property that
(i) A1 ∪ A2 ∪ A3 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and
(ii) A1 ∩ A2 ∩ A3 = ∅,
where ∅ denotes the empty set. Express the answer in the form 2^a * 3^b * 5^c *7^d, where a, b,
c, and d are nonnegative integers. ∪ means union, ∩ means intersection.
This is a very good problem for me to begin with, because it's pretty simple to state, and requires no complicated ideas to prove. Hopefully anyone reading this blog can understand it.
I solved the problem in like 5-10 minutes, but I forgot what an "ordered triple" was, so I thought I made a mistake, and continued for 1 hour, and had to use the book's hint, and arrived at the same solution as I had the first time, and then realized that an ordered triple means that (a,b,c) and (c,b,a) are different, and banged my head loudly against the desk.
Please please comment about how clear these solutions are, as I am pretty bad at explaining things.
So, I have two solutions to share:
Solution #1: (solution I found with a hint from the book):
This is basically saying, how many ways can you split {1,..10} into 3 sets, where elements can be in two sets at once, but not 3.
We can make a Venn diagram to represent this actually. Draw a Venn Diagram with 3 circles (like this), and cross out the section where all 3 circles intersect. (This is the section in white on the picture) If we fill this diagram, excluding the crossed-out part, with the numbers from 1 to 10, we can take the numbers in our 3 circles as A1, A2, A3. There are 6 different spaces in the Venn Diagram in which we can put numbers. So each number from 1 to 10 can go into any of the 6 spaces, so there are 6^10=2^10 * 3^10 ways of doing this.
Solution #2: (my solution)
Replace {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} with {1,2,3,4,....n}.
And call the number of sets f(n). I'm just going to find out how to compute f(n) in general, and then compute f(10). We do this by recursion. If we have a triple (A1, A2, A3) for some n, and then we replace n with n+1. That same triple satisfies the second property, but not the first. We can fix this by inserting n+1 into at least one of our sets.
(If we take a triple for n+1, we can remove all instances of n+1 and get a triple for n, so we don't "miss" any).
So how many ways can we do this? Well, we can add n+1 into A1, A2, or A3, which is 3 ways. But we can also add n+1 into 2 sets, as there is only a problem if it's in all 3. There are also 3 ways of doing that (adding it to A1, A2, or A2,A3, or A1,A3). So for each triple in n, there are 6 triples in n+1, so f(n+1)=6f(n).
f(1)=6, (Our choices are ({1},∅,∅), ({1},{1},∅) and all reorderings thereof).
So f(n)=6^n, f(10)=6^10=2^10 * 3^10.
I think the first solution is very nice, and that this is a pretty good problem, if a bit easy.
What I can take away from this is that early Putnam problems are not that hard(in general most contests get more difficult from year to year), and that I should really know what an ordered triple is.
Problem:
Determine, with proof, the number of ordered triples (A1,A2,A3) of sets which
have the property that
(i) A1 ∪ A2 ∪ A3 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and
(ii) A1 ∩ A2 ∩ A3 = ∅,
where ∅ denotes the empty set. Express the answer in the form 2^a * 3^b * 5^c *7^d, where a, b,
c, and d are nonnegative integers. ∪ means union, ∩ means intersection.
This is a very good problem for me to begin with, because it's pretty simple to state, and requires no complicated ideas to prove. Hopefully anyone reading this blog can understand it.
I solved the problem in like 5-10 minutes, but I forgot what an "ordered triple" was, so I thought I made a mistake, and continued for 1 hour, and had to use the book's hint, and arrived at the same solution as I had the first time, and then realized that an ordered triple means that (a,b,c) and (c,b,a) are different, and banged my head loudly against the desk.
Please please comment about how clear these solutions are, as I am pretty bad at explaining things.
So, I have two solutions to share:
Solution #1: (solution I found with a hint from the book):
This is basically saying, how many ways can you split {1,..10} into 3 sets, where elements can be in two sets at once, but not 3.
We can make a Venn diagram to represent this actually. Draw a Venn Diagram with 3 circles (like this), and cross out the section where all 3 circles intersect. (This is the section in white on the picture) If we fill this diagram, excluding the crossed-out part, with the numbers from 1 to 10, we can take the numbers in our 3 circles as A1, A2, A3. There are 6 different spaces in the Venn Diagram in which we can put numbers. So each number from 1 to 10 can go into any of the 6 spaces, so there are 6^10=2^10 * 3^10 ways of doing this.
