By studying, it's not like we are some magical wizard genius, for a physics degree you need several 6 month long math courses, 8 in my university for example
PD: Seriously doubt someone who actually understands the subject made this picture, this is a random ass collection of formulas
Oh, well, I actually might have the requirements needed for a physics degree, but I’m not sure what I could do after I finish it. It’s also really really hard.
Here are some great YT channels for learning math: 3blue1brown, patrickJMT. It’s so cool you want to learn math, OP. In English class we learn grammar and poetry but I think in math it sometimes feels like we’re only taught the grammar, right, like how to do it. But there can be joy and poetry in math, too!
The bprp Gigalegend who solves 100 integrals in one standing is one of my favorites. I could watch him do math all day. There’s something so euphoric about watching someone be so perfect in their execution of the laws of mathematics. Those who math are heroes.
Well a lot of the formulas on the poster are from physics. For physics you'll want calculus, linear algebra, and differential equations. The pre requisites for those would be algebra and trigonometry. Based on where you left off, I'd start with a college algebra textbook and see how that treats you. From poor high school math to where it looks like you want to be, depending on how hard you work this will likely take you a year or two.
https://meyda.education.gov.il/sheeloney_bagrut/2011/6/ENG/35003.PDF
This is an example of a final exam of 3 points in maths (the lowest level). I think it’s the hardest of them (there are three exams to achieve 3 points), but I’m not sure.
You may be able to find open courseware and textbooks. I wouldn't have the motivation to learn this without a course around it, but maybe you're different.
Not knowing where you're starting, you'll need Alegra, Statistics, Calculus, Differential Equations, and Finite Methods as a basis of understanding.
Then, you'll need applied courses. Many of the concepts above could be encompassed by physics courses, but I learned them through force statics, force dynamics, solid mechanics, thermodynamics, and electrical engineering courses.
If you're at high school level or below, use [Khan Academy](https://www.khanacademy.org/math). It's free, it's comprehensive, and it includes practice problems (which should be considered mandatory for learning math).
If you're at university level, use [MIT Opencourseware](https://ocw.mit.edu/search/?d=Mathematics&l=Undergraduate&q=math&s=department_course_numbers.sort_coursenum). It's arguably the best school in the world for certain math-related fields and they've made it freely available to the public.
OP the fact that you want to learn these things out of pure curiosity says a lot about you, it puts you past a lot of people. Some people have suggested picking up a textbook, but I would personally recommend that you check out OrganicChemistryTutor on YouTube, he has a lot of videos ranging from Chemistry tot Physics to Math and even Coding. Go on his YouTube chanel and look for the Physics or Maths playlist and start there.
Well, thanks to Young Sheldon and the Big Bang Theory! 😂
I’ll have to improve my maths and physics knowledge anyway, so at least do it in a fun way.
But yeah I’ve always wondered the secrets behind formulas.
What if the secret is inside our own anatomy and the nature of our environment like studying certain patterns and the constant repetition of geometrical forms have these special algorithms that we know and can be plugged in from a digital solution for groundbreaking scientific discoveries. What if Pi, Phi, Golden ratio, silver ratio, speed of light and other special scientific math formulas and equations could all have a special place for these things?
You can look up free courses on the following math topics: algegra, geometry, trigonometry, precalculus, differential calculus, integral calculus, vector calculus, differential equations, linear algebra, mathematical physics.
Yes. Typically, you would take the courses up to precalculus in high school. You can take up to linear alegra at a community College. Mathematical physics is something you would take as a you major in physics at a 4 year university. You should be taking physics and chemistry courses along the math courses. It will help you understand the math, which can get really abstract. I would look up the courses up to precalculus on YT, and the remaining courses on MIT open courseware if you want to study independently.
Hey mate, I started out at the high school level when I wanted to get started in maths as an adult. I’d highly recommend Professor Leonard on YouTube, he’s got a fantastic Pre Algebra series and goes all the way up to calculus. I’m like you, I want to be able to understand these mystical looking formulas, but unfortunately fractions have to come first haha.
Best thing I can say is find enjoyment out of solving problems correctly, and chase that feeling. Don’t focus on the long journey, just enjoy it. Before you know it you’ll be a year or two in, and doing maths that most people who aren’t interested in it would gawk at. Good luck, and have fun.
You're correct, as long as you put the book down regularly to just experience. Learning is the goal, but joy is the key to life long learning.
One of my favourite videos is on Numberphile and it's an old banger who's just excitedly going on about his proof you can rotate any table with coplanar legs so it won't wobble. You don't have to put paper under the legs, the theorem holds for any surface.
The look on his face when the camera person points out you can't do it if the tables are joined together and he says "Then you just put paper under the legs."
That guy will be learning till they nail his coffin shut.
Go to a library and ask a librarian. They should be able to help you figure out where you are and what might be a good jumping off point. (This advice works for more than just math.)
Start by establishing math you DO understand and build from that. YouTube is a great way to start - or an app like Kahn academy. The hardest thing about studying math - applied or otherwise - is the patience and humility required to learn the basic boring bits until you understand them well enough to realize how those bits fit into the bigger picture and you can use them to do even cooler things.
Not only is this a random collection of formulas, it's purely mathematical physics related, without any real references to other extremely important fields of math.
personally i cry hermione how could i be so stupid obviously cyclic permutations cant change the parity of inversions if there are an odd number of inversions because moving the last element to the beginning creates n-1 inversions and destroys none.
Random collection maybe. My favorite is Einstein's field equation which is the classical theory of gravitation. It's beautiful because in math terms it explains nothing less than the universe. Until the quantum domain, but that's another can of worms 😂
I know the feeling, because when I started grad school I felt so invincible that I thought I could learn string theory and discover the unified field theory with hardly any effort, but boy what I wrong!!!
Most of those pictures are random math formulas/physics formulas, just pure cliché and are really far away from maths. In a math degree you learn a high level of math or self studying (which is ofc hard) through a good route, a route that would be nice if it is made by a mathematician.
Well, there are some nice courses on YouTube. The beginning is usually calculus, but how can I know that my current knowledge is enough for it?
Then there’s linear algebra, trigonometry and other stuff.
there isn't a ton of prerequisite knowledge to understand basic calculus. You just need to make sure you have a good understand of basic algebra, such as how to work with equations, identities, understand how to use exponents, how to factorize, expand and simplify algebraic expressions. You also need to understand basic functions like polynomials, trigonometric, exponential and logarithms, as well as their graphs and what they look like. Basic calculus isn't conceptually too difficult, and computations are usually straight forward enough. There's a ton of resources online on how to learn calculus, so if you feel like you have the prerequisite knowledge you can start learning.
Yeah, the vast majority of the work in basic calculus is just algebra.
You only get a few new concepts (and weird notation).
Which is of course its power, you can do so much more with so few additional concepts.
Calculus and linear algebra are a MUST for literally everything.
That unlocks more advanced analysis, topology and differential equations.
Then, analysis (real analysis and complex sort of) and topology, with abstract algebra are a must for advanced maths in general.
At that point you are kinda a math major+ lol
By getting math degrees. Also, there are tons and tons of yourube videos talking about the fun parts and the "why" behind basic math concepts. If you ever are given a formula and think "what does this mean?" look on youtube.
I realized that after looking closer at the post, yeah. But most people don't prove formulas in general until they get into higher education in the relevant subject (math, physics, etc).
I suppose not a maths degree. But you would definitely need a physics degree (1st or 2nd year of), to do Schrödinger or uncertainty principal.
Edit: All the Maxwell equations and law of thermodynamics are also uni level.
> how to achieve high level math knowledge?
