1. Know What Your End Goal Is

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Proof by referencing obscure EU legalese that’s been outdated since 2003 but no one will look up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 think we all know this feeling of being stuck inside your routine. you’re not really sad but it just feels like something is missing. so i’m here to give you ideas on how to spice things up™️ (or just make life more enjoyable).

paint your nails in an exciting color. paint them in several colors idc. now every time you see your hands (which is very often) you see your super cool nails

listen to a new music genre. like something completely different. if you like rap you will listen to country music now. jam your heart out i know u want to (here & here are some playlists if u need any ideas)

on that note revisit songs you liked when you were younger. we gettin nostalgic

sometimes you just need to watch a good old vine compilation 

food!!! this can be such a huge factor. something as simple as switching your breakfast from toast to cereals, just smth new, can make a huge difference. try new things out, have fun (recipes here, here, here and here)

same thing with the things you drink! add lemon to your water, drink some tea, try iced coffee out, buy water from a diff company, …

a cute cup for your morning drink can really lighten up your mood too

get some magazines and cut things out you like. now get an a3 (a4 is okay too) paper and make a big collage

ikea trip? ikea trip!! don’t forget to eat smth there too yum

after showering put on some good smelling lotion and just enjoy the feeling

now put on your favorite underwear and an oversized shirt. maybe take some cute pics just for yourself. trust me you will feel better

rip a paper into little pieces

cuddle with your stuffed animal idc if you feel stupid, you will feel better

maybe spice things up with the way you look? try out a new hairstyle or invest in a new accessory you like (jewelry, hair ties / clips, belts, scarfs, etc.). it doesn’t have to be expensive, there’re lots of cute things in second-hand stores for example!

start a challenge in whatever you’re interested in. maybe for a hobby you always wanted to try out or pick up again. there’re tons of challenges on pinterest. i think i will try this one out though

write a love letter to yourself. you deserve one. fold it into a very small piece and put it into your pocket. this is now your lucky charm because trusting in yourself is all you need sometimes

buy groceries but this time with a friend or family member. catch up, have fun, buy some cookie dough and eat some cookies

picnics!!!!!!!! i love picnics!!!!! they’re so cute and actually super easy to organize. you can go alone or with someone else. just grab the food you have at home and a blanket and go to the nearest spot you find. even your garden or balcony. you can easily incorporate this into your day if you don’t have much time. instead of eating your dinner at your kitchen table you will go on a picnic now

if you have more time, you can bring a book with you or some art supplies and enjoy time outside

taking a walk listening to your fav album can help so much

change your bedding. you don’t even need to buy a new one, just wash it and get that feeling of freshness

open one of these sites (1, 2, 3): and read an article that seems interesting

buy flowers for yourself and put them in your room

change the color your laptop highlights things in

declutter your phone and laptop in general. set up some new backgrounds that make you happy

vary your commute. take the bus instead of the subway, get off a station earlier, or if you can, take the bike 

change the places you do things. try studying in the library or a café, scroll through your phone not in your bed but at the kitchen table, read on the floor, every small change adds into spicing things up

take a bath when you shower normally or the other way around

light candles in the evening

search for your old nintendo and play some games

stretch in the morning. even for 2 mins is good

download some new apps

try a no social media day

instead of a black / blue pen write in a different color (for example your groceries lists, on post-its, in your journal, …)

i hope some of these ideas can help you! most of the are easy to incorporate into your daily life and take no to little money.  have a nice day!! <3

7 Ways to organize your laptop because we can always be a little more organized on our devices (including myself). 

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

ways to end proofs

QED

which was what we wanted (abbreviated w⁵, or u¹⁰, or even v¹⁰)

■ (or □ for lemmas)

♥

So there.

The rest is obvious.

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 :)

As a language lover who can’t possibly afford all of the language lessons I would love to take, over the years I learned the best ways to self-learn them. This introductory phase doesn’t even require a textbook - I am sure everything here can be found online for free.

Disclaimer: this is the method that works the best for me, and I’m sharing it with the intention of helping other people who are stuck. There’s a million different ways to self-learn a language, so if this one doesn’t work out for you, don’t lose motivation!

Disclaimer 2: this method might not work with all languages. I’m sharing this knowledge keeping in mind my experience with Latin (in particular French, Spanish, etc) and East Asian (in particular Korean and Japanese) languages.

Without further ado, here are the steps: 

1. If you’re learning a language that uses a different alphabet, make sure that’s the first thing you learn

Relying on romanization is fine at first, but further down the path it will only serve to confuse you. Romanized words of these types of languages can be written in many different ways, so often they don’t even provide an accurate way of pronouncing them. Furthermore, as you make progress, you won’t be able to access a lot of content in your target language since you won’t find it romanized. 

2. Learn your first words

Before actually getting into all the grammar rules and whatnot, learn your first words! These include, among others:

Greetings

Answers (yes, no, maybe, etc)

Numbers

Please and thank you

Practice their pronunciation to get used to the language’s sounds, and how they’re written (especially if you have to use another alphabet - it’s a chance to practice your calligraphy!).