Solution #2: (my solution)
Replace {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} with {1,2,3,4,....n}.
And call the number of sets f(n). I'm just going to find out how to compute f(n) in general, and then compute f(10). We do this by recursion. If we have a triple (A1, A2, A3) for some n, and then we replace n with n+1. That same triple satisfies the second property, but not the first. We can fix this by inserting n+1 into at least one of our sets.
(If we take a triple for n+1, we can remove all instances of n+1 and get a triple for n, so we don't "miss" any).
So how many ways can we do this? Well, we can add n+1 into A1, A2, or A3, which is 3 ways. But we can also add n+1 into 2 sets, as there is only a problem if it's in all 3. There are also 3 ways of doing that (adding it to A1, A2, or A2,A3, or A1,A3). So for each triple in n, there are 6 triples in n+1, so f(n+1)=6f(n).
f(1)=6, (Our choices are ({1},∅,∅), ({1},{1},∅) and all reorderings thereof).
So f(n)=6^n, f(10)=6^10=2^10 * 3^10.
I think the first solution is very nice, and that this is a pretty good problem, if a bit easy.
What I can take away from this is that early Putnam problems are not that hard(in general most contests get more difficult from year to year), and that I should really know what an ordered triple is.
Background
I guess I should explain who I am and define clearly what I am trying to do, as competitive math is not really something most people know much about.
My name is Irit, I, for some perverse reason, enjoy doing math. I'm currently taking Math 2240 at Cornell University, and auditing Math 4130 and Math 4540.
The purpose of this project is to prepare for undergraduate math competitions, primarily Putnam.
There are two main reasons I want to do this, actually 3.
1. Success in undergraduate competitions is helpful for applying for summer research programs, certain jobs, and graduate schools.
2. I have done pretty badly in high school math competitions (primarily the AMC and AIME), and I would like to redeem myself in college.
3. I think such competitions can be a lot of fun.
The basic routine will be something like:
1 hour every day of solving problems, doing some research, and/or blogging.
Occasionally, I will take 3-6 hours to do some full competition.
I'm going to talk more about competitions and what they are later, as I don't want to give too much information in one sitting.
My name is Irit, I, for some perverse reason, enjoy doing math. I'm currently taking Math 2240 at Cornell University, and auditing Math 4130 and Math 4540.
The purpose of this project is to prepare for undergraduate math competitions, primarily Putnam.
There are two main reasons I want to do this, actually 3.
1. Success in undergraduate competitions is helpful for applying for summer research programs, certain jobs, and graduate schools.
2. I have done pretty badly in high school math competitions (primarily the AMC and AIME), and I would like to redeem myself in college.
3. I think such competitions can be a lot of fun.
The basic routine will be something like:
1 hour every day of solving problems, doing some research, and/or blogging.
Occasionally, I will take 3-6 hours to do some full competition.
I'm going to talk more about competitions and what they are later, as I don't want to give too much information in one sitting.
Monday, March 25, 2013
Project Change
I realized, after much deliberation, that I honestly was not enjoying my project. Cooking is fun, but I felt I was limited in what I could cook, and documenting it was a pain, and I felt it was sort of meaningless. The project was really becoming a chore. The straw that hit the camel's back was when I was given an assignment to read a past journal. The student, Niko Schaff, clearly loved his project, and, as a result, his journals were entertaining to read. Mine felt flat in comparison.
So I felt it was important to change my project to one that I could talk more easily about. I have always enjoyed math (more about my mathematical background will be revealed later)
I will attend a university next year (no idea which). There is a collegiate math competition called Putnam. I would probably end up entering this competition. To that end, I wish to improve my skills in problem-solving and competitive math.
(It is actually quite fortuitous that I could not pick a name for my blog, as a cooking-related name would be out of place).
I have begun preparations today, and I will document what I've done tomorrow, when I give my math background. (I think it will make much more sense in that context.)
So I felt it was important to change my project to one that I could talk more easily about. I have always enjoyed math (more about my mathematical background will be revealed later)
I will attend a university next year (no idea which). There is a collegiate math competition called Putnam. I would probably end up entering this competition. To that end, I wish to improve my skills in problem-solving and competitive math.
