#mathematics learning

[moonilit]

[er-cryptid]

alright nerds--

^tried to include as many as possible

[garbagechocolate]

What is the center and radius of the circle indicated by the equation?

(x−2)2+y2=36

-Cousin Throkmorton Anon

[maths-screaming]

Things That Are and Are Not Changing as a Result of Re-Teaching Myself Basic Math

Things That Are Changing

I am less anxious about basic math.

I have more tools for doing basic arithmetic problems.

I'm better at identifying which will be the fastest or easiest tool for any given problem.

I can more quickly and easily ID when an exact answer is needed or when an estimate will suffice.

I'm marginally better at noticing when an answer can't be correct.

Things That Are Not Changing

I still transpose numbers frequently.

I still transpose operations frequently (adding when I should subtract, dividing when I should multiply, etc.)

I still have initial anxiety when looking at a math problem, before the "oh yeah, I have more tools for addressing this now" kicks in.

I still frequently mix up my right and my left.

My sense of direction is still bad.

I cracked Maths - No Problem! Textbook 4A today, putting me halfway through the series. I'm making this list for future reference, because I suspect the things that aren't changing will continue to not change.

Better math education won't change the fact that I have dyscalculia. I didn't expect it to, but I also didn't know what it would or wouldn't change. When I started this, I didn't know where my dyscalculia ended and my poor math education or math anxiety began.

Still, if we can fix "poor math education" and "math anxiety," I'll be much further ahead than when I started - and more willing to live with the dyscalculia.

[lady-asphodel]

[learn your gacha: reference, explanation, interpretation- #2]

Dr. Ratio: Splash Art And Newton's Law

Mathematics are a core part of Dr. Ratio's character ! Especially his promotional elements. But what are those complicated numbers ? Because, yes, they actually mean something !

Let's dive together into the signification of one of Dr. Ratio's splash art equation !

NEWTON'S LAWS

On the top right of Dr. Ratio splash art, we can read: F= dP/dt.

This is a form of Newton's Second Law of motion.

What is it ?

Newton's Laws of motion are three physical laws about the relation of the motion of an object and the force acting on it. They originates from the Philosophiæ Naturalis Principia Mathematica (1687), which also contains Isaac Newton's law of universal gravitation. This book written in Latin was one of the most important work published in the history of science.

The Second Law of motion applies when forces are unbalanced, causing the object to be in motion.

The Second Law then is thus: the change of momentum is proportional to the force acting upon it.

Mathematical explanation:

Momentum depends on the matter, the speed and the direction of the object, which influences its value with time. This phenomenon in math is also called [time] derivative and can be applied to any variable.

In modern form, momentum is calculated like this: P= mv

Or: momentum = mass x velocity

Generally, mass doesn't change with time but velocity does (acceleration); thus force is calculated like this: F= m dv/dt

Or: force= mass x time derivative of velocity

[dv/dt > which is the acceleration]

So: F= ma

( ma stands for mass x acceleration )

In modern form, the Second Laws says that the time derivative of momentum is the force.

So: F = dP/dt

Note: it can also lead to incorrect results when variable mass is added to the equation ( time derivative of mass ). The variables must be included in the equation if mass changes with time.

So: F= dP/dt

And: P= mv

Thus: F= d (mv)/dt

So: F= dP/dt = ma OR F= ma

So; F is the net force. Then: acceleration is proportional to the net force and inversely to the mass of the object.

F= ma so a= F/m and m= F/a

With physic quantity, it is thus: N = kg x m/s²

Or: 1 Newton [net force] equals 1 kilograms [kg] multiplied by 1 metters per second squared [m/s²]

Ex: 1N = 1kg x 1 m/s²

Demonstration:

1)

Aventurine rolled his fucking 2 kg dice at an acceleration of 5 m/s², what is the net force aventurine applied to the dice?

F= 2x5 so....

Yes ! 10N ! He fucking won millions !

2)

Boothill throws goddamn bullets with a fudging net force of 12N at an acceleration of 10 m/s², what's the freaking mass of his bullet ?

m= 12/10 so.....

Boothill throws 1.2 kg bullets, wow ! Deadly !

3)

Sampo kicked a 6 kg bomb into the crowd of Belobog, his net force was 12N ! What was the acceleration ?

a= 12/6 so.....

Lame ! Only 2 m/s² !

Conclusion:

In other words, Newton's Second Law says:

" the lower the mass the greater the acceleration, and contrarily, the greater the mass the lower the acceleration. "

Which is why F1 cars have such low mass, so they can have more acceleration speed !

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Wow! I really struggled with that one because math isn't my forte at all. But I did my best to inform myself, understand it and then explaining it in a simpler and more entertaining way I hope.

For those wondering, learn your gacha is a concept I came up with where I explain, teach and interpret references in Honkai: Star Rail. I'm in no way an expert in all the subjects I talk about, but I do my best to thoroughly learn about it as accurately as I can !