3. Learn essential vocabulary and grammar

I call these “essential vocabulary/grammar” because they are words you must know to build sentences (other than verbs). These include:

Articles (definite, indefinite, partitive, etc)

Basic pronouns (personal, possessive, etc)

Depending on the language, basic grammatical particles

Sentence order! In many languages, the subject/verb/noun order is totally different. Make sure to know how your target language orders that.

Make sure to also learn their rules and remember the exceptions. The latter are always annoying, but don’t worry - as you progress, you will learn these by heart, and they will eventually come to you naturally!

4. Learn the most basic verbs in the present tense

Like the vocabulary of the previous step, verbs are also essential when building sentences. Now that you’re only a beginner, you don’t need to learn difficult verbs or tenses, so stick with the most used ones:

to be 

to have

to do/make

to say

to go

to know

to think

to see

to want

to give

5. More vocab!

Now that you know your verbs, complement your knowledge by adding more basic vocabulary. Here are some ideas:

Places

Food

Objects

Adjectives

Family members

Knowing these in addition to the grammar points you’ve learned will allow you to construct simple sentences, such as I am going home or This is my sister.

6. Practice for your level

Like many other people, I’m guilty of jumping straight into watching movies and shows in my target language, only to get frustrated with myself when I don’t understand anything despite everything I learned until then. Of course, I’m not saying you shouldn’t do it, since it does help you develop your listening skills (especially if you do it with subtitles!), but I have a tip for the ones who prefer an easier activity.

Look for children’s content! I know this sounds silly at first, but books, movies, shows, etc made for children usually use basic grammar and vocabulary. If you think about it, the listening exercises you find in language grammar books made for beginners often seem like they’re made for children for that reason. Therefore, if you can’t find clips and texts for your level easily, try following this tip!

A few more tips for self-learners + resources

Write a diary in your target language. Even if you don’t know that much, try describing your day the best way you can (even if that means you have to write everything in the present tense). That’s a way of understanding what sort of vocabulary is useful in your daily life and what are your weaknesses.

For you listening skills, other than Netflix, listen to music as well! Seize the opportunity to also learn the new vocabulary you find in the songs.

For speaking skills, if you don’t have anyone to practice with, read texts out loud and record yourself to check your pronunciation. If you’re up to it, finding friends online that speak your target language is also a great way of practicing dialogue!

Most used words in every language

Textbook masterpost

More helpful books!

Random tasks to practice your target language

My blog’s langblr tag for more helpful posts

Happy studying! ✨

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.

Writing a CV:

The perfect resume for someone with no experience (by businessinsider​)

Guide to writing a CV

Common grammar mistakes to avoid on your CV

How to explain a gap in your CV

How to overcome common CV issues

What not to do on your CV

Should I include hobbies and interests in my CV?

CV layout: dos and don'ts

Free CV template

School leaver CV template

CV templates and tips

More free CV templates

Example CVs

How to tailor your CV to different industry sectors

Writing a Cover Letter:

How to write a cover letter

How to overcome common cover letter problems

Graduate cover letter template

Career break cover letter template

School leaver cover letter template

Free cover letter template

Referencing:

How to get a reference

References: workers’ rights

How to deal with employment references

How to include references on a resume

Interviews:

How to answer common interview questions

How to prepare for an interview

The interview itself

Advice to help you ace the interview

Answer curveball interview questions

101 Interview Questions You’ll Never Fear Again

Second interview questions and answers

Telephone interview questions and answers

Questions you should not be asked

What to wear to an interview: bloggers’ top tips

Group interview tips: do’s and don'ts

Interview questions for employers: What you should be asking

What not to do at interview

What job can I do?

How to decide what job to look for

How to find a new job

How to search for jobs online

Jobs in the retail industry

Jobs in the engineering industry

Jobs in the fashion industry

Jobs in the IT industry

Jobs in the motoring industry

Jobs in sport

Jobs in the education industry

Jobs in the energy industry

Careers with animals

Jobs in the media industry

Jobs in the leisure & tourism industry

Jobs in the catering industry

Jobs for history lovers

Jobs for geography lovers

Jobs for English lovers

Jobs for maths lovers

Volunteering:

7 Simple ways to make the best of volunteering

Benefits of volunteering

Benefits of mentoring

Volunteer Abroad

Resignation:

Resignation letters: What you need to know

Resignation letter templates  

How to resign

How To Resign & Hand In Your Resignation Letter

Redundancy /Job Loss:

Deal with redundancy

Things to do if you lose your job

Claim Jobseeker’s Allowance

Jobseekers allowance (UK) overview

15 tips to survive a job loss

How to Cope With Job Loss and Move On

At work:

How to start a new job

How to have a good first day

How to hold onto your job

How to handle bullying in the workplace

Commuting: how far is too far?

How to get a promotion

Summer workwear advice

Office Style Trends 2015

What You Can (and Can’t) Wear to Work

Dealing with stress at work

How to deal with a brutal boss

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