A Benefit Of Going To Big Conferences Is That You Get To Learn About Math Concepts That Would Otherwise

[2.01 pm] Since morning I have been struggling with focusing on one thing.I did complete today's vector calculus stuff but with that I was also doing the drawing above and watching The wolf of Wall Street.My focus has been all over the place.I need to pull myself together.

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[7.57 pm] Done with 1 chapter of Analysis 1.It was about Cauchy sequences.I understood the proofs and was able to recreate them on my own.They were not perfect but I did get the gist.

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[9.18 pm] I am not going to finish the linear algebra chapter that I started.It is hard and I am not going to force myself.The world is not gonna end if I finish it a little late.So taking if slow.I did finish a chapter in group theory .I will do a bit of duolingo and sleep.I am planning on just doing vector calculus tomorrow and do duolingo the rest of the day.

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219 days left to go...

Will I make it ?

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

I'm kind of relieved today because I finally decided that I'll be studying more of combinatorics and algebraic geometry for my masters thesis and hopefully for my PhD as well.

Most of the time when I'm reading a mathematics textbook (currently studying Topology by Munkres) I feel like I will never understand what it is talking about.But the truth is I just have to take a deep breath and go ask for help near a prof or a friend.

#rambles #I know the sol but I get discouraged easily

Today I'm taking a break from life.

Place:Annecy

I am currently studying Analysis 1.In that they proved that the square root of 2 is an irrational number using the approximation of supremum concept and I'm floored.The proof itself makes use of 2 concepts (the completeness axiom and the law of trichotomy).I'm just in love with that proof right now.

Above are some pages from my journal.

Hope you are having a goody goody day 🍰

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!!

Heya!!

Today I revised some stuff (90% of the day lol) and did chapter 10.Chapter 10 is about the scenic viewpoint theorem,Bolzano-Weierstrass theorem for real and complex numbers.

Fun fact: Bolzano- Weiestrass theorem for reals makes use of the scenic view point theorem and monotonic sequence theorem but both of them are not valid in the complex numbers because complex numbers don't have order.

This chapter also discussed about Cauchy sequences (it has to satisfy a condition to be called that),some facts (and proofs!) about when it is bounded and such and finally the Cauchy convergent criteria.

I also did chapter 11.It is about the convergence of series.It initially told me what series means and some popular series ( telescoping,harmonic,geometric etc) and what do we mean when we say a series is convergent.It spoke about some nice theorems (involving series of non negative terms,comparison test,cauchy criteria,absolute convergence) and some examples based on the theorems.I did get one basic doubt and I'm sure my friend will be able to clear that out as well.He really has my back when it comes to these silly doubts ^_^

Sunday, 11th July 2021

Further Maths - Mechanics Mixed Exercise 2

Doing some mechanics questions to practise because it does my head in… I got this book from my parents earlier, as it’s an old present they found - looks super interesting! Today’s a funny day bc everyone’s waiting for the football tonight haha

🎵 Boulevard of Broken Dreams - Green Day

Answers to the summer studying challenge under the cut!

Keep reading

yeah

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.