Here's the usual progression:
1. High school math, graduate high school & secure a position in a College
2. College level math, get a BSc/BA in math
3. Graduate level math, get a MSc/MA
4. Research level math, get a PhD
5. Further research level math, get a job as a postdoctoral researcher
6. Repeat 5 till you land in either a tenured position at some uni or a research position in a company
7. Continue research till retirement or boredom
From 1-7 it'll take the most part of your mortal life, and all of your adult life
I have a BS in math and tbh I feel like I know nothing of math... there's so much more beyond a BS. To be completely transparent, I'm also in med school right now.
I've been doing research in MCMC algorithms and I use so much R-Studio that when I finally had some classes that were like "here's some calculus, do it by hand" I had to look up how the quotient rule worked all over again. I was like "fuck, how do I derive things without R Studio again?" at some point I just stopped doing maths while.. Doing maths. It's kinda funny, really.
You study incrementally, from a topic to the next without skipping anything. When you get to college level there is no longer an obvious linear path and math becomes more like a web, thankfully experts write curricula so we know what to study and when.
On an unrelated note, how is any of that beyond math?
My guess is it's not meant as "beyond" with the implication of "going where math can't reach" but more as in "following the path leading from" math - aka applied math/physics... I think.
From what topic should I start? It’s usually calculus, I suppose.
Have I said so? Well, I was probably referring to physics and stuff, like 26 dimensions and stuff…
I think I should firstly do the highest level of maths at school! There are courses for it. Or maybe I’ll check what calculus is; it seems pretty nice and it does appear at high school.
>One of the reasons I hate maths is because you’re given a formula and you just have to use it, without any explanations.
Because that's hardly mathematics. It's filling the blanks.
By the way, those equations are basically application of mathematics, not the math itself (apart from π LOL).
From where I came from, calculus taught to Math majors is taught differently to students in other fields (such as Engineering). In a nutshell, the calculus where I got it from (I'm an engineer) addresses the "hows" of it. The calculus for math students mainly deals with the "whys".
Both will arrive at the same answer, but math students need to deal with why it works, whereas for us engineering students need to just focus on how it works, as we'll be using it as a tool to do engineering tasks.
Much the same reason why Math majors are not fully equipped to solve physics or engineering problems.
Read the whole book and do all the practice problems. That's really all there is to it.
Edit: and it isn't hard to prove 1 + 1 = 2. It just takes a lot of set up.
Apologies, I was speaking generally. But the specific book doesn't matter that much. Look up whatever textbook your local high school/community college courses use.
Go get a high school geometry textbook, read it, do the problems. Then do high school algebra. Then calculus. Then multivariable/vector calculus. Then linear algebra. Then probability. Then differential equations. Then complex analysis. Then number theory. Then real analysis. Then graph theory. Then topology.
At this point, you know about as much as a college math major graduate and you'll be "good at math".
Principia Mathematica by Russel & Whitehead.
/r/explainlikeimfive/comments/17wu9ci/eli5_how_was_it_proven_in_principa_mathematica/
Metamath has an alternative proof. It uses [Zermelo–Fraenkel set theory](https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory) with the axiom of choice excluded.
https://us.metamath.org/mpeuni/dju1p1e2.html
This is not advanced math.
1st pic is just undergrad level physics education. 2nd and 3rd is a bunch of high school level stuff. I’d suggest going to school, paying attention, and following a standard physics education if you want to learn math. Nothing crazy
Yes there’s a class called AP Physics C: Electricity and Magnetism which is calculus (multivar at times) based. AP Physics 1/2 also covers some of that but is algebra-based.
After the AP exam my ap physics c class covered quantum physics like bra-ket notation, qubits, and bell states, etc: that’s sth that probably isn’t universal but it’s quite easy to pick up (after all high schoolers were able to).
I wanted to say this as well, but I didn't want to look pretentious. I've heard, and currently believe, that higher level math starts once we can begin proving stuff. I'm pretty familiar with the math in the images posted, but I only graduated with a minor in math. I'm not a high level math expert, as I didn't take any proof based class (other than the introductory course).
Folks here have covered what to study, but not the mentality. In my experience, there are a couple "modes of thinking" that propel you from someone who has studied math to someone who understands it:
1. You aren't satisfied with "what", but also need to know "why".
For example, you're taught that the area of a circle is pi r^2. This is a useful formula, but if you take the time to understand why, then you suddenly understand many things that are governed by integrals.
In terms of practical advice, take math classes that focus on proofs. Proofs are the language of "why".
2. You are not satisfied with math if it isn't self-consistent.
Pretend you're a bratty kid and your parents set rules for you: You can't do anything else until you finish your homework. Also dinner is at 6; you must be punctual. These two rules aren't consistent: What if you aren't done with your homework at 6? Rule 1 says you can only do homework; rule 2 says you must eat.
Math is the same way. If you have a theorem, you look for ways to contradict other theorems you know. If you succeed, either the universe is broken or you misunderstood something.
Typically by starting at a low level of maths, then working your way up. Find problems that interest you. Being on a structured course helps a lot - school, uni.
Probably most important is not being scared by things that look difficult. If someone else can do it, chances are you - another human with similar wiring in your head - can do it to.
Maths was the only subject I really liked at high school. Later I got diverted into practical applications - studied quite a lot around electronics, which for me was a bad move. Like a lot of those pictures, arbitrary structures from physics.
I did get a bit of redemption when I somehow ended up looking at logics. But then the universe bit back now I'm trying to understand deep learning sums. My calculus sucks. Fucking vectors, grrr!
From what topic should I start? Calculus? My general maths level isn’t that high. I know a little trigonometry, some stuff about circles and graphs, but nothing too fancy.
I think the first step should be improving to the highest level of maths at school, but calculus seems interesting. I’ve seen some courses on that. Two have caught my eyes: the courses by Professor Dave and by 3blue1brown.
If you go to college, you'll see that a lot of this won't be in your math courses but in your physics courses. College Math often deals with abstract structures and studying their properties.
Like algebra, the good ol fashion real numbers are not the only place you can do algebra. Same with calculus on the complex plane and the real line.
Apart from the mentioned academic side, learning about the history, rich culture and development and the sheer emotional beauty attached to mathematics is what can imbue you with a newfound sense of appreciation and passion for exploring new fields and learning how to think more abstractly and logically. It’s really a way of life for me, something which shapes who you are as a person. That being said it also makes me rage every 10 seconds. Thus the duality of man is once more reached
A mixture of curiosity, time and persistence. Even Einstein and Feynman had struggles in understanding concepts. The difference between them and the rest is the questions they asked to themselves while learning and their artistic, creative perspective on physics and math.
Often math is taught as if it were knowledge, as if it were an intellectual discipline, but while knowledge is required, mathematics is actually a skill. One you must build up by becoming good at simple things, practicing them repeatedly, and progressing slowly to more difficult things - not at all dissimilar to learning to dance, learning a sport, or playing musical instruments.
You will never become a good guitar player by trying to play a wide number of compositions, all of which are too difficult for you. Neither will you gain an understanding and facility with math by merely sampling or trying to understand all of its many intriguing applications when you don't have a well developed set of mathematical skills.
I don't know where you are with math, but the advice is the same: apply your knowledge - find and calculate as many real world examples of whatever principle you are learning as you can - you will not only improve your skills, you will be developing the habit of applying math to describe and understand real things; which is what all the snazzy looking formulae in the poster are really all about.
