25 II 2023
25 II 2023
I had an exam yesterday, one more to go. it was the written part, so 12+ hours of solving problems, exhausting just like before. I completed all of them, but of course I am not sure if my solutions are correct, I will find out on monday. I'm proud of the progress I've made
right now I'm studying for the second part, so the theory-oriented one, I can barely focus because I've already learned those things and now I have to relearn them again
I'm trying to prove all the theorems on my own. partly to see how much I remember, partly to see how much I'm willing to improvize. as they say, if you're using too much memory then you're doing something wrong so I'm hoping to be able to come up with the proofs without memorizing anything new
my technique for studying the theory for the exam is to first test myself on how much I remember by trying to write everything down and note where I'm unsure or don't remember at all. then I read the textbooks starting from the worst topics up to the better ones. when I encounter a long complicated proof I am trying to break it down into steps and give each step a "title" or a short description
for instance, the Baer criterion featured in the photo has the following steps:
only do "extenstions on ideals to R→M ⇒ M injective"
define the poset of extenstions of A → M, A ⊆ B and a contrario suppose there is a maximal element ≠B
use the assumption to define an ideal and a submodule that contradicts the maximality of the extension
it is much easier to fill out the details than to remember the whole thing. this is probably the biggest skill I acquired this semester, next to downloading lecture notes pdfs of random professors I find online lmao
a friend suggested that I could make a post about tips for reading math textbooks and papers. as for papers, I don't have enough experience to give any tips, but I can share how I approach reading the books
a big news in my life is that I got a job. I will be a programmer and I start in march. at first I am going to use mostly python, but in the long run they will have me learn java. I'm excited and terrified at the same time, this semester is gonna kill me
More Posts from Silenthoughtss and Others
28/05/2021
Hello 👋
Today I did the following stuff
Revised Physics
Started Linear algebra
Duolingo (French)
For linear algebra I'm currently watching videos by Sheldon Axler.They are short and to the point☘ Here is the link if anyone wants to check the videos out
I'm very tired today so off to bed.Ba bye and I hope you had a good day today if not,don't give a damn about this world, you are the best 🤗
2nd April 2023
It's 10.46 am right now.. I woke up at around 8.30,had breakfast, and cleaned my room while listening to an audiobook called 'Ethics:a very short introduction'.I have some complex analysis problems to solve.I am feeling lazy.Or maybe I am just afraid of failure and avoiding the task altogether.
It's 8.33 pm now.At around 4 pm I dragged myself out of my bed and started solving complex analysis problems.I did get around 20 problems done (that's my goal 20-25 problems a day and I'm happy).I have an event to attend on Tuesday so I did some online shopping for the same.I will have my dinner now and do some more problems and then go to bed.Btw that's the digital painting that I did yestrtday.It is my third one actually.It is just basic but still wanted to post it 😀.
Signing off
M
From tomorrow I'll be starting to study real analysis,Linear algebra.I have a feeling I am going to enjoy it.
4/06/2021
Heya!!
It's a beautiful day here and I have decided to do the following stuff
Complete revising Differential Equations ( I have an exam on it next week)
Finish the last assignment of Group theory
Revise Group theory Problems
I hope you have a wonderful day ^^<3
I got a proof wrong on an exam. No points.
Then, I thought about it for fifteen minutes outside of the exam, wrote it down, nailed it.
I showed a classmate and told him what happened. He looked frustrated. He’d clearly had this happen before, too (haven’t we all?). He said, “Don’t you hate it when that happens?”
I almost said yes. What the h*ck!? No. No, I do not hate it when I can fathom a deeply abstracted concept in mathematics. I never hate that. I the opposite of hate that. Expecting myself to immediately understand topics like this is unrealistic. I’m proud of being able to do it at all. Who cares if I did it in the exam or within the next hour? I DID IT. It’s mine now. I can do it whenever I want. Missing points on that problem doesn’t take the knowledge out of my brain. How dare I be taught that my knowledge is useless because I didn’t have it right at that moment. It’s just as good now.
Education is not about the arbitrary numeric number ascribed to your ability to do things quickly in an arbitrary, restricted time interval. Education is about being able to do progressively more things, to understand progressively complex things.
Tenacity and challenging yourself far beyond your limits is a hundred times more important than getting good grades. Because, when you’re one of .4 percent of the population who possess complete knowledge on a very complex topic, nobody cares how long it took you to do it, or how well you did it the first time you tried.
Grades don’t discover new mathematics. Mathematicians do (even the ones who failed a basic topic in mathematics because their base way of thinking was too complex). Grades don’t advance medical research. Scientists do (even the ones who had to apply for their PhD programs 3 times in a row before they got accepted). Grades don’t make science fiction into real-world technologies. Engineers do (even the ones who dropped out of school because they wanted to build things, not talk about building things).
Knowledge is power. Skills are power. Grades are constructs. Never trade actual understanding for a semblance of understanding.
Today I'm taking a break from life.
Place:Annecy
One can live magnificently in the world if one knows how to work and how to love.
-Leo Tolstoy
july 30, 2021
Hello! The fact few days have been horrible, and have I mentioned that my dad has made me take two SAT practice tests each day since yesterday?!?!?!?! This is the price of meeting your parents’ expectations T-T so I’m almost done with the math section and ofc I decided to abandon it and make a new post because why not?
And college applications open in two days and as you would expect, I am an AnxiousWreck™️
30th July - What would be your perfect summer day?
Just lazing around upstairs with all the windows open with a glass of orange juice and a rice bowl next to me while I watch The Disastrous Life of Saiki K until the end of time ;-;
A benefit of going to big conferences is that you get to learn about math concepts that would otherwise be outside your field. Such as
17/05/2021
Today I have classes till 4.30.I am not feeling great but I am determined not to be controlled by my negative thoughts.I will rest for some time after the classes then maybe have a cup of tea(I know drinking tea is not recommended after 2 lol but maybe an exception today), and start my work.Today I want to get done the following stuff
Complete revising my last week's maths content.(Hardly 15 minutes)
20 Problems from Group theory( at least 1 hour)
Group theory (Important actions and applications)(Maybe 90 minutes hopefully less lol)
Around 3 hours of work.Hehe not much but I'll be dead tired by the end of it.Okie see ya!
Hope you are having a wonderful day!!
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Aspiring Mathematician | I follow and like from my other blog | @mayusthings😇|Also my life just revolves around maths and books| tracking:heythoughtss|Open to asks,shoot'em
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