Ways To End Proofs

re: explaining algebraic topology to not-math people

Topology is the study of spaces. Topology basically just means geometry, and spaces basically just mean shapes. But this is (way, way, way, way, way) too hard.

Linear algebra is easy. It’s the easiest kind of math there is. It’s so easy that first-year undergrads can do it!

So, rather than study topological problems head-on, we try to find ways of converting them into linear algebra problems. There’s a trade-off between power and computability: we need to destroy enough topological information to end up with something that’s actually manageable, but retain enough that once we solve the algebraic problem, it still tells us something useful about the topological problem we started with.

Throughout math, the way we understand complicated objects is to build them out of/break them into/relate them to simpler objects. We analyze the simple objects first, then try to assemble that information into an understanding of the complicated thing we started with. For example, the factorization of integers into primes means we can usually understand things “one prime at a time” (where 0 is often counted as a prime), followed by a reconstruction procedure.

We’re interested in procedures for turning topology problems into linear algebra problems. Such a procedure is called a functor if, whenever things on the topology side are related in a certain way, the corresponding linear algebra objects are also related in a similar way. This allows us to reduce the problem of calculating the value of a functor on a crazy space to first calculating it on simple spaces (such as spheres), and then assembling the resulting algebraic data.

So functors from topology to linear algebra now become our main object of study. Once again, this is too hard: for example, the unstable homotopy functor remembers nearly everything about topology, and is essentially impossible to calculate (it technically doesn’t land in “linear” algebra, but that’s not important here, since we’re going to throw it away anyway).

The issue is that plain functoriality is actually a pathetically weak condition; we need our functors to establish a much closer tie between topological input and algebraic output. Sometimes people loosely use the term “extra functoriality” for this. In any case, we want to look at what are called excisive functors. These let you understand the result of gluing two spaces together in terms of the original spaces. For example, you can get the 2-sphere by bending two disks into hemispheres and gluing them together along the equator (a circle, or 1-sphere). The unstable homotopy of a disk is zero, and the unstable homotopy of a circle is easy, but the unstable homotopy of a 2-sphere is horrifyingly complicated and will probably never be fully known. On the other hand calculating the value of an excisive functor on a 1-sphere is equivalent to calculating it on a 2-sphere.

So now we restrict again to studying excisive functors from topology to linear algebra. A more common name for excisive functors is spectra. Remarkably, spectra themselves behave quite a lot like spaces! A partial explanation for this is that when we apply a spectrum to a space, what we’re actually doing is forcing that space to become a spectrum, and then having the two things play around with each other in spectra land.

So we can port over a lot of our geometric thinking to understand spectra. But, they also behave a lot like algebraic objects, which makes them a lot easier. There’s a totally crazy sense (which can be made precise) in which spectra are the linearization or “first derivative” of spaces.

(Strictly speaking what I’ve been calling excisive functors/spectra are actually what’s called “cohomology theories”. Every cohomology theory can be upgraded to a spectrum, although there’s a slight ambiguity in doing that. Cohomology theories do not behave like spaces: you can’t properly build fancy cohomology theories out of easier ones, which, as we have seen, is crucial to understanding anything.)

So now spectra become the main objects of study; this is the field of stable homotopy theory. Once again, this is too hard in general: stable homotopy, while more tractable than unstable homotopy, is still essentially impossible to calculate (it subsumes many extremely hard problems in other areas of mathematics, such as number theory). On the other hand there are lots of spectra which are easy to calculate:

The Eilenberg-Mac Lane spectrum H gives the singular (co)homology of a space, which essentially just counts how many holes a space has in each dimension. This is the easiest spectrum there is. It’s so easy that first-year graduate students can do it!

The complex K-theory spectrum KU and real K-theory spectrum KO tell you how many ways there are to slide a (real or complex) vector space around your topological space. KU is relatively computable, although KO is harder.

The various flavors of bordism spectra MO, MSO, MU, MSpin, MString measure how one space can fit inside another, up to an equivalence relation called (co?)bordism. Here, two ways X and Y of fitting one space inside another are called (co?)bordant if they fit together into a pair of pants, where X is the waist end and Y is the foot end. MO is very easy to calculate; the others are harder, but still doable (or at least MSO and MU are, not sure about the others). Bordism spectra come up a lot in physics/string theory; in particular MString is related to something called the “Witten genus”.