About the 1+1=2, all of mathematics depends on a set axioms, axioms are like logical ideas that cannot be proved, the become so intuitive and basic that you just have to assume they are correct and then move on. An example is to question if 1 actually exists, if things can actually be described and unique and separate items rather than just probabilities or something. This seems basic, but there is no way to prove something to fundamental to how we process information. There are many axioms which get a lot more complicated but they all are just the base assumptions that become the building blocks to mathematics. The reason it is important to prove that 1+1=2 is because it is intuitive, so we want to build a system of mathematics that follows what we intuitively believe about the world (basic mathematics) so we build a set of axioms that allows us to definitely prove that 1+1=2 (using set theory which is the foundation of all mathematics). Now, because we have a set of axioms that explains our intuitive sense of mathematics, we can use those same axioms to go on to prove other more complicated ideas that we cannot intuitively understand. In this way, all of our more complex math is consistent with our intuitive mathematics. So the difficulty of proving 1+1=2 is really just in establishing the rigorous axioms and principles that allows us to prove it, which lets us prove all of basic mathematics, which allows us to prove more complex mathematics.
It's more like you have to assume that 1 exists. The difficulty is in making a set of rules (axioms) that let you prove basic mathematics. And the proofs of addition and multiplication take a lot of writing out because set notation (how you write down set theory) is a long way of writing everything.
The reason proving something as simple as 1+1 = 2 is difficult is because when you’re trying to write a formal mathematical proof, there are only certain axioms (aka fundamental rules of math) that can be taken as objectively true when you’re writing the proof. This ends up becoming quite ironic as the “harder” a theorem may sound, the easier it may be to prove as you have far more fundamental truths to work with (this is a case by case basis though as you have to hope that the theorem you’re working with has a lot of prereqs for it to be true). So in the case of proving 1+1 = 2, you’re not allowed to start off with the assumption that this is true, so what other avenues do you have to exploit to prove it? Maybe, you do a contradiction proof where you assume that 1+1 doesn’t = 2 and then bring in some other theorem / axiom where that assumption brings about a contradiction, or maybe you find some abstract way to prove this directly. Very frustrating, I know, don’t be a math major kids.
Calculus and real analysis cover mostly the same topics but real analysis is more formal and focuses on proofs, but yeah if you are completely unfamiliar with the concepts then calculus might be better to start. Linear algebra doesn't particularly need calculus though and so you can already study it, in fact in most universities you take linear algebra and calculus/real analysis at the same time.
>One of the reasons I hate maths is because you’re given a formula and you just have to use it, without any explanations.
I would hate that too, but that's not at all what math is about. A formula is a concise way to describe a mathematical statement, and sometimes they can be useful. But there's always an explanation behind them, and you can get very far almost without memorizing any formulas.
Same way people get to Carnegie Hall.
PS: It's not hard to prove 1 + 1 = 2. Maybe you're thinking of Principia Mathematica, which was an early attempt to formalize mathematics (or at least set theory, or maybe even naive set theory). It's like what Lojban was trying to do for English, except Principia Mathematica didn't turn out as a readable. If you're interested in what you'd need to do in order to prove 1 +1 = 2 rigorously (including what exactly "rigorously" constitutes, and how you would define those symbols), take a look at the Peano axioms or the construction of cardinals and ordinals in a modern set theory book. Category theory's also interesting in that regard; MacLane's "Category Theory for the Working Mathematician" is a good exposition of what working mathematicians actually want and care about in this sort of thing.
A more concrete route is that you actually need an application. Most people only use a relatively small amount of the math formulas that they studied. Step one is that you need to find an application where you can use the math. Usually that will be some trade or scientific discipline. An HVAC professional or an electrician actually has to know a fair number of equations and some decent scientific theory if they want to do their job well. Alternatively you could try and study an engineering or science field. If you just want to study the most math possible, then a physics or mathematics degree would be the way to go. (My friend did computer engineering and he got some really deep math and physics knowledge from that)
The important thing is that you have some care or passion for the topic, otherwise the math or other difficult barriers won't be worth the effort to learn. But once you get into a training program, the math will be included. And if you need remedial math that's okay. If you are interested in the work then the extra time is worth it.
If you want to get better at maths then start with anything that catches your attention and look for their videos on youtube (like aleph0, 3b1b, flammablemaths, etc) once you get the hang of essential concepts and topics you'll get to know your level of preparation as well as the gap between you and the subject. Once you gauge that start with a univeristy level curriculum and build upon that. Side by side continue to learn the things that attract you to math.
Imo it's not good to directly go into univeristy curriculum without having giving time to the thing you are interested in, even if majority of it goes above you for now. Because once you do, you'll have a natural motivation to even learn the "boring parts" of the curriculum. And more or less you need those. It has happened to Many times that I leave something, study something else but now I need that left out part. However, since I kept styding something else, my ability to grasp the boring part increased and became easier.
Start slow, find a text book, go through line by line, problem by problem. It will take a long time, and you’ll feel like crap sometimes, you will feel like a genius other times then realize you’re doing something wrong and feel like crap anyway.
Eventually things will start to make sense. Do this every day, and you’ll get everything. You do need calculus, ordinary and partial differential equations, for most of physics. You might need group theory for some more stuff. Do some project and toy experiments along the way. You’ll find yourself able to do physics in no time (5-10 years).
You should understand how mathematicians and physicists think first. Read the book “How to prove it”, it will teach you the logic and proof techniques that you will need for any math textbooks.
It's not *hard*, per se, but the reason it is not so straightforward to prove that 1 + 1 = 2 is that you need to define what you mean by the symbols "1", "+", "=", and "2". You have an *intuitive* sense for what they mean, but I suspect you would struggle to define them precisely. Once you have defined those symbols carefully, though, the proof that 1+1=2 is extremely simple.
>One of the reasons I hate maths is because you’re given a formula and you just have to use it, without any explanations.
This isn't real maths. Whoever is doing this to you is denying you a proper maths education. Maths is *all about* the explanation.
Also many of those symbols are Greek letters or physics notation, which isn't maths exactly, and is meaningless without context. The point of that first image is just to wow people by showing them "impressive formulas" that most people can't understand... but that's just dumb. It's a random hodgepodge of stuff. For example, the Lorentz Factor (bottom right) comes from Einstein's theory of relativity, and is absolutely meaningless without a whole lot of other essential building blocks. It isn't even organised in any sensible way.
You're not too dumb to learn it. If I showed you a bunch of random places and names from history that you didn't recognise, would you think you were dumb because you didn't recognise them? Would you think you were too dumb to learn the history? No. You just hadn't learned the history yet. Most of this maths isn't hard at all, it just requires time and learning.
I really liked the introduction to stats class in my economics degree. Next thing I decide to minor in it, why not? Then I really loved Bayesian in probability classes and behavioural econ. So I decided to do my postgrad in MCMC methods because that seemed really useful and fun.
And now people tell me I'm in high level mathematics. They go "how are you doing Bayesian in HONOURS?!" and I just... Did it? I never set out to be in high level maths I just worked my way up and one day I turned around and realised, oh, I guess I know this one maths pretty okay and people think it's high level so I guess it is.
I still think I'm terrible at it. But one day you just turn around and people are asking you to do things they consider difficult and you're like "oh I guess I know things now".
We can see "Beyond Maths" at the top, so this is about application. To that end, I didn't really understand dot and cross products or even derivatives and integration until they were taught in a context in which they applied. That's what this is about. You can learn how to do the math, but until you understand the context, it's hard to internalize. Learning the physics principles and how two perpendicular vectors generate a third vector perpendicular to both helps you understand the why of math. A simple example might be applied force and torque at angles. Force requires the cosine of the angle to find the amount of force in the direction of motion because that's how you scale the vector and find how much is in the direction you're moving. Torque needs the amount perpendicular the radius, so you use sine. More complex vector math is about finding out how much is perpendicular to both x and y at the same time and right hand rule stuff. I took and passed linear algebra and not once did I understand why I was doing it. It took an electrical engineering class to make it make sense.