(It is actually quite fortuitous that I could not pick a name for my blog, as a cooking-related name would be out of place).
I have begun preparations today, and I will document what I've done tomorrow, when I give my math background. (I think it will make much more sense in that context.)
3 things I wish I had done differently.
1. I wish I had been more whole-hearted with my journal entries, and with my project in general. It feels as if it is becoming a chore.
2. I wish I had done more last week, due to travel and other circumstances, I couldn't really accomplish anything.
3. I honestly wish I had picked a different topic, I am not really interested in journaling about cooking. I am planning on changing my project, and will probably decide whether I do that tonight.
2. I wish I had done more last week, due to travel and other circumstances, I couldn't really accomplish anything.
3. I honestly wish I had picked a different topic, I am not really interested in journaling about cooking. I am planning on changing my project, and will probably decide whether I do that tonight.
Monday, March 18, 2013
Aminia Chicken Curry
Last week, I made a chicken curry based on a recipe from the internet. Aminia is a restaurant in Kolkata, my mother's hometown. It's a Muslim restaurant, and the only place her father would take her out to eat, so this dish both has some personal significance, and is relevant to my Muslim heritage. The video I used made a mutton curry, I replaced the mutton with chicken.
This process is actually pretty laborious. You need to boil many eggs and potatoes beforehand, and chop many vegetables, before doing the actual work of making the curry. My difficulties were compounded by the fact the video was in Bengali, which I can't understand very well, and my mother was out, so I couldn't ask her to translate. So I had to figure out what and how much ingredients I needed to use.
Because the recipe was so inexact, and I did not even follow it exactly, I will not include a recipe at this time. The video I used is available, if you can speak Bengali or just want to get a general idea of what goes into this curry.
http://www.youtube.com/watch?v=te1EYPFrFpA
The result was satisfactory, I enjoyed eating it. However, I was really stressed when making it, and the proportions were pretty terrible (I only realized part of the way through that the person in the video was making much more curry than I was), so there is obviously some room for improvement.
Pictures:
This process is actually pretty laborious. You need to boil many eggs and potatoes beforehand, and chop many vegetables, before doing the actual work of making the curry. My difficulties were compounded by the fact the video was in Bengali, which I can't understand very well, and my mother was out, so I couldn't ask her to translate. So I had to figure out what and how much ingredients I needed to use.
Because the recipe was so inexact, and I did not even follow it exactly, I will not include a recipe at this time. The video I used is available, if you can speak Bengali or just want to get a general idea of what goes into this curry.
http://www.youtube.com/watch?v=te1EYPFrFpA
The result was satisfactory, I enjoyed eating it. However, I was really stressed when making it, and the proportions were pretty terrible (I only realized part of the way through that the person in the video was making much more curry than I was), so there is obviously some room for improvement.
Pictures:
 |
| Mixed spices and liquid ingredients |
 |
| Essentially finished curry |
 |
| Vegetables, to be added near the end |
In Class Entry: 3/18
I was tasked with reading a journal of a previous WISE student last weekend. The student in question, Niko Schaff, was investing in the stock market for his project.
What I got out of doing this was that it is very important that journal entries be interesting and entertaining, as, in theory, they are actually being read. Niko's entries were relatively long, varied in topic, he talked sometimes about the philosophy and ethics of investing, sometimes about future plans, sometimes about what he did today. They were all a joy to read. His research entries were also very instructive, he explained things very simply, so anyone could understand.
Unfortunately, he made some grammar mistakes (e.g. a few theirs, theres, and they'res confused), sometimes his writing style was sort of strange. I think he was becoming a little more stressed and pressed for time closer to the end, so for a while his entries got much shorter.
I think my journal entries have been kind of boring, and I want to change that. So I will try to perhaps write them more like Niko does. I also want to do more research to inform my readers, as most people here know very little about India or Indian food. To that end, I will also take a leaf out of Niko's book and provide more extensive research entries.
What I got out of doing this was that it is very important that journal entries be interesting and entertaining, as, in theory, they are actually being read. Niko's entries were relatively long, varied in topic, he talked sometimes about the philosophy and ethics of investing, sometimes about future plans, sometimes about what he did today. They were all a joy to read. His research entries were also very instructive, he explained things very simply, so anyone could understand.