As mentioned before, when dealing with numbers it usually suffices to deal with just primes (and sometimes 0). The same strategy works with spectra: we can fix a prime p and focus only on the parts of stable homotopy theory which are “visible” to p. This is called localizing at the prime p, and is so ubiquitous that it’s often just done implicitly.

When we do this at the “prime” 0 (which is called rational homotopy theory), all the topology dies and we’re left with something completely algebraic. So this case is pretty easy, and we can focus our attention on the ordinary primes.

Thus far I’ve sort of heuristically said that some spectra are easy while others are hard; there is a a way of making this somewhat more precise. Once we localize at a prime p, stable homotopy theory splits into an onion (with infinitely many layers); these onions behave differently for each p, though, which is why we have to look at them one at a time. The outer (0th) layer is the rational Eilenberg-Mac Lane spectrum Hℚ, the first layer is more or less the complex K-theory spectrum KU, and in general things get “harder” the farther inwards you go. (The exception is that the “infinite” layer, which is the center of onion, is another Eilenberg-Mac Lane spectrum HF_p; while harder than the rational Eilenberg-Mac Lane spectrum Hℚ, this is still pretty easy to understand).

There are spectra K(n) which describe the n’th layer of the onion, as well as spectra E_n and E(n) which describe how the n’th layer fits together with the layers before/after it. (I don’t really understand this and might be lying here)

The second layer of the onion is related to elliptic curves, which are extremely important in number theory. For example, elliptic curves were central to the proof of Fermat’s Last Theorem. They’re also used extensively in cryptography (online banking, etc.). Studying the second layer led to the discovery of the spectra TMF, Tmf, and tmf, which respectively stand for TOPOLOGICAL MODULAR FORMS, Topological Modular Forms, and topological modular forms; these also show up in string theory. Mark Zuckerberg and Yuri Milner threw 3 million dollars at Jacob Lurie for (among other things) his work on understanding this.

The current consensus is that the layers after the second are too hard to understand in significant detail.

Proof by induction

Proof by contradiction

Proof by using a Renaissance painting as your header image

Proof by saying “QED” at the end

Proof by using that weird symbol which means “QED” at the end

Proof by dead thinker who predicted our current impasse with alarming clarity

Proof by reaction gif with unexamined racial undertones

Proof by procrastinating on replying to critics until a time when it would just be weird to bring that old debate up again

Proof by purposefully never replying to critics so as to build up an aura of unchallenged sagacity among your followers

Proof by accelerating the goalposts to .998 c

Proof by how the characters in a novel you read reacted to a situation that was kinda like this

Proof by referencing obscure EU legalese that’s been outdated since 2003 but no one will look up

Proof by referencing a single social science study

i love that the phrase is “in love” like love is a place. like somewhere you could live.

Because of coronavirus, a lot of recent grads are moving back home. After four years (or more) of freedom, being back home is a big adjustment and it’s easy to revert back to our teenage behaviors. Here are some of the things I’m doing to feel a little more like a grown up while I’m living at home!

i. make your space your own

Just cleaning out your room can make a huge difference. Donate your old clothes and take your old posters from high school down. If you’ve got the time and resources, a fresh coat of paint or new bedding can also do a lot to make your old room feel more adult. You can also rearrange furniture to make a workspace if you’ll be working from home or applying to jobs.

ii. set boundaries

Lovingly set some ground rules about how you can best support each other. This is especially important if you’ll be working or taking classes from home – let them know you’ll be unavailable during certain hours so they don’t barge into a Zoom meeting. 

iii. build a routine

Even if you’re not working or in class at the moment, it’s important to be intentional about your time. The biggest thing that contributed to me feeling like a kid when I first moved back was spending my days watching Netflix and napping. Which are totally valid! But add in other daily activities, like taking your dog for a walk and making yourself a nice breakfast.

iv. make time for friends

I normally hate virtual hangouts, but they’ve been so important for my mental health during quarantine. Schedule a weekly Zoom coffee date with your group of friends. FaceTime your old roommates. Meet your high school bestie in the park and have a distanced picnic (don’t forget masks!). Having a support system is so important right now!

v. find new hobbies

This is the perfect time to try out new hobbies. Plus, craft stores have been having great sales since they know everyone is cooped up all summer. I found some really fun craft kits that I never would have tried normally, and now I’m the proud owner of a woven frog wall hanging. A few ideas: painting, tie dying, embroidery, yoga, running, learning a new language, reading, etc.