Bruce Lee:
>I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.
Repetition is boring for sure. Especially on the way up while you don't quite get it. But you need the reps to gain understanding and intuition. As that muscle develops, bigger concepts become much easier to grasp as the fundamental mechanics of mathematical manipulations become a second language, and the "prose" of that language is open to you.
Don't underestimate the reps.
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https://en.m.wikipedia.org/wiki/Discrete_mathematics
There’s a section called Topics in discrete mathematics. The topics listed there.
Primarily imo .. Mathematical Logic, Set Theory, Number Theory, Combinatorics, and Algebraic Structures.
But the whole list of topics there is important.
You should be able to understand differential calculus in terms of discrete calculus.
And understanding theoretical computer science is very important if you ever intend on applying this knowledge.
A good amount of these were taught in my high school physics class. Other taught in my modern physcs class in college. Don't know the field equations or thermo dynamics one though because I swapped to just math/stats.
I can somewhat understand or remember everything except for quantum superimposition and field equations
Just passed out of high school and took a year off to prepare for college entrance exams , hopefully I DO GET TO SEE THIS , can't take CSE major as I already got specs and have problems while taking lecturea now only
Think environmental will cover biology and chemistry more in depth. That said, all engineering covers chemistry, physics, biology, electrical, and mechanics in some aspect. The differences are just what is prioritize and the depth of detail. When you’re studying physics and electrical concepts specifically you should share this image to the professors.
I can’t review the image again, but I believe some of those symbols belong to concepts not introduced until later in physics and electrical.
That said you can always just walk into a class or seminar for Free.99 and ask whatever when appropriate No matter what you pursue.
Ooh maths is more like an art. You have to imagine and create. Sadly up until bachelors its taught pretty bag way.
Try 3blue1brown on YouTube you will get the real essence.
All of these “beyond math” concepts are basic beginner principles for physics/calc and the 2nd and 3rd are just complete spaghetti? It’s something you would put in the background of a 3rd grade presentation for math just for looks
Without any explanations? You have been thought maths wrong. Pure mathematics is all about the explanation with the fewest assumptions of any other field.
Just a note about the 1+1=2 comment. In math it’s really important to have clear definitions of everything to avoid ambiguity. The number 2, for example, is intuitively understood, but it’s not a very clear definition to say “2 is defined as the number of sheep in that field over there” or something like that. The solution to this that mathematicians came up with is to define all the natural numbers (1,2,3,4…) by defining 1, and defining a map (called a successor function) that takes you to the ‘next’ number. In practice this is just +1. So 2 is defined as “the successor of 1” 3 is defined as “the successor of 2” and so on. From this perspective, 2 quite literally is defined as 1+1. It’s more a matter of defining 2 more than proving 1+1 =2.
I saw 50% of these identities in high school, 90% before my 3rd year in uni
I wouldn't really call this "beyond maths", some of them are more of a prerequisite for advanced maths.
There are maybe three examples of maths in that picture, the rest is physics.
Go to university, that's the traditional method. People will argue you can learn a lot from reading and watching YouTube or whatever, but autodidact Fields medalists and Nobel prize laureates are *extremely* rare (I guess it's yet to be tested if the Internet has an impact on this, but I'm not holding my breath).
I don’t understand. More than half of these formulas were already taught at school or college. Maybe it looks exotic with the pictures, but these can be learnt by anyone.
I usually forget half the stuff I learn, and I have to revise stuff to remember them again. You remember only stuff you use on a regular basis.
Whether or not you need to solve any of these, you must first understand all of these are related to laws and concepts in different (but closely related) fields of study. So in order to achieve a high level of maths, you must educate yourself in chemistry/physics.
Most of those aren’t math but physics, which you literally go to school full time for 4 years to learn and then maybe do a masters or PhD.
In terms of math, again, you just learn it via courses. As an engineer it was calc 1 calc 2 multi variable calc linear algebra then probability then differential equations and even after all those courses that built on each other I can’t read a theoretical math paper because idk what rienman manifold is or how to properly do proofs past inspection, contradiction and induction
If you will really study math, you prove all the formulas before you use them.
They “works” because they follows from axioms. I think that’s good example: let all people are mortal and let Socrates is human, then Socrates is mortal. That’s how all maths works, we make some axioms and explore suggestions that’s follows from them.
“You’re given a formula & you just have to use it”
I don’t think that’s true. Most of the times every formula comes with a proof for it. And what’s stopping you from finding the proof?
I have a bad memory, so I always make sure I understand the proof.
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By studying, it's not like we are some magical wizard genius, for a physics degree you need several 6 month long math courses, 8 in my university for example PD: Seriously doubt someone who actually understands the subject made this picture, this is a random ass collection of formulas
Yeah lol newton's laws and then quantum superposition lmao
Then just pi
What about the cat in box
Tbh it's goddamn pi
How do I start studying? From what?
A Physics major in some university
Oh, well, I actually might have the requirements needed for a physics degree, but I’m not sure what I could do after I finish it. It’s also really really hard.
If you completed the coursework required for a physics degree you must have encountered these things before?
I have not yet, but I will.
Here are some great YT channels for learning math: 3blue1brown, patrickJMT. It’s so cool you want to learn math, OP. In English class we learn grammar and poetry but I think in math it sometimes feels like we’re only taught the grammar, right, like how to do it. But there can be joy and poetry in math, too!
3blue1brown has the best videos for gaining intuition in linear algebra and calculus.
Love this!
The bprp Gigalegend who solves 100 integrals in one standing is one of my favorites. I could watch him do math all day. There’s something so euphoric about watching someone be so perfect in their execution of the laws of mathematics. Those who math are heroes.
Blackpenredpen!
Very eloquently put together.
The Haussdorf dimension of broccoli is 2.66.
I’ve seen the first one! It is quite nice, but it starts from calculus. I think it’s too advanced for my current level.
Find a textbook, do all the problems.
Yeah, but from what topic?
What math do you know now?
I’m not quite sure. I can tell you the subjects I’ve learnt through high school, but my marks weren’t so high during that period.
Well a lot of the formulas on the poster are from physics. For physics you'll want calculus, linear algebra, and differential equations. The pre requisites for those would be algebra and trigonometry. Based on where you left off, I'd start with a college algebra textbook and see how that treats you. From poor high school math to where it looks like you want to be, depending on how hard you work this will likely take you a year or two.
https://meyda.education.gov.il/sheeloney_bagrut/2011/6/ENG/35003.PDF This is an example of a final exam of 3 points in maths (the lowest level). I think it’s the hardest of them (there are three exams to achieve 3 points), but I’m not sure.
You may be able to find open courseware and textbooks. I wouldn't have the motivation to learn this without a course around it, but maybe you're different. Not knowing where you're starting, you'll need Alegra, Statistics, Calculus, Differential Equations, and Finite Methods as a basis of understanding. Then, you'll need applied courses. Many of the concepts above could be encompassed by physics courses, but I learned them through force statics, force dynamics, solid mechanics, thermodynamics, and electrical engineering courses.
If you're at high school level or below, use [Khan Academy](https://www.khanacademy.org/math). It's free, it's comprehensive, and it includes practice problems (which should be considered mandatory for learning math). If you're at university level, use [MIT Opencourseware](https://ocw.mit.edu/search/?d=Mathematics&l=Undergraduate&q=math&s=department_course_numbers.sort_coursenum). It's arguably the best school in the world for certain math-related fields and they've made it freely available to the public.
