Latest Posts by silenthoughtss - Page 2

30th July 2020

🌿What would be your perfect summer day? 🌿

Wake up late,have a light breakfast,pack a good lunch and go to a nearby scenic water place with my family.My family includes my parents,my cousins,my uncles and aunts.Eat a ton of fruits,play a lot of games,make a truck load of memories and fall asleep on my mommy's shoulder in the car on the way back home.

30th July 2020

🌿What would be your perfect summer day? 🌿

Wake up late,have a light breakfast,pack a good lunch and go to a nearby scenic water place with my family.My family includes my parents,my cousins,my uncles and aunts.Eat a ton of fruits,play a lot of games,make a truck load of memories and fall asleep on my mommy's shoulder in the car on the way back home.

Today was a good day ^_^

I completed

The first chapter of Analysis 2.The first chapter is all about limits.

I also did half of chapter 13 of analysis 1.

I also solved like 15 problems of analysis 1.

I loved the chapter of power series.It was kinda cool.I also liked the chapter of limits.I am looking forward to study tomorrow's chapter ^_^

(PS:The picture is some old notes of group theory)

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. 

Heya! I finished chapter 12 of Analysis 1.It was I think the toughest chapter so far but it's not that tough that I'll loose my sleep over it.I also got the above book from Amazon today.The title is sexist but so is history 🤷🏻‍♀️I started from the last chapter and made some notes on it.I also revised chapter 8 today.Otherthan that it was a pretty chill day.I also answered an ask on Tumblr.I thought it was important to answer the question correctly and so I tried to the best of my ability 🐰

Now Nighty Nighty you guys

I hope you had a good day <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 ^_^

Heya!!

So today I just revised the first four easy chapters of analysis 1 and then I started chapter 12 (Analysis 1).Chapter 12 is about tests for convergent series like the leibinz test for alternating series,comparison tests (there are two of them) and a lot more which I will be doing tomorrow.I am feeling very tired today.I didn’t even do much.I just had 2 hours of statistics exam and have been feeling tired ever since.Maybe I did not rest enough after the exam or maybe I just have to go and sleep now.

I did place an order for some multivitamin pills though.This is the first time I’ll be using the brand so let’s just see how that goes and apart from that I telephoned two of my school teachers.Here in India it’s guru Poornima (Basically Teacher’s Day according to the Hindu calendar) and it was lovely talking to them.I really do miss them a lot.I also put a sheet mask on in the evening hoping that it’ll make me feel better.It did but I’m still tired so I’m just gonna go sleep.

Aww look at you cutie reading everything hehe I hope your day went better^_^

See you tomorrow <3

Dead Poets Society as Chaotic Academia, pinterest

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 ^_^

Which day are you counting down to? Are you giving an important example?

Hey!

I am preparing for IIT-JAM mathematics exam.It'll be in February next year.

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🌿

🌿2021 Summer Studying Challenge 🌿

Thank You to @myhoneststudyblr for creating this challenge ^^

🌸July 1 2021🌸

🌱What are your plans for this summer?🌱

I intend to complete 3 courses from YouTube.(Linear algebra,Real analysis and Differential equations).I'll be doing this by watching one lecture of LA or DE or one of RA everyday.

Perfect the proofs of Analysis 1,2,Linear algebra (Theory and computational)

Solve and perfect the problems of Vector calculus, Integral Calculus, Linear algebra , Real analysis.

🌼I also want to remember throughout this challenge that I am more capable than what I believe.🌼

🌱Day 2 of Summer Studying Challenge🌱

🌸July 2 2021🌸

🐼Do you have a specific goal for this summer ?🐼

I want to become more confident in my abilities by the end of the summer^^

🐻Today I did the following stuff🐻

Completed Assignment 3 of Vector Calculus

Completed chapter 2 of Linear algebra.

Completed chapter 1 of real analysis.

Duolingo French.

🐿Happy Summer 🐿

🐼3rd July and 4th July of Summer Studying Challenge 2021🐼

Do you have a lot of work this summer?

The work is not a lot but I do need to be disciplined to get it all done.

What is the most important task that you need to complete this summer ?

I have to complete my mathematics assignments.These include Vector Calculus, Integral Calculus, Real Analysis, Linear algebra and Group theory.It might look like it's a lot but it is not.I have been struggling with Group theory assignment 3.It has been such a nightmare lol.I did speak to my maths professor about this and he said he will help me out.So a bit relived for that.

Heya!!

Today I revised all the topics I covered in Analysis 1 so far and did chapter 8 and 9.

Chapter 8 is about the algebra of limits.In there I learnt how to write proofs using ε-N method.There were quite a number of cases (with examples!).Most of them were good and could be deduced easily from previous theorems and axioms but I did find 4 proofs a little challenging.I have noted them down and I’ll be discussing those with my prof soon.