Having a long-term project to work towards – like a larger art project or trying to master a difficult yoga pose – helps to keep the days from running together.

vi. find ways to feel “normal”

Everyone, no matter their living situation, is feeling really upended right now. Find the little ways to bring back pieces of your “normal” life. Learn how to make your favorite coffee shop drink at home. Cook for yourself. Wake up at your normal time even if you don’t have to. Keep up with your normal exercise and self care routines – they’re more important now than ever!

In light of me graduating tomorrow, I’ve decided to make a bit of a guide for those younger students who have not yet experienced college. Keep in mind, I am American and attended an American university while living on campus.

LAUNDRY/CLOTHING/FASHION

hand wash your intimates (panties and bras). they’ll last longer.

don’t get wrapped up in sticking to an aesthetic. just wear what’s clean

hang the next day’s outfit on your closet door

have one outfit for every occasion

invest in plain solid colored tops, a business formal and business casual outfit, and comfortable shoes

fold a plain t-shirt, roll it up tiny and stick it in a bag. keep this in your everyday bag if possible in the event a guy named Eric spills coffee on you in Bio

use scarves, plaid shirts, belts, ties, etc to spice up your wardrobe. but also, its fine to wear the sweatpants and hoodie to every class

THE LIBRARY

don’t get attached to just one singular spot. explore like you’re in a video game looking for hidden items.

sometimes you end up working in the library for their full operating hours. keep a travel bag with toothbrush/toothpaste/floss, mini bottle of face wash, pads/tampons, pain reliever, hair ties, and chapstick. just in case you stay until 2am at closing and you have an 8am and you know you won’t get much sleep.

have cash on you, have money on your student card, have your ID with you at all times and USE EVERY RESOURCE they offer.

minimize how much you bring. my library had desktop computers but also you can borrow macs and ipads for a period of time. also, they have chargers you can borrow.

photocopy, print, scan, etc is your friend. borrow a textbook from a friend for a day and have your own copy in minutes at the library.

follow the rules of the land. don’t be that guy/girl/person.

FOOD/DINING HALL

plan your meals

budget your meal plan so you don’t end up starving during finals week

KNOW EVERY SINGLE DEAL/SALE/SPECIAL OFFERED AT FAST FOOD JOINTS

eat with others, especially when you’re struggling to get food

if it isn’t essential, don’t buy it

never shop hungry

make lists before you grocery shop. shop more on the outer rings of the stores where the fresh, healthy food is

DRINK WATER

cook like you’re trying to survive a harsh winter. leftovers that last. carbs and protein heavy.

have family send you care packages with essentials you can’t get where you are.

GET THE RECIPES FOR YOUR FAVORITE HOMECOOKED MEALS

CLASSES

unless you invented mornings or are the god Apollo, please refrain from taking 8AM classes

never make big gaps in between your classes in one day. schedules should maximize efficiency. have enough time to eat and pee between classes and nothing more.

office hours. go to them. no matter what your status in the class is. you want those letter of recommendations, don’t you?

sit in the front

do the readings, write down questions you have, take good notes, make sure all your questions are answered before class is over

make friends with your classmates. emailing the whole class to get notes you missed is a huge nono

make money by being someone’s note-taker

go to tutoring sessions

make besties with your TA

STUDYING/HOMEWORK

never work on outside assignments in class

start the day you get an assignment even if it’s due next month

the minute you start a new unit, prepare for that inevitable test

you should spend hours studying for each subject. daily. for the best results

online homework is hard to remember. make phone alerts

download apps that won’t let you procrastinate on your computer when you need to study. i use writer’s block.