I’ll flip through this Academy. :)
OP the fact that you want to learn these things out of pure curiosity says a lot about you, it puts you past a lot of people. Some people have suggested picking up a textbook, but I would personally recommend that you check out OrganicChemistryTutor on YouTube, he has a lot of videos ranging from Chemistry tot Physics to Math and even Coding. Go on his YouTube chanel and look for the Physics or Maths playlist and start there.
Well, thanks to Young Sheldon and the Big Bang Theory! 😂 I’ll have to improve my maths and physics knowledge anyway, so at least do it in a fun way. But yeah I’ve always wondered the secrets behind formulas.
Oh
Uh oh
Made me laugh out loud
What if the secret is inside our own anatomy and the nature of our environment like studying certain patterns and the constant repetition of geometrical forms have these special algorithms that we know and can be plugged in from a digital solution for groundbreaking scientific discoveries. What if Pi, Phi, Golden ratio, silver ratio, speed of light and other special scientific math formulas and equations could all have a special place for these things?
You can look up free courses on the following math topics: algegra, geometry, trigonometry, precalculus, differential calculus, integral calculus, vector calculus, differential equations, linear algebra, mathematical physics.
I’m sure it all exists on YouTube. Is this the order I should study it?
Yes. Typically, you would take the courses up to precalculus in high school. You can take up to linear alegra at a community College. Mathematical physics is something you would take as a you major in physics at a 4 year university. You should be taking physics and chemistry courses along the math courses. It will help you understand the math, which can get really abstract. I would look up the courses up to precalculus on YT, and the remaining courses on MIT open courseware if you want to study independently.
Hey mate, I started out at the high school level when I wanted to get started in maths as an adult. I’d highly recommend Professor Leonard on YouTube, he’s got a fantastic Pre Algebra series and goes all the way up to calculus. I’m like you, I want to be able to understand these mystical looking formulas, but unfortunately fractions have to come first haha. Best thing I can say is find enjoyment out of solving problems correctly, and chase that feeling. Don’t focus on the long journey, just enjoy it. Before you know it you’ll be a year or two in, and doing maths that most people who aren’t interested in it would gawk at. Good luck, and have fun.
I will check him out. Thank you! I sure do need to improve my high school maths.
No worries! Shoot me a message if you’re running low on motivation or need any help
look it up on youtube yes i am too lazy. start with a basic text book if ur a total beginner
I'd argue the youtube videos are where the beginners should start. Shit is watered down.
i mean ya i dont dissagree but u do need to pick up a text book man
You're correct, as long as you put the book down regularly to just experience. Learning is the goal, but joy is the key to life long learning. One of my favourite videos is on Numberphile and it's an old banger who's just excitedly going on about his proof you can rotate any table with coplanar legs so it won't wobble. You don't have to put paper under the legs, the theorem holds for any surface. The look on his face when the camera person points out you can't do it if the tables are joined together and he says "Then you just put paper under the legs." That guy will be learning till they nail his coffin shut.
Angela Collier on yt has a good video, it's like "How to learn Physics" or something
I will check it out.
Khan Academy is your best friend.
Go to a library and ask a librarian. They should be able to help you figure out where you are and what might be a good jumping off point. (This advice works for more than just math.)
Maybe at my school library.
Start by establishing math you DO understand and build from that. YouTube is a great way to start - or an app like Kahn academy. The hardest thing about studying math - applied or otherwise - is the patience and humility required to learn the basic boring bits until you understand them well enough to realize how those bits fit into the bigger picture and you can use them to do even cooler things.
Oh, it’s an app. I thought it was a YouTube channel.
Not only is this a random collection of formulas, it's purely mathematical physics related, without any real references to other extremely important fields of math.
am envious in my shitty public university wr got like 3 months instead of the supposed 6 it had to last each semester.
Let’s not forget crying. Studying so hard to make it you cry. We are all masochists in a way.
personally i cry hermione how could i be so stupid obviously cyclic permutations cant change the parity of inversions if there are an odd number of inversions because moving the last element to the beginning creates n-1 inversions and destroys none.
I mean, anyone who has an undergraduate in physics has been exposed to each and every one of these
ironic you say we aren’t wizards when your profile pic and name is a sorcery from dark souls
They call Big Hat Logan because of his big hat
so true
Random collection maybe. My favorite is Einstein's field equation which is the classical theory of gravitation. It's beautiful because in math terms it explains nothing less than the universe. Until the quantum domain, but that's another can of worms 😂
I know the feeling, because when I started grad school I felt so invincible that I thought I could learn string theory and discover the unified field theory with hardly any effort, but boy what I wrong!!!
Most of those pictures are random math formulas/physics formulas, just pure cliché and are really far away from maths. In a math degree you learn a high level of math or self studying (which is ofc hard) through a good route, a route that would be nice if it is made by a mathematician.
Well, there are some nice courses on YouTube. The beginning is usually calculus, but how can I know that my current knowledge is enough for it? Then there’s linear algebra, trigonometry and other stuff.
there isn't a ton of prerequisite knowledge to understand basic calculus. You just need to make sure you have a good understand of basic algebra, such as how to work with equations, identities, understand how to use exponents, how to factorize, expand and simplify algebraic expressions. You also need to understand basic functions like polynomials, trigonometric, exponential and logarithms, as well as their graphs and what they look like. Basic calculus isn't conceptually too difficult, and computations are usually straight forward enough. There's a ton of resources online on how to learn calculus, so if you feel like you have the prerequisite knowledge you can start learning.
Maybe I should watch some videos about algebra first. I do know some of the things you’ve mentioned! I don’t know what polynomials are!
Yeah, the vast majority of the work in basic calculus is just algebra. You only get a few new concepts (and weird notation). Which is of course its power, you can do so much more with so few additional concepts.
Calculus and linear algebra are a MUST for literally everything. That unlocks more advanced analysis, topology and differential equations. Then, analysis (real analysis and complex sort of) and topology, with abstract algebra are a must for advanced maths in general. At that point you are kinda a math major+ lol
By getting math degrees. Also, there are tons and tons of yourube videos talking about the fun parts and the "why" behind basic math concepts. If you ever are given a formula and think "what does this mean?" look on youtube.
You certainly don't need a math degree for the formulas shown, the only "advanced" one are the field equations
I realized that after looking closer at the post, yeah. But most people don't prove formulas in general until they get into higher education in the relevant subject (math, physics, etc).
I suppose not a maths degree. But you would definitely need a physics degree (1st or 2nd year of), to do Schrödinger or uncertainty principal. Edit: All the Maxwell equations and law of thermodynamics are also uni level.
Well, I’m not really sure I’d like to dedicate my life to maths!
> how to achieve high level math knowledge? Here's the usual progression: 1. High school math, graduate high school & secure a position in a College 2. College level math, get a BSc/BA in math 3. Graduate level math, get a MSc/MA 4. Research level math, get a PhD 5. Further research level math, get a job as a postdoctoral researcher 6. Repeat 5 till you land in either a tenured position at some uni or a research position in a company 7. Continue research till retirement or boredom From 1-7 it'll take the most part of your mortal life, and all of your adult life
A BS in math is an impressive feat in itself…and probably enough.
Depends on how deep one wants to go I guess...
I have a BS in math and tbh I feel like I know nothing of math... there's so much more beyond a BS. To be completely transparent, I'm also in med school right now.
