One Of My Favorite Thing I’ve Learned About Animals Studies Is That You Should Avoid Using Colorful

Lagrange Markipliers or something idk I forgot all my multivariable calc.

Here’s a long but important comic for you <3

Accepting ourselves the way we are means we allow ourselves the things we need to make life a little easier. You don’t have to fight it, it’s ok have different needs to others. You are worthy of kindness, so be kind to you <3

love from the sad ghost club <3

Shop / About Us / FAQ’s / comics / Archive / Subscribe / Theme

Complex Number Grapher

https://jutanium.github.io/ComplexNumberGrapher/

This grapher is really fun to play around with! 

A normal function takes in a number, x, and outputs another number, y. But a complex function takes in a complex point on a plane (a+bi) and outputs another complex point. Without 4 dimensions, it would be impossible to graph a complex function :(

The creator of this project instead uses complex domain coloring which they explain much better than I have here so you should 100% go and check it out!

Look at this cool function I got:

f(z)=(sin(z^3))^((cos(z))/2)

omg I want this so much, I could share my ideas and things I learned

I think tumblr should let us post diagrammes and graphs and tables. We can be trusted with math. I promiss.

good point! I should add to my list the golden rule of asking yourself "does this thing that I'm currently trying actually work for me". in the meantine I had a conversation with a friend who said that for her not caring about the aesthetics of notes decreases the effectiveness of studying, my perspective definitely isn't The Only Correct One

the best method is the one that works. it's perfectly okay to benefit from notes, from making them pretty, it's also perfectly okay to limit the notes. it was a surprising discovery for me that taking notes doesn't help with my learning, because my whole life I've been told to always take notes. but of course this isn't going to work for everyone, thank you for pointing this out

tips for studying math

I thought I could share what I learned about studying math so far. it will be very subjective with no scientific sources, pure personal experience, hence one shouldn't expect all of this to work, I merely hope to give some ideas

1. note taking

some time ago I stopped caring about making my notes pretty and it was a great decision – they are supposed to be useful. moreover, I try to write as little as possible. this way my notes contain only crucial information and I might actually use them later because finding things becomes much easier. there is no point in writing down everything, a lot of the time it suffices to know where to find things in the textbook later. also, I noticed that taking notes doesn't actually help me remember, I use it to process information that I'm reading, and if I write down too many details it becomes very chaotic. when I'm trying to process as much as possible in the spot while reading I'm better at structuring the information. so my suggestion would be to stop caring about the aesthetics and try to write down only what is the most important (such as definitions, statements of theorems, useful facts)

2. active learning

do not write down the proof as is, instead write down general steps and then try to fill in the details. it would be perfect to prove everything from scratch, but that's rarely realistic, especially when the exam is in a few days. breaking the proof down into steps and describing the general idea of each step naturally raises questions such as "why is this part important, what is the goal of this calculation, how to describe this reasoning in one sentence, what are we actually doing here". sometimes it's possible to give the proof purely in words, that's also a good idea. it's also much more engaging and creative than passively writing things down. another thing that makes learning more active is trying to come up with examples for the definitions

3. exercises

many textbooks give exercises between definitions and theorem, doing them right away is generally a good idea, that's another way to make studying more active. I also like to take a look at the exercises at the end of the chapter (if that's the case) once in a while to see which ones I could do with what I already learned and try to do them. sometimes it's really hard to solve problems freshly after studying the theory and that's what worked out examples are for, it helps. mamy textbooks offer solutions of exercises, I like to compare the "official" ones with mine. it's obviously better than reading the solution before solving the problem on my own, but when I'm stuck for a long time I check if my idea for the solution at least makes sense. if it's similar to the solution from the book then I know I should just keep going