study before you go to bed, then pause and continue once you wake up

PUBLIC SPEAKING/PRESENTATIONS

record yourself while you practice

don’t stare at one person the whole time you’re speaking. pick three in different locations around the room

if you need to pause and look at your notes, do it naturally and comfortably. even announce that you’re taking a second to check your notes

take frequent short pauses to avoid saying uhhh and ummm while you’re trying to remember something

ask that your audience save questions for the end

practice (3x)

perform your script to a friend first. have them act as your audience, teacher, and the bad scenarios that can happen when you prepare but everything goes to shit

Hey, I’m back with another masterpost. I decided to include some of my tips.

Use the forest app to keep you off your phone, your phone is a distractions you face when studying

Try making a to-do list to plan out how much time you take to do each task so you keep track of time

Set rewards i.e. if I finish this task at 9am instead of 9.30am, I’ll watch my favourite tv show for 1 hour instead of 30mins.

How to be disciplined

I guess this is pretty much like a habit. So try to maybe start small, i.e. study 10 mins each day and gradually increase the time limit if you feel comfortable doing so. The reason I chose 10 mins is because it seems like a very short period of time so it’s easier for you to get to work.

How to manage studies with social media

Always set a time period for your school work. For example, after 30 minutes of browsing through your social media, force yourself to do a piece of school work. That way, you will still get work done instead of browsing through your social media all day long.

If you realise on tumblr, I don’t come up with an original post every day and I tend to reblog my old post or queue others posts so don’t stress too much on coming up with a post. For instagram, you could try to take pictures all during the weekend, so you don’t have to stress taking them after school, etc.  But it is important to always put studies first before your social media.

Consider switching off your phone or even deleting your social media apps or deactivating them during exams period if they are really getting in the way of your studies.

Plan

How to schedule your day when you’re unemployed by @businessinsider

How to stick your plans by @cafeinated

How to make and stick to your study plan by @sherlocks-study

Create long term study plan + how to stick to study routines by @studyforyourself

Start

How to start studying by @studylou

How to start working when you really don’t feel like it? by @studentstoolbox

What to do when you really don’t want to study by @yeon-studies

How to stop scrolling through tumblr for 3 hours when you have work by @effectivestudies

More productive

How to become more productive by @to-work-or-not-to-work

How I increased my productivity by 3 times by @brbimstudying

4 secrets to efficiency

The ivy lee method for peak productivity by @harcules

General

How to study as a busy student by @julstudies

Use studyblr to become productive by @determinationandcaffeine

Take a productive break by @thestudycoffee

5 things everyone should do on sunday night by @staedtlers-and-stabilos

Productivity 101 by @lets-study-together

The no bullshit guide to getting your shit together: for the lazy student by @knoweldge

Habits

8 morning habits for productivity by @eintsein

The 8 habits of highly productive people by @medicinasanguis

Habits of highly effective people by @onlinecounsellingcollege

6 habits for maximum productivity by @livingthatlibrarylifestyle

How to develop self discipline

How to wake up earlier by @gurl

Motivation

Focus and motivation by @katsdesk

Whenever you’re feeling unmotivated and sleepy by @evergreenstudies

How to stay awake while studying without caffeine by @getshitsdone

How to be productive + motivated on weekends by @studywithinspo

Procrastination

Types of procrastination and how to deal with them by @emmastudies

How to stop procrastination

How to stop procrastinating by @cutestudystuff

15 productivity hacks for procrastinators by @engincrd

Unconventional methods to beat procrastination by @hawkestudies

What type of procrastinator are you by @b-uwu-ng

Eliminating procrastination and distraction during a study session by @simply-study

Productive when travelling

productive commutes by @universi-tea

productivity on road trips by @intellectys

Tips

7 productivity tips by @simmonestudies

10 small tips to improve your productivity

The dutch student’s productivity tips by @thedutchstudent

My top 10 tips for productivity by @lovelybluepanda

21 tips to become the most productive person you know by @studying-towards-success