I hope you enjoyed it and see you for the next one !

[imperfect-autodidact]

After 8 minutes of utter anger and 6 minutes of reflection I realised something:

My problem isn’t the counting.

It is word problems.

Like I had a meltdown with all those dice, cards, digits and lists of letters, but it all disappeared when I encountered the problem with mathematical symbols. Very easy proof, I haven’t lost any calories while writing it. Nice, right?

Fuck word problems, I’m going to make some tea and add whiskey in it to wind down

[stone-cold-groove]

Mathematics: The Story of Numbers, Symbols and Space. The Golden Library of Knowledge - 1958.

[juniedahmed]

Neptune Planet

Diameter : 30,775 miles ( 49,528 km )

Mass : 102,000 million million million tons

Temperature : -225°C ( extrêmes not available )

Distance from Sun : 2794 million miles ( 4497 million Km )

Length of day : 19.2 hours

Length of year : 164.79 earth years

Surface Gravity : 1 kg = 1.18 kg

#Neptune

#photochallenge #everyoneシ゚ #science #knowledge #spacescience #astronomy #education #physics #Educational #sun #earth #astrology #astronaut #astrophysics #NASA #uk #spaceexploration #university #college #school #spaceshuttle #astrophotography

#solarpower #solarenergy #energy #spacewalk

[ramenwithbroccoli]

not to be controversial on main, but i really do feel like way more people would enjoy maths if someone properly explained it to them & they didn't have a hanging threat of failing an exam above their heads

[algebraic-dumbass]

this might be a dumb question but like. how do you learn math without a class/curriculum to follow. i have a pretty solid calculus understanding and I want to pursue more advanced math but like im not sure where to start. what even is like category theory it sounds so cool but so scary???. do you have any recommendations on specific fields to begin to look into/whether its best to learn via courses or textbooks or lectures/etc.? any advice would be super appreciated!! dope blog by the way

thanks for the compliment!

first of all it's not a dumb question. trust me i'm the algebraic-dumbass I know what I'm talking about. okay so uh. how does one learn math without a class? it's already hard to learn math WITH a class, so uhhh expect to need motivation. i would recommend making friends with people who know more math than you so you have like, a bit more motivation, and also because math gets much easier if you have people you can ask questions to. Also, learning math can be kind of isolating - most people have no clue what we do.

That said, how does one learn more advanced math?

Well i'm gonna give my opinion, but if anyone has more advice to give, feel free to reblog and share. I suppose the best way to learn math on your own would be through books. You can complement them with video lectures if you want, a lot of them are freely available on the internet. In all cases, it is very important you do exercises when learning: it helps, but it's also the fun part (math is not a spectator sport!). I will say that if you're like me, working on your own can be quite hard. But I will say this: it is a skill, and learning it as early as possible will help you tremendously (I'm still learning it and i'm struggling. if anyone has advice reblog and share it for me actually i need it please)

Unfortunately, for ""basic"" (I'm not saying this to say it's easy but because factually I'm going to talk about the first topics you learn in math after highschool) math topics, I can't really give that much informed book recommendations as I learned through classes. So if anyone has book recommandations, do reblog with them. Anyways. In my opinion the most important skill you need to go further right now is your ability to do proofs!

That's right, proofs! Reasoning and stuff. All the math after highschool is more-or-less based on explaining why something is true, and it's really awesome. For instance, you might know that you can't write the square root of 2 as a fraction of two integers (it's irrational). But do you know why? Would you be able to explain why? Yes you would, or at least, you will! For proof-writing, I have heard good things about The Book of Proof. I've also heard good things about "The Art of Problem Solving", though I think this one is maybe a bit more competition-math oriented. Once you have a grasp on proofs, you will be ready to tackle the first two big topics one learns in math: real analysis, and linear algebra.

Real analysis is about sequences of real numbers, functions on the real numbers and what you can do with them. You will learn about limits, continuity, derivatives, integrals, series, all sorts of stuff you have already seen in calculus, except this time it will be much more proof-oriented (if you want an example of an actual problem, here's one: let (p_n) and (q_n) be two sequences of nonzero integers such that p_n/q_n converges to an irrational number x. Show that |p_n| and |q_n| both diverge to infinity). For this I have heard good things about Terence Tao's Analysis I (pdf link).

Linear algebra is a part of abstract algebra. Abstract algebra is about looking at structures. For instance, you might notice similarities between different situations: if you have two real numbers, you can add them together and get a third real number. Same for functions. Same for vectors. Same for polynomials... and so on. Linear algebra is specifically the study of structures called vector spaces, and maps that preserve that structure (linear maps). Don't worry if you don't get what I mean right away - you'll get it once you learn all the words. Linear algebra shows up everywhere, it is very fundamental. Also, if you know how to multiply matrices, but you've never been told why the way we do it is a bit weird, the answer is in linear algebra. I have heard good things about Sheldon Axler's Linear Algebra Done RIght.