Unfortunately, he made some grammar mistakes (e.g. a few theirs, theres, and they'res confused), sometimes his writing style was sort of strange. I think he was becoming a little more stressed and pressed for time closer to the end, so for a while his entries got much shorter.
I think my journal entries have been kind of boring, and I want to change that. So I will try to perhaps write them more like Niko does. I also want to do more research to inform my readers, as most people here know very little about India or Indian food. To that end, I will also take a leaf out of Niko's book and provide more extensive research entries.
Saturday, March 16, 2013
Why make ____?
The question has been posed to me, "why do I make the particular dishes I make?" The answer is primarily because many of them were quick and easy, thus suitable for making in college, and because they use ingredients we already have. There isn't a super-cohesive set of principles, nor do I think should there be.
However, I have ended up making many rice dishes, and I think it might be worthwhile to spend some time focusing on how rice is handled in different countries, and their similarities. (The Spanish, Balkans, and Iranians all have dishes that are basically pulao, they are known as paella, pilav, and polo, respectively.)
The first "complicated" thing I made was a chicken curry, modeled after one from a Muslim restaurant my mother used to frequent as a child. I chose this primarily because of its relevance to my cultural heritage, and will document it tomorrow.
However, I have ended up making many rice dishes, and I think it might be worthwhile to spend some time focusing on how rice is handled in different countries, and their similarities. (The Spanish, Balkans, and Iranians all have dishes that are basically pulao, they are known as paella, pilav, and polo, respectively.)
The first "complicated" thing I made was a chicken curry, modeled after one from a Muslim restaurant my mother used to frequent as a child. I chose this primarily because of its relevance to my cultural heritage, and will document it tomorrow.
An Indian Pantry
It is obviously important, when cooking, to keep a well stocked pantry. I sought to learn what sort of ingredients, spices, etc. I would need, if I wanted to be able to cook most Indian dishes. This list is primarily from prior knowledge, with additional information provided by research. Most of these items are used all over India.
Misc:
Rice, preferably Basmati.
Oil for cooking.
Ghee (clarified butter, used a substitute for oil in some cases)
Spices:
Ginger paste/garlic paste
Turmeric
Asafoetida (commonly called heeng (I have no idea how to properly Romanize this))
Nigella seeds (called Kalonji)
Paprika
Chili Powder
Coriander seeds and powder
Cumin
Cloves
Cinnamon
Bay leaves
Curry leaves
Peppercorns
Rock Salt
Mustard seeds
Vegetables:
Onions (used in absolutely everything)
Tomatoes (used to provide liquid)
Fenugreek (labeled Methi in Indian stores)
Legumes:
Chickpeas, lentils.
Meats are somewhat interchangeable, with the exception of pork, which is very rare in India. You can basically just buy some arbitrary cut of meat and make something with it, so there isn't a need to "stock up" on particular meat. Seafood is similar, but you need to have a pretty good idea of what fish to use. (Generally relatively bland fish such as tilapia work, avoid fish that have no place in Indian cuisine that are strongly flavored, such as salmon). Shrimp is also very common. Also, meat and fish does not keep indefinitely, so putting it in a "pantry" is often impractical, but I think these are worth mentioning here nonetheless.
Misc:
Rice, preferably Basmati.
Oil for cooking.
Ghee (clarified butter, used a substitute for oil in some cases)
Spices:
Ginger paste/garlic paste
Turmeric
Asafoetida (commonly called heeng (I have no idea how to properly Romanize this))
Nigella seeds (called Kalonji)
Paprika
Chili Powder
Coriander seeds and powder
Cumin
Cloves
Cinnamon
Bay leaves
Curry leaves
Peppercorns
Rock Salt
Mustard seeds
Vegetables:
Onions (used in absolutely everything)
Tomatoes (used to provide liquid)
Fenugreek (labeled Methi in Indian stores)
Legumes:
Chickpeas, lentils.
Meats are somewhat interchangeable, with the exception of pork, which is very rare in India. You can basically just buy some arbitrary cut of meat and make something with it, so there isn't a need to "stock up" on particular meat. Seafood is similar, but you need to have a pretty good idea of what fish to use. (Generally relatively bland fish such as tilapia work, avoid fish that have no place in Indian cuisine that are strongly flavored, such as salmon). Shrimp is also very common. Also, meat and fish does not keep indefinitely, so putting it in a "pantry" is often impractical, but I think these are worth mentioning here nonetheless.
