The StudyBubbleTea

Basis vectors are best thought of in the context of roads.

Imagine you are in a city - X which has only roads that are perpendicular to one another.

You can reach any part of the city but the only constraint is that you need to move along these perpendicular roads to get there.

Now lets say you go to another city-Y which has a different structure of roads.

In this case as well you can get from one part of the city to any other, but you have to travel these ‘Sheared cubic’ pathways to get there.

Just like these roads determine how you move about in the city,

Basis Vectors encode information on how you move about on a plane.

What do I mean by that ?

The basis vector of City-X is given as:

This to be read as - “ If you would like to move in City-X you can only do so by taking 1 step in the x-direction or 1 step in the y-direction ”

The basis vector of City-Y is given as:

This to be read as - “ If you would like to move in City-Y you can only do so by taking 1 step in the x-direction or  1 step along the diagonal OB ”

Conclusion:

By having the knowledge about the Basis Vectors of any city, you can travel to any destination by merely scaling these basis vectors.

As an example, lets say need to get to the point (3,2), then in City-X,  you would take 2 steps in the x-direction and 3 steps in the y-direction

And similarly in City-Y, you would take 1 step along the x -direction and 2 steps along the diagonal OB.

One is commonly asked to prove in college as part of a linear algebra problem set that matrix multiplication is not commutative. i.e If A and B are two matrices then :

But without getting into the Algebra part of it, why should this even be true ? Let’s use linear transformations to get a feel for it.

If A and B are two Linear Transformations namely Rotation and Shear. Then it means that.

Is that true? Well, lets perform these linear operations on a unit square and find out:

(Rotation)(Shearing)

(Shearing)(Rotation)

You can clearly see that the resultant shape is not the same upon the two transformations.

This means that the order of matrix multiplication matters a lot ! ( or matrix multiplication is not commutative.)

One is commonly asked to prove in college as part of a linear algebra problem set that matrix multiplication is not commutative. i.e If A and B are two matrices then :

But without getting into the Algebra part of it, why should this even be true ? Let’s use linear transformations to get a feel for it.

If A and B are two Linear Transformations namely Rotation and Shear. Then it means that.

Is that true? Well, lets perform these linear operations on a unit square and find out:

(Rotation)(Shearing)

(Shearing)(Rotation)

You can clearly see that the resultant shape is not the same upon the two transformations.

This means that the order of matrix multiplication matters a lot ! ( or matrix multiplication is not commutative.)

Give yourself a specified grieving time. You’re going to feel absolutely miserable after you fail - disappointed, angry at both yourself and your university/professors, emotionally drained and you’re probably going to convince yourself that you ARE a failure, so why do anything, ever again? You’re going to lie in bed all day and wallow in your own negativity for a while, and you need to let yourself do this! But - after a day or two, you’re also going to need to have a stern talk with yourself, have a cry if you need to and make yourself physically move on from this. Get up, take a shower, have a cup of coffee and go for a walk. Make yourself feel like a human being again, and then have another talk with yourself - this time, focusing on “ok, so what can I do about this?”

Identify the reason behind your failure. Did you procrastinate it to death? Why? Were you scared of failure? Were you scared of success? Do you feel like it’s too big, too much for you to handle? Did it stress you out to the point of being paralyzed to even begin? Do you simply just hate that class so much you’d rather feel like this for failing it than face it? You didn’t have the time? You didn’t make the time?

Forgive yourself. Personally, I could answer yes to all of those questions. I was a mess during my second year of uni, and I just couldn’t dig myself out of the hole I was in. Everything piled up, fast, and I just didn’t have the energy to deal with any of it. I’m not proud of myself, but I also no longer resent myself for this. Even if you didn’t have any “real” reasons for failing, you still need to find it within yourself to allow yourself to move on from this. Otherwise, you’re just trapping yourself in a loop of guilt and self-flagellation which is only going to stop you from actually doing anything to make it better.