Tips and tricks for busy students by @roeum

Time management

Managing time

How to manage time by @solar-citrus

How i manage my time by @pensandmachines

Time management 

Tips

Time management tips by @365text

Time management tips for busy students

Time management tips

Tips for time management by @holocrams

26 time management hacks I’d wish I’d known at 20 by @geekvitamin

How to make the best use of your time by @tbhstudying

5 ways to manage your time efficiently by @quadrtics

Printables

Daily planner by @arystudies

Weekly planner by @studyblrbunny

Productivity printables by @thearialligraphyproject

Habit tracker by @candydsgn

Schedules by @kouiro

Bullet journal

My 2016 bullet journal setup

Sounds

Study sounds by @studyquill

Other masterposts by me

Printables

College

Apps for students

Note taking

Math

Bullet journal

icon credit to @nerdastically

Before I started my final year of uni I was stressing out about finding a job. I did quite a bit of research and planning, and managed to receive a job offer before I even finished my degree!

Here are a few tips I would give to those of you in the same situation:

1. Know what your end goal is

Before you start aimlessly applying for jobs, take some time to think about where you actually want to go with your career. Where would you actually like to end up?

Do some searching and see what type of jobs exist in the area you want to work in. Search though graduate job sites, your universities careers website, or just Google. Make a list of all the jobs that appeal to you, and if you find any, make sure you note when applications open & close so you don’t miss out.

2. Google your name & clean up your social media act 

Employers are using Google to find out about potential employees, so if you search your name and something embarrassing turns up in the top results (i.e. drunk facebook photos/inappropriate comments etc), either delete the posts or make your account private. When I did this I discovered that there was someone with the same name as me who posted really embarrassing stuff, so I created a bunch of social media accounts with my real name on all of them to move those out of the top results. 

I’m not saying you can’t be the real you on social media, but try to keep things that you wouldn’t want a potential employer to see on your private accounts.

I would recommend taking at least one professional photo to use as your photo on social media sites.

Also make a LinkedIn! It’s really boring but employers use it and you can follow companies you are interested in. Add in all your skills and experience and write up a summary letting everyone know what kind of work you are looking for.

3. Sign up to all of the graduate job sites 

In Australia GradConnection is really good, but other countries will have different sites. It probably won’t be hard to find them! 

Graduate job sites generally list a huge number of jobs from mainly large companies, as well as when applications open and close. Some of the good ones have a blog with tips to help you improve your applications. You can usually make your own profile which employers can look through.

If it is an option, opt in to email alerts, especially if you can get them tailored to the field you want to work in. It serves as a good reminder for submitting applications, and you may find a new job to apply for through the alerts.

Remember this isn’t the only way to find jobs! Smaller companies sometimes advertise through your university careers website, or general websites like Indeed, SEEK, etc, so make sure you look in a few places before ending your search.

4. Jazz up your resume and cover letter

I don’t mean making them bright pink or anything, but make them stand out in a professional way.

Resume tips:

Tailor your skills/experiences to the job you are applying for. Look through the job description and skills required and make sure you cover each skill on your resume.

When describing your skills, don’t just use examples from university. Try to use examples from part-time work, clubs you have joined and extracurricular activities as well.

Also don’t be too wordy, it probably won’t be read. Simple one or two sentence dot points should be okay.

Use a professional email! Plz don’t use sexygal@hotmail.com etc

Include a link to your LinkedIn/professional twitter etc in your contact details

Don’t submit a 20 page resume! It will most likely be deleted/thrown in the trash. Stick to 1-3 pages depending on your experience and make sure everything is actually relevant.

Inspiration

Resources [1] [2] [3] [4] [5]

Cover letter tips:

Mention why you want the job

Try to mention something about the company that you like - e.g. that they work with a specific charity or they provide excellent training. Do your research!

Don’t drone on like a robot - keep it interesting and use your voice

Keep it to 1 page - don’t make the HR person’s job harder for them

Find out who to address it to - you can usually google who the hiring manager is

Resources [1] [2] [3] [4]

Also:

If you can, get your school’s career adviser to look over your resume and cover letter

Always submit your resume & cover letter as a PDF - it looks way more professional if you read it on the computer

Format it nicely, keep it consistent between everything you submit in your application

ok this is probably obvious but CHECK YOUR SPELLING!!~~~

Try using Canva to make your resume pretty

5. Make a personal website 

If you want to stand out more than other applicants, make your own personal website and include a link in your application. Make sure it looks professional and highlights the best you.