Restaurant Indian Cuisine.
The question was posed to me why so many "restaurant" Indian dishes come from the North. (e.g. tandoori chicken, naan, etc). I couldn't furnish an answer so I decided to do some research. However, this was actually pretty fruitless. I learned that there were many Sikh laborers in the U.S in the early 20th century. Sikhs are from Punjab, an area in North India, so I guessed that this was the reason why there were so many North Indian restaurants. However, this doesn't really explain why this is true in other countries. As it turns out, my theory was correct but for the wrong reasons. My mother explained to me that there is not a great tradition of restaurants in India, and most Indian restaurants are owned by Punjabis. So Punjabis who emigrated from India took their traditions with them, and established new restaurants. Afterwards, I wanted to find an internet source that said something similar, but again, I was fruitless. (Searching for this sort of demographic information is apparently quite difficult).
This is not to say that all Indian restaurants are owned by Punjabis, or even that all dishes in an Indian restaurant owned by Punjabis are North Indian. Partially because exact authenticity is not a concern when not marketing to Indians, many such restaurants feature dishes from all over India, such as idli or dosa. (This is not a criticism, it's not as if they don't have a right to do this, and it is definitely a sound business decision)
This is not to say that all Indian restaurants are owned by Punjabis, or even that all dishes in an Indian restaurant owned by Punjabis are North Indian. Partially because exact authenticity is not a concern when not marketing to Indians, many such restaurants feature dishes from all over India, such as idli or dosa. (This is not a criticism, it's not as if they don't have a right to do this, and it is definitely a sound business decision)
Sunday, March 10, 2013
Response to Barn Video
In WISE on Wednesday, we watched a video made by a past WISE student, as his project, documenting the project of someone else, who was trying to build a barn. I think the video was well-made, as it captured well the process of doing such a project. He documented both the successes of the project (cutting of the beams, finishing the barn, figuring out how to transport cut beams), and the failures (delay of barn, arguments with father, etc.), and dealt with common pitfalls in such projects (things taking longer than expected). I think the video certainly serves its purpose: to communicate the experience of doing a WISE project. It is also quite fitting, given the purpose of the video and the subject matter, that most of the music was made by students.
The biggest criticism I can think of is that the title screen that plays clips from the video often features a very annoying sawing sound, and that is honestly quite minor.
The biggest criticism I can think of is that the title screen that plays clips from the video often features a very annoying sawing sound, and that is honestly quite minor.
Tomato Rice
This is another pulao dish in the vein of junglee pulao. However, it is primarily South Indian. It is also very simple:
The recipe is essentially identical to this:
http://www.umakitchen.com/2012/08/tomato-rice.html
I used no chili, no mustard seeds, and used 1.5 cups of rice instead of 1 cup.
The result was excellent. I was completely happy with how it turned out. I will probably revisit this again, to make sure I can make it with no recipe, as it is something I want to make often in the future.
The recipe is essentially identical to this:
http://www.umakitchen.com/2012/08/tomato-rice.html
I used no chili, no mustard seeds, and used 1.5 cups of rice instead of 1 cup.
The result was excellent. I was completely happy with how it turned out. I will probably revisit this again, to make sure I can make it with no recipe, as it is something I want to make often in the future.
Aloo Methi
I am basically going to write all the posts for this week over this weekend, because I am obviously very good at time management. On Sunday I made aloo methi (literally fenugreek potato). In essence, it is potato, cooked in mustard oil with fenugreek leaves. It is incredibly easy to make, but is also an acquired taste.
Recipe:
Small potatoes.
Mustard oil.
Water.
Chili
Fenugreek leaves.
Nigella seeds
Recipe:
Cook the seeds in the mustard oil until they begin to splutter, add a chili pepper.
When the spices are cooked, add the potatoes, mix until coated fully with oil.
Add crushed fenugreek and cover potatoes with water. (If you are using fresh greens, no water is necessary)
Cover pot and cook until potatoes are soft.
If there is remaining water, uncover the pot and cook until water is evaporated.
Result:
This honestly tasted terrible. I didn't do anything wrong in preparing it, I just don't particularly like mustard oil or fenugreek. I should perhaps avoid those two ingredients in the future.
