Mathematics - Blog Posts

[10.04 am] I am planning on waking up at 4 tomorrow and eventually make it a habit.I'll keep updating you guys on that xx

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[9.51 pm] Today I wrote my last chemistry exam for life and I couldn't be happier.Next year onwards I can just have maths courses so no more chem fuss.Tomorrow I have my law exam so preparing for that.It is an extra subject.I am not at my best today.I have been anxious all day and hopefully I will feel fine tomorrow.

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214 days left to go...

Will I make it? 49 assignments...23 courses..1 tiny room...

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

Sangaku Saturday #12

Having mentioned previously how mathematical schools were organised during the Edo period in Japan, we can briefly talk about how mathematicians of the time worked. This was a time of near-perfect isolation, but some information from the outside did reach Japanese scholars via the Dutch outpost near Nagasaki. In fact, a whole field of work became known as "Dutch studies" or rangaku.

One such example was Fujioka Yûichi (藤岡雄市, a.k.a. Arisada), a surveyor from Matsue. I have only been able to find extra information on him on Kotobank: lived 1820-1850, described first as a wasanka (practitioner of Japanese mathematics), who also worked in astronomy, geography and "Dutch studies". The Matsue City History Museum displays some of the tools he would have used in his day: ruler, compass and chain, and counting sticks to perform calculations on the fly.

No doubt that those who had access to European knowledge would have seen the calculus revolution that was going on at the time. Some instances of differential and integral calculus can be found in Japan, but the theory was never formalised, owing to the secretive and clannish culture of the day.

That said, let's have a look at where our "three circles in a triangle" problem stands.

The crucial step is to solve this equation,

and I suggested that we start with a test case, setting the sizes of the triangle SON as SO = h = 4 and ON = k = 3. Therefore, simply, the square root of h is 2, and h²+k² = 16+9 = 25 = 5², and our equation is

x = 1 is an obvious solution, because 32+64 = 96 = 48+48. This means we can deduce a solution to our problem:

Hooray! We did it!

What do you mean, "six"? The triangle is 4x3, that last radius makes the third circle way larger...

Okay, looking back at how the problem was formulated, one has to admit that this is a solution: the third circle is tangent to the first two, and to two sides of the triangle SNN' - you just need to extend the side NN' to see it.

But evidently, we're not done.

[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.

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[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

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217 days left to go...

Will I make it ?

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

Day 1

Assignment: Classwork of Vector Calculus

[11.32 am]I have ODE lab viva soon and I am terrified but hopefully, it will be over soon. I have given myself the task of completing 20 problems of vector calculus.

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[3.20 pm] I did start but there has been a dip in my motivation.So I guess I will just take a nice bath, cook some snacks for myself and my parents and then sit and study again.

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[9.45 pm] I am done for the day.Today I did some problems on vector calculus.I don't know why but I felt tired in the evening and just could not sit and solve stuff so I did not force myself.There is some kind of peace in calculating the angle between two very complex surfaces don't you think? Only if I had more energy to go through it.But now I remember also loving the concept of directional derivative.It is not done yet so gotta continue tomorrow.

222 days left to go..

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

26/05/2021

Salut 👋

I just finished 30 minutes of French 🇫🇷 in Duolingo.I love the way it sounds 🤭So today I have decided to do the following stuff

Simple Harmonic Motion

Group theory Problems

Mathematics and statistics revision

I'm hungry,I'll go prepare my breakfast now.Ba bye have a wonderful day!

18/05/2021

Hello 👋

It is currently 6.40 in the morning and I just finished doing my duolingo lessons.(I am learning French and about to complete check point one.If you know any good movies in French do let me know,I'm struggling to find some good stuff lol).

Today I want to complete the following stuff

Revise yesterday's work and do Group Theory(Important actions and applications)

Solve 10 Problems on Group Theory

Complete revising last week's maths and start revising last week's stats.

I wish a very wonderful day to you ❣ Happy, restful and productive! Don't overdo anything, health always comes first!!

Image credits: Pinterest

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.

16/05/2015

I just finished revising for group theory. It's about 5.30 in the evening and I thought I'd have it completed by 9 in the morning lol. So anyways now I plan on covering the following topics

Group acting on sets

Orbits and stabilizers

Revise maths and catch up with this week's work

Solve 10 problems on Group Theory

Wish me luck and I hope you are having a better day than me!❣

Sometimes it is the people no one imagines anything of who do the things that no one can imagine

Joan Clarke

Calculus

Time Travel Mathematics

Hypersphere mathematics identity verification

Apply timeviewers.org equations and mathematics to stabilizing wormholes and detection of projections such as whole or partial masks for souls, and falsely sourced wormhole communications or projections.

Maryam Mirzakhani was an Iranian mathematician and a professor of mathematics at Stanford University. She was the first-ever female winner of the prestigious Fields Medal prize and the first Iranian to be honoured with the award.

Mirzakhani was born in Tehran, Iran. She attended Farzanegan School, which was part of the National Organization for Development of Exceptional Talents. In both 1994 and 1995 she won the International Mathematical Olympiads for high-school students. In the 1995 International Mathematical Olympiad, she became the first Iranian student to achieve a perfect score and to win two gold medals.

