Hi Everyone, Here’s The Folder :)

What does FTC say?

It says that if a person takes the derivative of a function and then integrates it over a region on the number line say [a, b] then this is the same as evaluating the function on its endpoints.

What does the Green's Theorem say?

Green's Theorem is the fundamental theorem of calculus in 2 dimensions.Instead of taking the derivative of a single variable function we take the curl of a 2 variable function.Instead of integrating this over a number line we integrate it on the xy plane.Instead of evaluating the function at the two endpoints a and b and taking the difference, we take the line integral of the function and integrate it around the curve in a counterclockwise direction.

What does the stokes' theorem say?

Stokes' theorem is the fundamental theorem of calculus in 3 dimensions. Instead of taking the derivative of a single variable function, we take the three-dimensional curl. Instead of integrating this over a number line, we integrate it on the surface (To evaluate the surface integral one has to dot the vector field with unit normal vectors). Instead of evaluating the function at the two endpoints a and b and taking the difference, we take the line integral of the function and integrate it around the curve on a surface in a counterclockwise direction just like in Green's Theorem.

Do you have any favourite theorem(s)? I'd love to know xx

oh okay i like this. and of course i have favorite theorems, mostly based on how useful they are. here you go :

fermat's theorem (for congruences)

lagrange's theorem

fundamental theorem of finite abelian groups

density theorem

fundamental theorem of calculus (the one which uses riemann integrals)

wilson's theorem (for congruences)

special mention : squeeze theorem (mainly cause of the name)

Zero to the power of anything is zero. Anything to the zeroth power is one. So what is zero to the zeroth power?

The world's most cited mathematicians would seem to be in disagreement about the issue

Hello! If you don't mind can you tell me how you organised your journal for your academics.I am a maths major and I wanted to do that for my proofs as well.I did try searching on the internet but I didn't get anything good.

Thank You in advance xx

It was a really basic format honestly ! So these are all the journals I kept during my whole undergraduate degree.

The black ones were for course and module information, lecture notes, to do lists and essay plans.

The dark and light yellow were a reading journal and a dissertation journal. I wanted to separate my own impressions of texts and I wanted to keep all my dissertation research and planning in one separate place as obviously I was conducting it by myself.

Black Journals

At the start of every year I would write down all the essential information from each of the four modules I was taking. This is an example (I have whited out the name and email of my course convened and lecturer for privacy reasons). But it includes contact information, lecture and seminar hours and locations, learning outcomes and assessment criteria (the things you will be assessed on, obviously paying attention to these helped me get top grades), assessment information (how many essays or exams I had that year and how much they contributed to my final mark and how many words they were) and finally the primary reading list.

This is what a spread of my lecture notes looks like. I always hand wrote my lecture notes because I couldn’t retain information and didn’t enjoy using a laptop. In my first two years I used a rough notebook to write them down then wrote them up neatly later, which was too time consuming for third year. But by that time I had developed my note taking skills and felt confident writing them up as I listened in the lecture. I just wrote the name of the module and the text we were studying and the date for reference. I would change to a red pen for anything I felt was key information. I know most people won’t like this method but I write fast and quite neatly !

My to do lists, essay plans etc didn’t really have a format obviously. I just wrote down what I needed to do, did some rough mind mapping, occasionally put a little doodle in. My essay plans were sort of all over the place but this is where I did my essential planning and then rough work tended to be on scraps of paper or on the draft essay document. The first is a checklist at the end of the year and the second is one of the essay plans/brainstorms for an essay I got a first in.

Yellow Journals

(i.) Reading Journal

I kept a reading journal throughout university, which I wish I had used more. It’s literally just a brain dump of all my thoughts and impressions of what I was reading and any quotes I found relevant. I included secondary reading in this too in my final year. It’s something I’m going to carry on with because I love having somewhere to keep my stream of consciousness about literature. It was so helpful for me to read over this when I was writing my essays because there were some really insightful bits of analysis or key things that I had forgotten and needed reminding of. Highly recommend everyone doing this, if not on paper then on a document on your laptop !

(ii.) Dissertation Journal

There was very little method to this journal. But having it all in one place really kept me organised. It was a place of messy but very important brainstorming, figuring out and rough work. It’s the sort of thing that’s probably only coherent to me. I just wrote down what I needed to do as I went along. So in the early stages there was a lot of trial ideas, there was pages of information about how we should structure and deal with our dissertations from lectures, deadlines etc.

The first image is the first page where I started writing out some vague ideas about the topics I wanted my dissertation to address and which literature that worked with. The last two are just an example of what some of my working out looked like, how I was deciding to structure my argument, and which secondary materials and theorists I would use for each chapter. But there were all sorts of things in there, random tangential points and ideas I needed to note down, tips about how to write an effective dissertation etc. It ended up being my highest grade so this definitely worked for me !

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

🌟3rd August 2021 🌟

Summer Studying Challenge by @myhoneststudyblr

Q. What is your least favourite thing about the beach?

Probably getting sand in my hair lol

📷 The picture attached is my bujo spread for the first week of August.

📚Currenly Reading : Men of Mathematics by E T Bell.

[8.08 am] Just finished revising all the vector calculus that I have done so far. I will do 10 more pages of vector calculus today. Just praying to God that this day goes well.

***

[12.29] I studied vector calculus for an hour and so done with it for today. I will later check out Paul's online notes to see if I can use them for my next two chapters. But for now, I'll watch a movie.

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[10.18] I completed three chapters of analysis 1.Omgggg.I was listening to some om chantings in the afternoon because I was getting stressed. It did help and made my day go so much better. I still haven't figured out how I will remember the proofs. I understand them and only vaguely reconstruct them. I just have to remember that I don't need to stress about it. I'll eventually get to know about it. If you guys know how to do it then please let me know <3

***

217 days left to go...

Will I make it ?

The Mayriit Project.Stay tuned on a Tumblr blog near you.

[10.26 pm] Tomorrow’s my chemistry final.So just hoping that it goes well.Today I completed Differential calculus and vector calculus course.I still have problems to do though but that is 2 down out of 50 assignments ^^ (Happiest Dance lol).It felt nice to cross of that from my monthly goals spread.

I hope your day went well.If not there is a fresh tomorrow waiting for you.<3

***

215 days left to go…

Will I make it ?

The Mayuriit Project.Stay tuned on a Tumblr blog near you.

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!

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 ^_^

To Kill A Mocking Bird By Harper Lee

"Shoot all the blue jays you want,if you can hit'em, but remember it's a sin to kill a mocking bird"

This book throws light on various topics like prejudice, racism, civil rights, gender roles, perception, integrity without discussing them explicitly yet showing us a way to comprehend all of the topics and their effects on society.

The events take place in Maycomb, Alabama around the 1930s. It is as seen through the eyes of Scott Finch, a young bright girl of 6, inquisitive and brave to say the least. The book has the power to connect with the reader at a deeper level and help change the perspective on how one sees the world and the people in it.