Recipe:
Small potatoes.
Mustard oil.
Water.
Chili
Fenugreek leaves.
Nigella seeds
Recipe:
When the spices are cooked, add the potatoes, mix until coated fully with oil.
Add crushed fenugreek and cover potatoes with water. (If you are using fresh greens, no water is necessary)
Cover pot and cook until potatoes are soft.
If there is remaining water, uncover the pot and cook until water is evaporated.
Result:
This honestly tasted terrible. I didn't do anything wrong in preparing it, I just don't particularly like mustard oil or fenugreek. I should perhaps avoid those two ingredients in the future.
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| Cooking the nigella |
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| Finished product |
Sunday, March 3, 2013
Indian Cuisine by Region
India is a pretty diverse place. Between states, there are massive differences in customs, language, culture, and cuisine. The level of diversity is not present in any other country, most people don't realize that there is no real "national language" of India. (There are around 21 official languages, probably the two most widely spoken are Hindi and English) So I think a blog related to Indian food would not be complete without at least a cursory explanation of the differences in Indian cuisine by region. There are 28 states, and several territories in India, one post is not really enough to deal with the specific cuisines of all of them. So I am just going to talk about North, South, and East, and West.
South: This is the region my father comes from. It contains states such as Kerala and Tamil Nadu. It is predominantly Hindu, and has many Brahmins, so vegetarian dishes are prevalent. Southerners also often cook with tamarind and coconut milk as flavoring agents. They also use sea-fish in coastal areas. Regional dishes include avial, a mixture of vegetables cooked in coconut milk, dosa, a crepe made with rice and lentil flour, and idli, a cake (not sweet) made with rice and lentil batter.
East: Includes Kolkata, the city where my mother is from. It contains states such as West Bengal and Bihar. There are many "Bengalis" in this region, who eat primarily of river fish, notably the hilsa (similar to shad),and use sugar in their savory dishes. They also use mustard seeds and mustard oil. There are also more Muslims in the East, who often eat meat, particularly mutton, potatoes, and other root vegetables, among other things.
North: This is where a lot of "restaurant" Indian food originates. It contains states such as Punjab. Here the tandoor, a clay oven, is very prominent. Thus popular dishes in the North include Naan and Tandoori Chicken.
West: Western cuisine has been described as a combination of Northern and Southern. Probably the most well-known Western specialty is Vindaloo, a curry made with vinegar. West India contains states such as Goa and Maharashtra. Goan cuisine is actually pretty special in itself, as Goa was a Portugese colony for quite some time, and Goan food reflects this. (They use more pork and beef than the rest of India, and are noted for their sausages, which are similar to the Iberian chorizo)
South: This is the region my father comes from. It contains states such as Kerala and Tamil Nadu. It is predominantly Hindu, and has many Brahmins, so vegetarian dishes are prevalent. Southerners also often cook with tamarind and coconut milk as flavoring agents. They also use sea-fish in coastal areas. Regional dishes include avial, a mixture of vegetables cooked in coconut milk, dosa, a crepe made with rice and lentil flour, and idli, a cake (not sweet) made with rice and lentil batter.
East: Includes Kolkata, the city where my mother is from. It contains states such as West Bengal and Bihar. There are many "Bengalis" in this region, who eat primarily of river fish, notably the hilsa (similar to shad),and use sugar in their savory dishes. They also use mustard seeds and mustard oil. There are also more Muslims in the East, who often eat meat, particularly mutton, potatoes, and other root vegetables, among other things.
North: This is where a lot of "restaurant" Indian food originates. It contains states such as Punjab. Here the tandoor, a clay oven, is very prominent. Thus popular dishes in the North include Naan and Tandoori Chicken.
West: Western cuisine has been described as a combination of Northern and Southern. Probably the most well-known Western specialty is Vindaloo, a curry made with vinegar. West India contains states such as Goa and Maharashtra. Goan cuisine is actually pretty special in itself, as Goa was a Portugese colony for quite some time, and Goan food reflects this. (They use more pork and beef than the rest of India, and are noted for their sausages, which are similar to the Iberian chorizo)
Qeema
On Friday, I made Qeema, or ground meat. This is a very standard Muslim dish. I used the National Indian Association for Women's cookbook for guidelines, but made some small changes, as their recipe was very terse. The steps that go into this recipe are actually pretty standard to many Indian dishes. So it would be very instructive for me to provide a step-by-step account of what I did.