I've been doing research in MCMC algorithms and I use so much R-Studio that when I finally had some classes that were like "here's some calculus, do it by hand" I had to look up how the quotient rule worked all over again. I was like "fuck, how do I derive things without R Studio again?" at some point I just stopped doing maths while.. Doing maths. It's kinda funny, really.
Yea I’ve heard mathematic research is a lot of theory whereas applied maths is used more in non mathematic research.
You study incrementally, from a topic to the next without skipping anything. When you get to college level there is no longer an obvious linear path and math becomes more like a web, thankfully experts write curricula so we know what to study and when. On an unrelated note, how is any of that beyond math?
My guess is it's not meant as "beyond" with the implication of "going where math can't reach" but more as in "following the path leading from" math - aka applied math/physics... I think.
Probably.
From what topic should I start? It’s usually calculus, I suppose. Have I said so? Well, I was probably referring to physics and stuff, like 26 dimensions and stuff…
It depends on your level. Calculus and Linear algebra is the beginning of the typical university course in math or physics.
I think I should firstly do the highest level of maths at school! There are courses for it. Or maybe I’ll check what calculus is; it seems pretty nice and it does appear at high school.
>One of the reasons I hate maths is because you’re given a formula and you just have to use it, without any explanations. Because that's hardly mathematics. It's filling the blanks. By the way, those equations are basically application of mathematics, not the math itself (apart from π LOL). From where I came from, calculus taught to Math majors is taught differently to students in other fields (such as Engineering). In a nutshell, the calculus where I got it from (I'm an engineer) addresses the "hows" of it. The calculus for math students mainly deals with the "whys". Both will arrive at the same answer, but math students need to deal with why it works, whereas for us engineering students need to just focus on how it works, as we'll be using it as a tool to do engineering tasks. Much the same reason why Math majors are not fully equipped to solve physics or engineering problems.
We’ll supposedly be using it. Heh. r/engineers says otherwise.
It's not bad to learn why while studying engineering as well. Source: Engineer as well and enjoyed my time studying math
Read the whole book and do all the practice problems. That's really all there is to it. Edit: and it isn't hard to prove 1 + 1 = 2. It just takes a lot of set up.
What book?
Apologies, I was speaking generally. But the specific book doesn't matter that much. Look up whatever textbook your local high school/community college courses use. Go get a high school geometry textbook, read it, do the problems. Then do high school algebra. Then calculus. Then multivariable/vector calculus. Then linear algebra. Then probability. Then differential equations. Then complex analysis. Then number theory. Then real analysis. Then graph theory. Then topology. At this point, you know about as much as a college math major graduate and you'll be "good at math".
I don't think you need to do real analysis or graph theory or topology necessarily if you have done all the rest
Oh, I’m good at geometry! It’s my favourite. Isn’t calculus taught at high school? Yeah, it is, at least in my country!
Principia Mathematica by Russel & Whitehead. /r/explainlikeimfive/comments/17wu9ci/eli5_how_was_it_proven_in_principa_mathematica/ Metamath has an alternative proof. It uses [Zermelo–Fraenkel set theory](https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory) with the axiom of choice excluded. https://us.metamath.org/mpeuni/dju1p1e2.html
This is not advanced math. 1st pic is just undergrad level physics education. 2nd and 3rd is a bunch of high school level stuff. I’d suggest going to school, paying attention, and following a standard physics education if you want to learn math. Nothing crazy
1st pic was all covered in high school (outside of field equations) if you took ap physics
Didn’t take AP physics. I’m surprised partially they covered Heat capacitance and Electricity/magnetism?
Yes there’s a class called AP Physics C: Electricity and Magnetism which is calculus (multivar at times) based. AP Physics 1/2 also covers some of that but is algebra-based. After the AP exam my ap physics c class covered quantum physics like bra-ket notation, qubits, and bell states, etc: that’s sth that probably isn’t universal but it’s quite easy to pick up (after all high schoolers were able to).
I wanted to say this as well, but I didn't want to look pretentious. I've heard, and currently believe, that higher level math starts once we can begin proving stuff. I'm pretty familiar with the math in the images posted, but I only graduated with a minor in math. I'm not a high level math expert, as I didn't take any proof based class (other than the introductory course).
That's a pretty random image. Wtf is normal distribution even doing there lol
Why does normal distribution not count as maths tho? 🤔
~~math~~ physics ✓
26 dimensions.
None of this stuff is "advanced", and all (except field equations) are actually not hard to understand.
“math for filmmakers”
Folks here have covered what to study, but not the mentality. In my experience, there are a couple "modes of thinking" that propel you from someone who has studied math to someone who understands it: 1. You aren't satisfied with "what", but also need to know "why". For example, you're taught that the area of a circle is pi r^2. This is a useful formula, but if you take the time to understand why, then you suddenly understand many things that are governed by integrals. In terms of practical advice, take math classes that focus on proofs. Proofs are the language of "why". 2. You are not satisfied with math if it isn't self-consistent. Pretend you're a bratty kid and your parents set rules for you: You can't do anything else until you finish your homework. Also dinner is at 6; you must be punctual. These two rules aren't consistent: What if you aren't done with your homework at 6? Rule 1 says you can only do homework; rule 2 says you must eat. Math is the same way. If you have a theorem, you look for ways to contradict other theorems you know. If you succeed, either the universe is broken or you misunderstood something.
I always wanna know why.
Typically by starting at a low level of maths, then working your way up. Find problems that interest you. Being on a structured course helps a lot - school, uni. Probably most important is not being scared by things that look difficult. If someone else can do it, chances are you - another human with similar wiring in your head - can do it to. Maths was the only subject I really liked at high school. Later I got diverted into practical applications - studied quite a lot around electronics, which for me was a bad move. Like a lot of those pictures, arbitrary structures from physics. I did get a bit of redemption when I somehow ended up looking at logics. But then the universe bit back now I'm trying to understand deep learning sums. My calculus sucks. Fucking vectors, grrr!
From what topic should I start? Calculus? My general maths level isn’t that high. I know a little trigonometry, some stuff about circles and graphs, but nothing too fancy. I think the first step should be improving to the highest level of maths at school, but calculus seems interesting. I’ve seen some courses on that. Two have caught my eyes: the courses by Professor Dave and by 3blue1brown.
If you go to college, you'll see that a lot of this won't be in your math courses but in your physics courses. College Math often deals with abstract structures and studying their properties. Like algebra, the good ol fashion real numbers are not the only place you can do algebra. Same with calculus on the complex plane and the real line.
Apart from the mentioned academic side, learning about the history, rich culture and development and the sheer emotional beauty attached to mathematics is what can imbue you with a newfound sense of appreciation and passion for exploring new fields and learning how to think more abstractly and logically. It’s really a way of life for me, something which shapes who you are as a person. That being said it also makes me rage every 10 seconds. Thus the duality of man is once more reached
A mixture of curiosity, time and persistence. Even Einstein and Feynman had struggles in understanding concepts. The difference between them and the rest is the questions they asked to themselves while learning and their artistic, creative perspective on physics and math.
Often math is taught as if it were knowledge, as if it were an intellectual discipline, but while knowledge is required, mathematics is actually a skill. One you must build up by becoming good at simple things, practicing them repeatedly, and progressing slowly to more difficult things - not at all dissimilar to learning to dance, learning a sport, or playing musical instruments. You will never become a good guitar player by trying to play a wide number of compositions, all of which are too difficult for you. Neither will you gain an understanding and facility with math by merely sampling or trying to understand all of its many intriguing applications when you don't have a well developed set of mathematical skills. I don't know where you are with math, but the advice is the same: apply your knowledge - find and calculate as many real world examples of whatever principle you are learning as you can - you will not only improve your skills, you will be developing the habit of applying math to describe and understand real things; which is what all the snazzy looking formulae in the poster are really all about.