Make a game plan. Sit down with your notes, and skim over everything. Determine what you need to do in order to get this done and WRITE IT DOWN. Find online resources that will help you when you get stuck. Find someone to explain the things that are still flying over your head. If your professors/assistants are approachable, ask them for pointers. Look for blogs or ask your classmates how they dealt with this class. If you get stuck on something, move on and come back to it later, but DO COME BACK TO IT. Maybe research what study technique is best suited for this particular exam, try to get some past exam papers so you can see what your prof focuses on - in short, try to make it as easy for yourself as possible to do the work and get payoff!

Once you make a plan, do your best to stick to it. It’s hard to get back in the studying game after a long rut. It’s even harder when you know you’ve already failed this once, and the fear of that happening again is constantly looming over your head. But, the only way you have any chance of beating this is by trying. Get up in the morning, look over your game plan, do things over and over again until they finally stick, allow for it to take time. If you fall back, that’s ok, you’ll do better tomorrow. Take breaks, but don’t let them last a week. Get some sleep. Go for walks. Try to eat healthy. Even if you don’t put as much work in as you’ve scheduled for that day, that’s ok too, you did something - and that’s always better than doing nothing!

Give yourself scheduled break-time! Prevent burnout at all cost! If you’re anything like me, you have now achieved a delicate balance of productivity and PANIC, and it’s very prone to tipping on either side depending on your frame of mind. Do anything you can to keep it in the productive zone, which includes giving yourself time to recharge. Take “activity breaks”- don’t let yourself just sit and stare at the material on your screen all day, get up and move around, wash the dishes, make yourself a snack, play some music and dance around… whatever works for you! Also, set an “ending time” to your day and STOP THEN. All-nighters fueled on the panic of “I didn’t do everything I needed to do today” are the absolute worst thing you can do to yourself. Get some rest and try again tomorrow.  

Find a commitment device. Either it be an app, a studyblr, a classmate, a friend, your mum - whatever works for you! Find a way to keep yourself accountable for what you’re doing and it’s going to help to keep you actually doing it.

And, finally, the thing I wanted to share the most:

Try the 5-second rule to keep yourself motivated.

This is a life-saver for people like me, who procrastinate as a reaction to stress. The “5-second rule” was invented by Mel Robbins, who used this method and is now a successful business-woman after her life literally fell apart. If you have time, please do yourself the favor of watching this video (x). In short, she has found a scientific way of beating procrastination, (even reigning in the symptoms of anxiety and depression) which is this: Every time you catch yourself thinking about doing something, be it as small as “Oh, I should probably take out the trash.” or “Oh, I really should study for this scary exam.” count down from 5, breathe in, and GO. This is going to stop your brain from having the time to talk you out of it.

She did her research and found out that, by counting down 5,4,3,2,1 you are actually not giving your brain the chance to react in a way that’s going to stop you from doing whatever it is that you know you need to be doing, because it’s going to shift to the prefrontal cortex, which is the decision making part, from the basal ganglia - which is where your habits live. Procrastination is actually a habit your brain has developed in order to protect you from emotional hurt - of fear of not being good enough, or failing, or being laughed at, etc. It also works for intrusive thoughts, I’ve found - every time you can feel yourself sinking down that hole, when your mind goes “Why are you even doing this, you know you’re not good enough, so why bother?”  try counting down from 5, take a deep breath, imagine yourself succeeding and go back to it. So, if you have done all of the above, made plan after plan and scheduled everything to death, but somehow just can’t make yourself do it - give this a try, it might just be the thing to get you going.

hello hello!!!

so, i’ve been dead on this blog for a good half year. to anyone who still follows me, thank you so so much. it really means alot, especially considering how inactive i have been on here since the start of 2018.

long story short, i was in a bad place with my health physically and mentally, and the first half of 2018 proved itself to be quite a hard one.

however, i’ve been doing a lot better as of late, and my interest in studyblr has once again been resparked!!!

since i was gone for so long, i find that my dash has become quite inactive.

- a complete breakdown of all the organic synthesis reactions -