You will need:
4 Medium Onions**
1 lb. ground meat.
Oil
3 tsp Coriander**
3.5 tsp Cumin**
1.5 tsp Chili Powder**
Salt
1.5 tsp ginger paste **
1.5 tsp garlic paste**
Optional:
Whatever "hard' vegetables you want:
(e.g. potato, carrot, turnip)
Peas (frozen)
Some tomato.
**these are all things that you absolutely need to have if you want to cook almost anything Indian.
First, chop the onions and cook them in oil, in a large pot, until they completely caramelize. (The degree to which you cook the onions depends on where your dish is from, this is a Muslim dish, so cook the onions completely.)
Add the ginger and garlic paste, then the meat, and salt. Cover the pot and cook for about 15 minutes, until the meat is brown. Add the spices and "hard" vegetables, and the tomato if you elected to include that. Cook for another 6-7 minutes. Add water and then cook on a low heat setting. Add the frozen peas just a little bit before you stop cooking, you want enough time to thaw the peas and cook them a bit.
If this were any sort of curry, the steps would actually be quite similar, but you would add a large amount of water and/or tomato at some point to provide a liquid. (This is why this recipe is so instructive).
The result came out pretty well, the biggest issue was that I got impatient and did not caramelize the onions enough, but that was fairly minor.
You will need:
4 Medium Onions**
1 lb. ground meat.
Oil
3 tsp Coriander**
3.5 tsp Cumin**
1.5 tsp Chili Powder**
Salt
1.5 tsp ginger paste **
1.5 tsp garlic paste**
Optional:
Whatever "hard' vegetables you want:
(e.g. potato, carrot, turnip)
Peas (frozen)
Some tomato.
**these are all things that you absolutely need to have if you want to cook almost anything Indian.
First, chop the onions and cook them in oil, in a large pot, until they completely caramelize. (The degree to which you cook the onions depends on where your dish is from, this is a Muslim dish, so cook the onions completely.)
Add the ginger and garlic paste, then the meat, and salt. Cover the pot and cook for about 15 minutes, until the meat is brown. Add the spices and "hard" vegetables, and the tomato if you elected to include that. Cook for another 6-7 minutes. Add water and then cook on a low heat setting. Add the frozen peas just a little bit before you stop cooking, you want enough time to thaw the peas and cook them a bit.
If this were any sort of curry, the steps would actually be quite similar, but you would add a large amount of water and/or tomato at some point to provide a liquid. (This is why this recipe is so instructive).
The result came out pretty well, the biggest issue was that I got impatient and did not caramelize the onions enough, but that was fairly minor.
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| Cooking the onions |
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| Adding spices and vegetables |
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| Finally complete! |
Rice
A few days ago, I made rice. This may seem stupid to blog about, but it is something absolutely fundamental in Indian cooking. Furthermore, I made it in a perhaps unconventional manner: in a microwave. I think my readership (or lack thereof) will find knowing how too do this useful at some point. So here is the method:
You need a little less than one cup of rice per person. Wash the rice in a strainer until the water draining out runs clear. Now, place the rice in a microwave-safe vessel, with a lid. Now, add water. You want probably 1.5 cups water for each cup of rice. (I use Basmati rice, because, despite being white rice, it has a lower glycemic index, and my father is a diabetic. Basmati rice tends to expand more, so I needed 2 cups of water per cup of rice). Cook the rice for 6 minutes covered, 8 minutes uncovered, then 6 minutes covered again.
Alternatively, you could just buy a rice cooker. That is probably a better idea.
You need a little less than one cup of rice per person. Wash the rice in a strainer until the water draining out runs clear. Now, place the rice in a microwave-safe vessel, with a lid. Now, add water. You want probably 1.5 cups water for each cup of rice. (I use Basmati rice, because, despite being white rice, it has a lower glycemic index, and my father is a diabetic. Basmati rice tends to expand more, so I needed 2 cups of water per cup of rice). Cook the rice for 6 minutes covered, 8 minutes uncovered, then 6 minutes covered again.
Alternatively, you could just buy a rice cooker. That is probably a better idea.
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