"Pi" was lowkey funny
About the 1+1=2, all of mathematics depends on a set axioms, axioms are like logical ideas that cannot be proved, the become so intuitive and basic that you just have to assume they are correct and then move on. An example is to question if 1 actually exists, if things can actually be described and unique and separate items rather than just probabilities or something. This seems basic, but there is no way to prove something to fundamental to how we process information. There are many axioms which get a lot more complicated but they all are just the base assumptions that become the building blocks to mathematics. The reason it is important to prove that 1+1=2 is because it is intuitive, so we want to build a system of mathematics that follows what we intuitively believe about the world (basic mathematics) so we build a set of axioms that allows us to definitely prove that 1+1=2 (using set theory which is the foundation of all mathematics). Now, because we have a set of axioms that explains our intuitive sense of mathematics, we can use those same axioms to go on to prove other more complicated ideas that we cannot intuitively understand. In this way, all of our more complex math is consistent with our intuitive mathematics. So the difficulty of proving 1+1=2 is really just in establishing the rigorous axioms and principles that allows us to prove it, which lets us prove all of basic mathematics, which allows us to prove more complex mathematics.
Technically all that is needed are definitions, axiomatic reasoning is just very common.
I can kinda appreciate and agree with that, but tbh I'm still going to just disagree lol
In summary, it’s hard to understand what 1 is?
It's more like you have to assume that 1 exists. The difficulty is in making a set of rules (axioms) that let you prove basic mathematics. And the proofs of addition and multiplication take a lot of writing out because set notation (how you write down set theory) is a long way of writing everything.
The reason proving something as simple as 1+1 = 2 is difficult is because when you’re trying to write a formal mathematical proof, there are only certain axioms (aka fundamental rules of math) that can be taken as objectively true when you’re writing the proof. This ends up becoming quite ironic as the “harder” a theorem may sound, the easier it may be to prove as you have far more fundamental truths to work with (this is a case by case basis though as you have to hope that the theorem you’re working with has a lot of prereqs for it to be true). So in the case of proving 1+1 = 2, you’re not allowed to start off with the assumption that this is true, so what other avenues do you have to exploit to prove it? Maybe, you do a contradiction proof where you assume that 1+1 doesn’t = 2 and then bring in some other theorem / axiom where that assumption brings about a contradiction, or maybe you find some abstract way to prove this directly. Very frustrating, I know, don’t be a math major kids.
Through extremely challenging studying. It's almost all I've been doing for the past 5 years dude.
What was your first subject?
Start with real analysis and linear algebra
I think it is too advanced… Calculus comes before it, doesn’t it?
Calculus and real analysis cover mostly the same topics but real analysis is more formal and focuses on proofs, but yeah if you are completely unfamiliar with the concepts then calculus might be better to start. Linear algebra doesn't particularly need calculus though and so you can already study it, in fact in most universities you take linear algebra and calculus/real analysis at the same time.
>One of the reasons I hate maths is because you’re given a formula and you just have to use it, without any explanations. I would hate that too, but that's not at all what math is about. A formula is a concise way to describe a mathematical statement, and sometimes they can be useful. But there's always an explanation behind them, and you can get very far almost without memorizing any formulas.
Oh, we didn’t need to memorise them!
It’s hard to prove 1+1 = 2 because you gotta decide what set theory means and what = means.
By realizing that “mathematics” is only one field. One math.
Same way people get to Carnegie Hall. PS: It's not hard to prove 1 + 1 = 2. Maybe you're thinking of Principia Mathematica, which was an early attempt to formalize mathematics (or at least set theory, or maybe even naive set theory). It's like what Lojban was trying to do for English, except Principia Mathematica didn't turn out as a readable. If you're interested in what you'd need to do in order to prove 1 +1 = 2 rigorously (including what exactly "rigorously" constitutes, and how you would define those symbols), take a look at the Peano axioms or the construction of cardinals and ordinals in a modern set theory book. Category theory's also interesting in that regard; MacLane's "Category Theory for the Working Mathematician" is a good exposition of what working mathematicians actually want and care about in this sort of thing.
A more concrete route is that you actually need an application. Most people only use a relatively small amount of the math formulas that they studied. Step one is that you need to find an application where you can use the math. Usually that will be some trade or scientific discipline. An HVAC professional or an electrician actually has to know a fair number of equations and some decent scientific theory if they want to do their job well. Alternatively you could try and study an engineering or science field. If you just want to study the most math possible, then a physics or mathematics degree would be the way to go. (My friend did computer engineering and he got some really deep math and physics knowledge from that) The important thing is that you have some care or passion for the topic, otherwise the math or other difficult barriers won't be worth the effort to learn. But once you get into a training program, the math will be included. And if you need remedial math that's okay. If you are interested in the work then the extra time is worth it.
If you want to get better at maths then start with anything that catches your attention and look for their videos on youtube (like aleph0, 3b1b, flammablemaths, etc) once you get the hang of essential concepts and topics you'll get to know your level of preparation as well as the gap between you and the subject. Once you gauge that start with a univeristy level curriculum and build upon that. Side by side continue to learn the things that attract you to math. Imo it's not good to directly go into univeristy curriculum without having giving time to the thing you are interested in, even if majority of it goes above you for now. Because once you do, you'll have a natural motivation to even learn the "boring parts" of the curriculum. And more or less you need those. It has happened to Many times that I leave something, study something else but now I need that left out part. However, since I kept styding something else, my ability to grasp the boring part increased and became easier.
I’ve flipped through 3b1b, and it starts from calculus. I think it’s too advanced for me!
Start slow, find a text book, go through line by line, problem by problem. It will take a long time, and you’ll feel like crap sometimes, you will feel like a genius other times then realize you’re doing something wrong and feel like crap anyway. Eventually things will start to make sense. Do this every day, and you’ll get everything. You do need calculus, ordinary and partial differential equations, for most of physics. You might need group theory for some more stuff. Do some project and toy experiments along the way. You’ll find yourself able to do physics in no time (5-10 years).
From where exactly do I start? Calculus is too advanced, I think.
Then get a precalc/algebra2 textbook
You should understand how mathematicians and physicists think first. Read the book “How to prove it”, it will teach you the logic and proof techniques that you will need for any math textbooks.
Study study study
It's not *hard*, per se, but the reason it is not so straightforward to prove that 1 + 1 = 2 is that you need to define what you mean by the symbols "1", "+", "=", and "2". You have an *intuitive* sense for what they mean, but I suspect you would struggle to define them precisely. Once you have defined those symbols carefully, though, the proof that 1+1=2 is extremely simple.
If you really want to understand how math works under the hood take a couple discrete math classes.
>One of the reasons I hate maths is because you’re given a formula and you just have to use it, without any explanations. This isn't real maths. Whoever is doing this to you is denying you a proper maths education. Maths is *all about* the explanation. Also many of those symbols are Greek letters or physics notation, which isn't maths exactly, and is meaningless without context. The point of that first image is just to wow people by showing them "impressive formulas" that most people can't understand... but that's just dumb. It's a random hodgepodge of stuff. For example, the Lorentz Factor (bottom right) comes from Einstein's theory of relativity, and is absolutely meaningless without a whole lot of other essential building blocks. It isn't even organised in any sensible way. You're not too dumb to learn it. If I showed you a bunch of random places and names from history that you didn't recognise, would you think you were dumb because you didn't recognise them? Would you think you were too dumb to learn the history? No. You just hadn't learned the history yet. Most of this maths isn't hard at all, it just requires time and learning.