After these two, you can learn various topics. Group theory, point-set topology, measure theory, ring theory, more and more stuff opens up to you. As for category theory, it is (from my pov) a useful tool to unify a lot of things in math, and a convenient language to use in various contexts. That said, I think you need to know the "lots of things" and "various contexts" to appreciate it (in math at least - I can't speak for computer scientists, I just know they also do category theory, for other purposes). So I don't know if jumping into it straight away would be very fun. But once you know a bit more math, sure, go ahead. I have heard a lot of good things about Paolo Aluffi's Algebra: Chapter 0 (pdf link). It's an abstract algebra book (it does a lot: group theory, ring theory, field theory, and even homological algebra!), and it also introduces category theory extremely early, to ease the reader into using it. In fact the book has very little prerequisites - if I'm not mistaken, you could start reading it once you know how to do proofs. it even does linear algebra! But it does so with an extremely algebraic perspective, which might be a bit non-standard. Still, if you feel like it, you could read it.

To conclude I'd say I don't really belive there's a "correct" way to learn math. Sure, if you pursue pure math, at some point, you're going to need to be able to read books, and that point has come for me, but like I'm doing a master's, you can get through your bachelor's without really touching a book. I believe everyone works differently - some people love seminars, some don't. Some people love working with other people, some prefer to focus on math by themselves. Some like algebra, some like analysis. The only true opinion I have on doing math is that I fully believe the only reason you should do it is for fun.

Hope I was at least of some help <3

[saltypearl712]

Did you know in Mean Girls Baldi was also part of the Mathletes

[physicsgoblin]

Physics and Mathematics Resources (plus some Chemistry):

I will update this because I know I have more recommend textbooks somewhere in my files, I'm just too tired to look right now. Latest update: 5/13/25

Physics:

The Science Spot--Mostly lesson plans for teaching kids

The Physics Classroom Tutorial--Has interactive online activities and models. Some videos and also some chemistry stuff.

HyperPhysics--Quite possibly the best resource I've ever seen because it shows how all concepts are linked together. The site isn't loading for me but it says it's up. There is a downloadable version on the Internet Archive (though it doesn't look as nice and clean). EDIT: I found a GitHub that lets you clone and download the html so you can click through it offline and it works! If people are interested I can make a tutorial, it was very easy.

PhET--A ton of demonstrations and tutorials. Also has some for mathematics and chemistry.

Paradigms Physics Notes--this was the curriculum that was used in my junior and senior classes. A lot of stuff here. If you are interest about teaching physics using this method, you can read more here.

Quantum Mathamatica Add-on--Useful for calculations.

The Hypertextbook--uhh lots here. Problems, solutions, explanations, etc.

oPhysics--interactive physics software.

MiniPhysics--more demonstrations and interactive software.

Michel van Biezen--really clear work-throughs of many subjects (algebra, calculus, chemistry, physics). He actually has a tumblr but has been active in like a decade @ilectureonline

Mathematics:

Paul's Online Math Notes--Got my whole class through junior and senior year

Calculator Soup--a lot of different kinds of calculators

3Blue1Brown--Very interesting youtube channel that shows a lot of calculus and linear algebraic principals visually or in intuitive ways.

Mathologer--more interesting advanced mathematical concepts.

General:

OpenStax--Free textbooks, legally

[alhaithamexplains]

[casjam]

Day 19/100

No thoughts, head empty.

More math... Ugh.

I'm so tired right now. when I got home, I needed a nap, but it wasn't long. Tbh, if it was a long nap, I'd probably be more tired than before it.

Funny thing: My old chemistry teacher was so hard to deal with last year, but recently, I've been missing it. I went to talk to him and I told him about how I was feeling. He then asked if I had heard the term: Stalkhom Syndrome before 😭 Omg

[chahtawordoftheday]

Chahta word of the day #52

Four-Ushta

Here’s a pronunciation guide:

[imperfect-autodidact]

It is strange to observe on a daily basis how mental health can deteriorate. I enjoy solving math problems and yet I haven’t touched a textbook for several weeks, because I feel numb. Because sometimes I want not to exist.

But then I try to remember what is it all for. Not a paper from university I am not yet enrolled at. Not for “having a career” somewhere in the future. But because I am bursting from ideas, because these ideas might one day contribute to collective humanity. Too ambitious? Maybe, but it is a legitimate reason to go further.

I have never been able to reflect on myself. Politics, history, literature, science, art - whatever, my analysis is always deep and surprises people. But as of turning 29 I still have no idea who I am.

Maybe it is time to start asking.

Now something tells me I will be able to get back to math soon enough, because she is the ultimate Beauty I have encountered so far apart from the night sky. And this Beauty is worth fighting for and living for.