Chapter 9 was about monotonic sequences.In there I learnt about the monotonic sequence theorem and the proof of this theorem is very cute.This theorem's proof is very intresting because it connects to the theorem where square root of 2 is proved as irrational but it is more general.So it patches all the gaps on the real number line quit nicely.There were some examples too which I liked and I also learnt the steps of proving a theorem when monotonicity is involved.

It was a pretty cool day.

I hope you had a good day too^_^

***

The Mayuriit Project

Will I make it? Stay tuned to find out!

206 days left…

🐻5th July -  Do you have any special plans or activities for this summer?🐻

I plan on learning some cooking.The other day I experimented with some paneer recipes I found on Instagram and I have been making soya noodles a lot lately as well.They have become my comfort food 🐿I have attached an image I took of my noodles this afternoon.

🐰6th July - What do you usually do during the summer? Is anything different this year?🐰

For me summer means a lot of cycling.My dad and me wake up early in the morning and just ride our bikes till we are tired.There is a nice sun rise spot where we can have tea and enjoy the sunrise..This time we couldn't do it a lot because of covid but we did try to drink tea while enjoying the sunrise on our terrace but oh boy I do miss cycling.

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.

***

[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.

***

[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..

[9.33 am] I already finished studying 20 problems of vector calculus.I did line integrals and piecewise functions.I am not that confident in calculating the integrals of Piece wise functions though so gotta work on that.

***

[1.11] Yayy just finished a chapter in group theory.I was explaining it aloud and my mom came in and said "You are gonna hurt your throat". I don't know just feeling nice about it.Maybe something like appreciating little stuff ^^

***

[10.35 pm] Yayy (happy dance) done for the day.So let me tell you what happened after the previous update.So I slept in the afternoon and my dad woke me up saying my mom was preparing my favourite sabudana vada ( Maybe I'll take a picture next time?).Yeah so the evening started nicely.Then I did a chapter of analysis. 1.I did some drawing and colouring (I'll put the pic here ) I thought it was messy and did not like it but my friends did (Yeah I sent it to them ^^).After dinner I did half a chapter of linear algebra and I am calling it a day day day.

***

221 days left to go...

Will I make it ?

The Mayuriit Project.Staytuned on a Tumblr blog near you.

[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.

***

[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.

***

219 days left to go...

Will I make it ?

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

[3.48 pm]The piecewise functions that I didn't like can be solved easily using greens theorem (Happy dance ).The only condition is that the terms gotta be continuous and bounded.I did complete my targeted 20 problems a day but not at all satisfied with the topic.So I am going to do the same topic tomorrow again but I will find some different problems.It suuuuuuuccccckkkksss when you do problems and still need more problems to perfect the concept but I am going to be patient because everything will be just fine after a year.

***

[10.43 pm] I usually wind up with my studies by now but I haven't yet finished some of it. So I am going to sit for 30 more minutes and finish it all off and not push it to tomorrow. I was helping my friend with experimental values for a physics experiment. You know those scientific notations I always used to find them boring when I first learnt about them but now after actually using them so many times I have come to appreciate them very much. Those notations feel like these delicate things to me now. You gotta handle those notations with care and when you do it will give you get such an accurate answer.its just a very nice feeling to see it come together.

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[11.45] I completed a chapter of real analysis 1 and a very small chapter in group theory.I wanted to do a bit of linear algebra but I changed my mind and so I am gonna do it tomorrow.

***

220 days left to go...

Will I make it ?

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

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 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 🍰

I really want to get into math. What book do you recommend reading!

Great question! Here are some fun ones that are still informative and that really opened up my eyes to what math truly is:

How to Solve It  by George Polya. This is a classic and the title speaks for itself: it is about how to reason mathematically.

Hyperspace by Michio Kaku. This one is mathy and sciencey. It is very geometrical and shows how our view of geometry has changed throughout history and how it has influenced science. Kaku is my favorite author.

Proof and Refutations by Imre Lakatos. Another classic. This one has to do with how mathematical proof advances our mathematical knowledge, in other words what professional mathematicians do. It is also surprisingly funny.

Other recommendations?

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.

From tomorrow I'll be starting to study real analysis,Linear algebra.I have a feeling I am going to enjoy it.

Math notes on graph theory!

Love is sympathy,tolerance and patience.

[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

July 15, 2021

Here’s a screenshot of my Notion homepage for today! I got my template from here, but I’ve customized it a lot too! :) I’ve also started managing my work based on my energy levels and it’s literally so easy??? Like, I don’t know how I didn’t think of this earlier.

15th July - Are there any special events for you in the summer? (for example, birthdays, festivals, etc.)

If you count the college application process, then yeah