4. textbooks and other sources

finding the right book is so important. I don't even want to think about all the time I wasted trying to work with a book that just wasn't it. when I need a textbook for something I google "best textbooks for [topic]" and usually there is already a discussion on MSE where people recommend sources and explain why they think that source is a good one, which also gives the idea of how it's written and what to expect. a lot of professors share their lecture/class notes online, which contain user-friendly explenations, examples, exercises chosen by experienced teachers to do in their class, sometimes you can even find exercises with solutions. using the internet is such an important skill

5. studying for exams

do not study the material in a linear order, instead do it by layers. skim everything to get the general idea of which topics need the most work, which can be skipped, then study by priority. other than that it's usually better to know the sketch of every proof than to know a half of them in great detail and the rest not at all. it's similar when it comes to practice problems, do not spend half of your time on easy stuff that could easily be skipped, it's better to practice a bit of everything than to be an expert in half of the topics and unable to solve easy problems from the rest. if the past papers are available they can be a good tool to take a "mock exam" after studying for some time, it gives an opoortunity to see, again, which topics need the most work

6. examples and counterexamples

there are those theorems with statements that take up half of the page because there are just so many assumptions. finding counterexamples for each assumption usually helps with that. when I have a lot of definitions to learn, thinking of examples for them makes everything more specific therefore easier to remember

7. motivation

and by that I mean motivation of concepts. learning something new is much easier if it's motivated with an interesting example, a question, or application. it's easier to learn something when I know that it will be useful later, it's worth it to try to make things more interesting

8. studying for exams vs studying longterm

oftentimes it is the case that the exam itself requires learning some specific types of problems, which do not really matter in the long run. of course, preparing for exams is important, but keep in mind that what really matters is learning things that will be useful in the future especially when they are relevant to the field of choice. just because "this will not be on the test" doesn't always mean it can be skipped

ok I think that's all I have for now. I hope someone will find these helpful and feel free to share yours

that sounds a bit like mystery flesh pit national park

I’m Christian and respect the order of creation as God intended it but I’m not gonna lie if I could take a massive vat of agar and grow an alive shopping mall made out of red blood and meat and feed it living human bodies to make it expand larger with more shops and amenities, Without hesitation, Without question I would do exactly that

this looks so great! I need to check this out as well

25 VIII 2022

I found the most beautiful math book I have ever seen

it covers the basics of algebraic topology: homotopy, homology, spectral sequences and some other stuff

one of the authors (Fomenko) was a student when this book was being published, he made all the drawings. imagine being an artist and a mathematician aaand making math art

just look at them

other than those drawing masterpieces there are illustrations of mathematical concepts

I'm studying homology right now, so it brings me joy to know that this book exists. I don't know how well it's written yet, but from skimming the first few pages it seems fine

I just finished watching a lecture about exact sequences and I find the concept of homology really pretty: it's like measuring to what extent the sequence of abelian groups fails to be exact

I'm trying to find my way of taking notes. time and again I catch myself zoning out and passively writing down the definitions, so right now I avoid taking notes until it's with a goal of using the writing as a tool for acquiring understanding. I'm trying to create the representations of objects and their basic relations in my mind at first, then maybe use the process of note-taking to further analyze less obvious properties and solving some problems

I will post more about it in the future, we'll see how that goes

I know one person who started phd without master's but that's in computer science and he already had a research startup running independently. he had a med degree already and his research is about using ML in medicine, so he was granted a "special permission" to start a phd. the guy is a very hard-working genius

now when it comes to math, one of my friends claimed that it is possible to start phd after bsc if someone graduates magna cum laude or something. I never heard of that before and it sounds insane, so I asked my advisor about it and he never heard of that either lol moreover he said that it's a stupid idea unless someone already has a few publications

afaik in the US the undergraduate degree takes 4 years and phd takes 5, it's like a mix of masters and the actual phd, so I guess it evens itself out

okay this might sound stupid to a lot of you but I thought you need a masters degree before you can do a PhD. so weird to me seeing 22 year olds doing a PhD after a bachelors degree. I don't know where I got this idea but I'm having a hard time rearranging my world view around this, even though this is so inconsequential thing to be wrong about xd