Day 1

29/05/2021

Heya

I hope today treated you well

So today I did the following stuff

Revised Linear Algebra and revised the anki cards of linear algebra that I made yesterday

Did some problems on linear algebra

The surest way to succeed is through repetition of the material and by solving past papers 📝 So make sure you do finish it 3 Days before the exam.

Peace✌️

Started studying differential geometry for fun.I just hope I complete what I have started and not give up in between.

#let's see how far I go #maths

The feeling of contentment after understanding the proofs from a chapter is all that I’ll ever want and need.

#mathblr

I love nights because I can peacefully think about proofs without self made restrictions (To do lists and life)

25/05/2021

I'm gonna try and take this day slowly.Yesterday I could not do anything at all because my anxiety decided it wanted to take over my day.So today I'll try doing the following stuff

Duolingo (I'm learning French) ☑

Groups Revision ( 5 subtopics)

10 Problems

Group theory Problems

Catching up with Differential Equations ☑

I know its a lot but not pressuring myself to complete it.Just an outline and ample amount of stuff to choose from.

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

What she says: I’m fine

What she means: How come Rene Descartes is only remembered as a philosopher, and the guy who said “I think therefore I am”? The Cartesian plane is NAMED after him and still only hard mathematicians know that he invented it. Also, the whole Newton/Leibniz argument completely ignores the fact that Descartes allowed both of them to discover calculus, because of his theories/ideas and invaluable work with exponents - he literally laid the foundations of calculus but no one mentions him when discussing who invented it. He even invented the modern notation of writing powers as superscripts as well as the convention of using x,y,z for variables and a,b,c for constants. Most importantly he INVENTED ANALYTIC GEOMETRY and pulled everyone’s collective heads out of their collective asses. He was one of the greatest mathematicians. But yeah, a cool philosopher too, let’s let “Cogito Ergo Sum” be his only legacy.

My July spread 🐻

In the above picture I have a calender where I put down major events, tracker for my habits, a monthly check in for reflection and improvement.

Happy and Blessed July to you ^^<3🌿

Hello! I really like your blog and it somehow makes me feel good and safe, your notes are really pretty! When I look at them they seem so interesting and I wish to understand them but the problem is I haven't even started university (I have just finished high school) and I'm kind of scared thinking it would be too difficult for me to grasp. It is just so different from high school math but at the same much more fascinating. Do you perhaps have any advice on how to introduce myself to it, where to start? Or should I just wait for the classes to start and then study?Best wishes to you!! Thank you

Hey @dantesdream !

I just want you to know that mathematics is difficult at the University level but it is not more difficult than any other university course.It is just different.📚

So how is mathematics different and why you shouldn't get discouraged by it?

There is an entire book written on it.It is called 'Alex's Adventures in Numberland' written by Alex Bellos.There is one particular page that I really like.It talks about how are brain perceives the world around us on a logarithmic scale but mathematics is linear and that is why we have to put the extra effort into it (To convert logarithmic to linear) but according to me this extra effort is far less than wading through hundreds of textbooks often contradicting each other that many other university courses require. Here is the cover page of the book I recommended if you would like to read it.

Apart from having a positive attitude towards it I think it'll be great if you could start studying it before your university begins.

So from where should you start?

If you know where you'll be going for your university studies then you can check if your university has uploaded their notes online and start accordingly.Some old students also usually post their notes,so see if you can get your hands on them.If these two options fail then there are two more.Oxford university has made all their mathematics notes avalilable.You can start with their Introduction to mathematics and complex numbers course (I'll put the link at the end).A student from Cambridge University named Dexter Chua also has made his notes available.You can start with Numbers and sets if you use his notes (Again I'll put the link at the end).

Oxford notes:

https://courses.maths.ox.ac.uk/overview/undergraduate

Dexter's notes:

https://dec41.user.srcf.net/notes/

You should be fine with these but the beginning steps into mathematics needs a little more help.You can use the book called as 'How to prove it:A structured approach' by Daniel J. Velleman.If you can read this with the first course that you are taking (your university notes or Oxbridge notes) then I think you'll enjoy the course more just like I did.Here is the image of the book

If you want to know more then I'm just a message away so feel free to ask your doubts.

And thank you for all your compliments hehe ^_^

august 25, 2021

Hey guys! I’m so sorry I haven’t posted anything lately but school’s been quite busy and I’m trying to keep up with my school work. Yesterday, I had my first meeting with the mentor I’m going to perform research with, along with the other members of the lab. I’m really excited for it! 

24th August - What three things would you take to your desert island?

My phone, a large supply of food and a blanket! ^-^