Mirzakhani continued her education at Sharif University of Technology in Tehran, where she earned a BSc in Mathematics. After this, she undertook a  a Ph.D. from Harvard University. She worked under the supervision of the Fields Medalist Curtis T. McMullen, and her dissertation focused on Simple Geodesics on Hyperbolic Surfaces and Volume of the Moduli Space of Curves. She had a unique way of working, and “would spend hours on the floor with supersized canvases of paper, sketching out ideas, drawing diagrams and formulae, often leading Anahita [her daughter] to say, “Oh, Mommy is painting again!” Mirzankhani said that “I don’t have any particular recipe [for developing new proofs] … It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.”

From 2004 to 2008 she was a Clay Mathematics Institute Research Fellow and an assistant professor at Princeton University. She then became a professor at Stanford University where she specialized in theoretical mathematics including moduli spaces, Teichmüller theory, hyperbolic geometry, Ergodic theory and symplectic geometry.” 

In 2014, Mirzakhani was awarded the Fields Medal prize for her work on complex geometry and dynamic systems, becoming the first-ever female winner and the first Iranian to be honoured with the award. During her lifetime, she won a number of awards including the 2009 Blumenthal Award for the Advancement of Research in Pure Mathematics and the 2013 Satter Prize of the American Mathematical Society. She worked up until her death in 2017, and was still producing amazing mathematics during her battle with cancer over the last few years.

Sources here, here, here, here and here

2 march 2025

woah okay so my boards start tomorrow and i finished most of my revision yesterday, for today my only goal is to solve integration pyq and other model papers.

to do :

integration pyq

model papers for math

it’s a pretty chill day but i am kinda stressed cuz math isn’t my strongest subject 😭 i really wished boards started with pcb to give me some confidence in my upcoming exams but yeah wtv, it is what it is

anyways, i left probability for today and i just finished it. i feel pretty good today, not sick at all so that’s good. i pulled an all nighter last night and got a quick two hour nap at 8 am cuz my brain would not process more math without rest but i feel pretty okay and not tired even after my all nighter

anyways goodluck for today loves <3 stay hydrated

💌

i’m so happy this is my last math exam ever

Do you think two weeks is enough for revisions for a math exam..?

Hey Anon! :D

I would say yeah, it's more than enough if you know how to manage your time and revise effectively. Personally, the time doesn't really matter much if you know how to revise well :)

Math Tips

(Pictures are not mine)

Well, let me tell you, we all have this love-hate relationship with this subject, right? The worst part is that when you don't know what the heck is going on, so, as a girl who studied maths (2 Volumes/textbooks) on her own during the year she was homeschooled, here are some tips and tricks that I did to get an A+ in my math finals!

Get your syllabus together

In the beginning I had no damn idea what was going on and it was just confusing. I had to do the first thing I did was taken my index/table of contents and mark the chapters which i knew very well and the ones I had no clue about. And then i arranged them with the marking scheme, like which one carries the most marks etc etc and study accordingly.

Complete lessons/chapters that you already know

When you finish off the things you already know then that's gonna give you the confidence you need even if you know only 1-2 chapters, learn it throughout and make sure that you'll get the answer no matter how twisted the sum is. If you're doubtful about the whole textbook like any normal person.... Start with the easy ones. (I know there are literally really no "easy" chapters, spare me)

Harder chapters need hard work

Most chapters like Trigonometry proofs, Geometry proofs, Algebra, Graphs, Mensuration and Calculus etc need more than minimum effort but here's a trick, what is the common thing in this? Yes, they're all formulae and theorem based which goes to my next point. These chapters are completely based on how much you've understood your basics.

Formulae and theorem cheatsheets

Make a list of all formulae and the theorem used in the book, write them chapter wise and no printouts or digital notes. Take a paper and write it down, no excuses. It helps you while you're practicing, revising and in the last minute review, it helped me damn much. Remember, maths is a sport. The basic formulae must come to you like reflexes.

YouTube is your best friend.

For every single chapter, go and watch the basics and how a sum is done step by step. A recommendation for this is Organic Chemistry Tutor who literally is one of the reasons i passed. He has videos from basic geometry, trigonometry, statistics to calculus. Search for your own YouTubers and be clear with concepts.

Math is fully memorization

Memorize formulae and theorems with the back of your hand, you should be able to recall them within seconds. Be thorough.

Memorize basic math values (if calculator isn't allowed)

Do this if you have a majority of chapters like Statistics, Mensuration, Profit/loss calculation etc, where large numbers are concerned. Memorize the first 10 square, cube, decimal and multiplication values. It may be dry but there are literally songs available for these things, I'm serious, i learnt the first 10 cube roots by listening to Senorita xD Search for rhymes and they'll definitely be many!!

Work it out!!!!!!

Can't stress this enough, atleast 30-40 mins is the minimum for maths. I'm serious, work out each sum, don't ever think it's a waste, you'll see the results. Practice makes perfect. Work out every single sum, from examples to exercise ones cause let's be honest, our examiners love to take problems from every nook and cranny of the book.

Whiteboard method

So, I made this up and it actually works, if you have a whiteboard or anything else, once you completed a chapter, take a random page and whatever sums you have on those two pages, you need to complete within a given time limit. It helps you to identify your weak points and where the hell you're losing both time and effort and not to mention that it gives you confidence boost up.

Hope this helps :))