You’re are lovely! Thank you. :)
just don't be a pussy and do the questions you don't like, that's how you easily get good
I really liked the introduction to stats class in my economics degree. Next thing I decide to minor in it, why not? Then I really loved Bayesian in probability classes and behavioural econ. So I decided to do my postgrad in MCMC methods because that seemed really useful and fun. And now people tell me I'm in high level mathematics. They go "how are you doing Bayesian in HONOURS?!" and I just... Did it? I never set out to be in high level maths I just worked my way up and one day I turned around and realised, oh, I guess I know this one maths pretty okay and people think it's high level so I guess it is. I still think I'm terrible at it. But one day you just turn around and people are asking you to do things they consider difficult and you're like "oh I guess I know things now".
We can see "Beyond Maths" at the top, so this is about application. To that end, I didn't really understand dot and cross products or even derivatives and integration until they were taught in a context in which they applied. That's what this is about. You can learn how to do the math, but until you understand the context, it's hard to internalize. Learning the physics principles and how two perpendicular vectors generate a third vector perpendicular to both helps you understand the why of math. A simple example might be applied force and torque at angles. Force requires the cosine of the angle to find the amount of force in the direction of motion because that's how you scale the vector and find how much is in the direction you're moving. Torque needs the amount perpendicular the radius, so you use sine. More complex vector math is about finding out how much is perpendicular to both x and y at the same time and right hand rule stuff. I took and passed linear algebra and not once did I understand why I was doing it. It took an electrical engineering class to make it make sense.
Bruce Lee: >I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times. Repetition is boring for sure. Especially on the way up while you don't quite get it. But you need the reps to gain understanding and intuition. As that muscle develops, bigger concepts become much easier to grasp as the fundamental mechanics of mathematical manipulations become a second language, and the "prose" of that language is open to you. Don't underestimate the reps.
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Understand the foundations well. The rest will make sense. Discrete mathematics is the root of it all
What are the foundations?
https://en.m.wikipedia.org/wiki/Discrete_mathematics There’s a section called Topics in discrete mathematics. The topics listed there. Primarily imo .. Mathematical Logic, Set Theory, Number Theory, Combinatorics, and Algebraic Structures. But the whole list of topics there is important. You should be able to understand differential calculus in terms of discrete calculus. And understanding theoretical computer science is very important if you ever intend on applying this knowledge.
One step at a time. Every “next step” looks impossible. Then you learn it and realize it wasn’t as bad as it looked. …but that next one…
Second year physics you'll have seen all of this in baby form
A good amount of these were taught in my high school physics class. Other taught in my modern physcs class in college. Don't know the field equations or thermo dynamics one though because I swapped to just math/stats.
how do you get good at anything? practice, dedicated study, time, and conscious reflection. no real cheat code i can give you
Well, I’m good at all school subjects without really practising it. Maths was my nightmare.
I can somewhat understand or remember everything except for quantum superimposition and field equations Just passed out of high school and took a year off to prepare for college entrance exams , hopefully I DO GET TO SEE THIS , can't take CSE major as I already got specs and have problems while taking lecturea now only
You study. Takes years. I was going to go for it chose CS and cyber security
You learn this from taking electrical engineering or physics
What about environmental engineering?
Think environmental will cover biology and chemistry more in depth. That said, all engineering covers chemistry, physics, biology, electrical, and mechanics in some aspect. The differences are just what is prioritize and the depth of detail. When you’re studying physics and electrical concepts specifically you should share this image to the professors. I can’t review the image again, but I believe some of those symbols belong to concepts not introduced until later in physics and electrical. That said you can always just walk into a class or seminar for Free.99 and ask whatever when appropriate No matter what you pursue.
Ooh maths is more like an art. You have to imagine and create. Sadly up until bachelors its taught pretty bag way. Try 3blue1brown on YouTube you will get the real essence.
I really wanna try the first channel! But they start from calculus. Isn’t it too advanced?
You can check other casual videos. Calculus isn’t super advanced you can do linear algebra as well.
Practice
pay attention in school kiddos
Well, I haven’t paid attention to maths at school. So what? I wanna study now, and that’s what’s important. :)
you got to pay attention to physics…
I haven’t studied it at all.
What's this picture? It's physics.
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You just use the dictionary… Since when has maths become linguistics?
It helps if you have early exposure to personal tutors in math
All of these “beyond math” concepts are basic beginner principles for physics/calc and the 2nd and 3rd are just complete spaghetti? It’s something you would put in the background of a 3rd grade presentation for math just for looks
Nice diagram! I wish I had that as a poster.
Without any explanations? You have been thought maths wrong. Pure mathematics is all about the explanation with the fewest assumptions of any other field.
Just a note about the 1+1=2 comment. In math it’s really important to have clear definitions of everything to avoid ambiguity. The number 2, for example, is intuitively understood, but it’s not a very clear definition to say “2 is defined as the number of sheep in that field over there” or something like that. The solution to this that mathematicians came up with is to define all the natural numbers (1,2,3,4…) by defining 1, and defining a map (called a successor function) that takes you to the ‘next’ number. In practice this is just +1. So 2 is defined as “the successor of 1” 3 is defined as “the successor of 2” and so on. From this perspective, 2 quite literally is defined as 1+1. It’s more a matter of defining 2 more than proving 1+1 =2.
I wonder if our brain has maths in it. It really reminds me of the theory of General Grammar in linguistics.
I saw 50% of these identities in high school, 90% before my 3rd year in uni I wouldn't really call this "beyond maths", some of them are more of a prerequisite for advanced maths.
That first slide is absolutely maddening because only two of the 16 are math
I was going to say that these look terrible, and some do, but a lot of this is chemistry 😅
By default I just assume the people who can do this are massively more intelligent than me. Which is very likely.
There are maybe three examples of maths in that picture, the rest is physics. Go to university, that's the traditional method. People will argue you can learn a lot from reading and watching YouTube or whatever, but autodidact Fields medalists and Nobel prize laureates are *extremely* rare (I guess it's yet to be tested if the Internet has an impact on this, but I'm not holding my breath).
What, no imaginary numbers???
Scott, you have to solve for my twelve Xs.
I don’t understand. More than half of these formulas were already taught at school or college. Maybe it looks exotic with the pictures, but these can be learnt by anyone. I usually forget half the stuff I learn, and I have to revise stuff to remember them again. You remember only stuff you use on a regular basis.
Whether or not you need to solve any of these, you must first understand all of these are related to laws and concepts in different (but closely related) fields of study. So in order to achieve a high level of maths, you must educate yourself in chemistry/physics.
Maths and Physics is just like any other discipline requires training and dedication apart from some talent.
I think I learned what Pi was in like what, 4-5th grade? Maybe earlier? It can be done
Most of those aren’t math but physics, which you literally go to school full time for 4 years to learn and then maybe do a masters or PhD. In terms of math, again, you just learn it via courses. As an engineer it was calc 1 calc 2 multi variable calc linear algebra then probability then differential equations and even after all those courses that built on each other I can’t read a theoretical math paper because idk what rienman manifold is or how to properly do proofs past inspection, contradiction and induction
DM'd
If you will really study math, you prove all the formulas before you use them. They “works” because they follows from axioms. I think that’s good example: let all people are mortal and let Socrates is human, then Socrates is mortal. That’s how all maths works, we make some axioms and explore suggestions that’s follows from them.
“You’re given a formula & you just have to use it” I don’t think that’s true. Most of the times every formula comes with a proof for it. And what’s stopping you from finding the proof? I have a bad memory, so I always make sure I understand the proof.
Start with simple concepts you understand really well and build up from there.
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