Things to include:

Samples of your work

Links to your (professional) social media pages

A short description of yourself, your professional interests and where you would like to head in your career

A blog if you are really looking to stand out

Skills, experience etc

Resources [1] [2] [3] 

6. Network 

Contact someone from your dream company and ask them if they would like to go for coffee/ask to chat. If you know someone or even know someone with a contact - reach out to them! Try to get them to put in a good word for you - people usually like to help others out.

Attend careers festivals and meet people from the places you want to apply

Ask around - your lecturers/fellow students/friends’ parents might know some important people

Ask what the company is really looking for in its candidates

Resources [1] [2] [3]

7. Online tests

If you are invited to do an online test as part of the recruitment process, find out what type it is and see if you can get your hands on a practice piece. If it is a personality test there is usually no way to prepare - just be honest.

I found online forums really good for this. If you’re applying for a large company, chances are there are tons of people who have done the same test and there could be existing forums about this. See what people said about them and if there is anyway to prepare.

Some of these honestly aren’t bad. For one application the test I had to do was actually a game, and for others it was standard logic questions - it all depends on the job!

Resources: [1] [2] [3]

8. Interviews

Interviews are probably the worst part of looking for work - but it’s something you need to get good at. With larger companies, online interviews are becoming the new big thing because they are cheaper to run and it is quicker to weed out candidates. Usually a question will pop up on the screen for a minute or two and then you will have a couple minutes to record your response via a webcam - you won’t be speaking to an actual person so it can be a bit awkward, so i’d suggest practicing first.

Interview tips:

Practice answering common interview questions - try to memorize a few responses such as the most common one “tell me about yourself”

Research the company again before going in to refresh your memory. Find out when they started, if they have grown recently or changed their direction.

Bring in questions - trust me, they WILL ask if you have questions

Dress appropriately

blue makes you look trustworthy, black looks professional, plz don’t wear orange

in online interviews you have the advantage of not wearing pants ;)

Bring a copy of your resume & make sure you have it memorized

Make sure you know where the interview is being held

Don’t cross your arms/yawn

Smile and be friendly!

Pretend you are a confident person, even if you are secretly about to wet yourself ;)

Thank the interviewer afterwards

Resources [1] [2] [3] [4] [5] [6]

9. Get some experience

It really sucks when you are looking for a job when everywhere wants someone with experience. 

Do an internship - you could get a job offer at the end

Volunteer somewhere in your field

Get a part-time/casual job while you study

If all else fails, try an online course - MOOCs are short courses you can usually do online for free. Do one that relates to the type of work you are looking for, it shows initiative and that you are actually interested in the field and dedicated. 

10. Apply everywhere 

I don’t mean somewhere that requires 10 years of experience, but don’t discredit a job just because it’s not exactly what you want to do. Try applying to places that are slightly outside of your field, as long as you have enough skills and experience to do it well - it could end up being something you love!

The more places you apply - the higher your chances of hearing back. But make sure your applications are of a high quality! Don’t just send out identical resumes/cover letters.

11. Don’t give up!

I applied for soooo many jobs in my final year. It was super stressful and I got rejected outright tons of times. I did a few online interviews and face-to-face interviews and some of them I never heard back from. This is not the end of the world! Find out what you did wrong, ask for feedback and do better in your next application/interview. You can do this!

More links & resources

97 actions you should take to become THE person companies want to hire - College Info Geek

Preparing for the future by @studysthesia

Job hunting advice by @harryjamcs

How to get a job fast as hell by @thechronicleofshe

lol

p.s. good luck & don’t neglect your grades too ;-)

Don't allow others to consume you. If they don't call, go to sleep. If they don't message you, put away your phone & have a good day. If they are distant and refuse to tell you what's wrong, go home and do something fun. You live for yourself first. They are secondary.

My much requested list of resources for studying astrophysics. Happy learning!

Getting Stuff Done: How to Deal With Lack of Motivation

“How can I stay disciplined?”

“How can I get things done if I don’t feel like doing them?”

“How can I overcome my lack of motivation?”

As a college student who has had their fair share of being absolutely unmotivated to do anything, I know it can be hard to get things done if you don’t feel like doing them. Luckily, there are some things you can do to become more motivated to finish your homework, write your paper, study for your exam, or whatever tasks you have on your plate.

Part 1: Increasing motivation

Break up your tasks

Just thinking about one huge task is going to intimidate you so much that you’d rather leave it till later, when the urgency of time pushes you to complete it, than start now.

Breaking up your big tasks into smaller ones will make your tasks seem less daunting. Since you won’t be as intimidated by the amount of effort it might take to complete these tasks, you’ll be more likely to start doing them.

For studying, this can be something like ‘make flashcards for units 1-3’ or ‘practice past exam papers: 2015 + 2016’. For writing papers, this could be writing an outline, doing research for each point of your outline, writing the first 3 paragraphs, etc.

Working on small tasks at a time will also make you less prone to distractions since you only need to focus for a short length of time.

Make small goals and reward yourself

These goals could be accomplishing one of the smaller subtasks above, or achieving a certain grade on a practice test, or finishing a section of your study plan - as long as you’re working towards something.

The rewards? Maybe going out to eat, watching something, or even just time off. Hopefully these rewards will motivate you to complete your task.

I know some people are more inclined to do their work if they’re punished for not doing it, rather than rewarded for doing it, so if you wanna take the ‘punishment’ approach, you could do something like not allowing yourself to use social media until you finish a set of tasks - this is essentially the same thing, just thought about in a different manner. However, you should always be careful with these punishments/restrictions, because sometimes they can end up harming your health and productivity (e.g. ‘I can’t take a break until I finish all of my homework’).

Part 2: Not relying on motivation

Of course, you can’t always expect yourself to be motivated all the time. In fact, it’s very ineffective to rely on motivation to get things done; motivation is fleeting. Here’s an alternative: self-discipline. But how does it work?

Establish a study routine

Humans are creatures of habit. Even if you’re a P-type (like me), habits are hard to break. So making a habit of accomplishing your tasks/studying at a set time every day will help you, well, accomplish them. For example, it’s a lot easier to get your homework done every day if you do it at the same time - e.g. once you come home from school - rather than doing it ‘whenever you have time’.

Having a study routine will also make you less likely to be distracted since you know that that period of time had a purpose. If you’re trying this out for the first time, you might wanna completely get rid of distractions so that you can focus (e.g. putting your phone in your bag, on silent). However, with practice, I found that my phone or any other sources of distraction don’t really bother me anymore since I’ve had tons of practice resisting the urge to pick up my phone whenever there’s a notification, for example.

Schedule in time for breaks

This ties in well with the point about rewards: the break might be the reward for your studying. However, this doesn’t always have to be the case. You shouldn’t always think of relaxing as merely a reward for studying or accomplishing your tasks, but rather a necessity for the well-being of your mind. This sort of approach to breaks ensures that you actually let your brain rest once in a while.

After taking a break, your mind will be refreshed and revitalized, and you should have more than enough energy to continue with your other tasks.

Some of you asked - with regards to my previous post on The Mandatory Midday Break - how I can limit myself to exactly an hour, and to be honest, the answer is habit. It’s like having a habit of showering at the same time every day and not extend the length of time you spend in the bathroom (except in certain circumstances, like during a day off, I guess).

This is why it’s important to schedule your breaks and establish a study routine or habit - not only does it ensure you get enough rest, but it also prevents you from extending your break so that you don’t become unproductive and leave a ton of tasks unfinished.

It can be hard to motivate yourself to accomplish all your tasks, but there are things you can do to increase your motivation. However, you can’t expect to be motivated all the time, and you shouldn’t rely on motivation to get things done. Discipline and habit are the most important tools you can use to be efficient and productive without having to be motivated.

Hope this post has been helpful, and, as always, feel free to drop me an ask if you have an ask. Have an awesome week :)