Understanding math.

[Anonymous No.10122638]

>graduated HS
How do I understand Mathematics? And by that I mean UNDERSTAND Mathematics, seeing the patterns, not just being able to solve the problem.

Thanks bros.

[Anonymous No.10122821]

Practice practice practice.

[Anonymous No.10122824]

>>10122821
Brainlet

[Anonymous No.10122828]

>>10122638
>UNDERSTAND Mathematics, seeing the patterns
Shrooms.
>not just being able to solve the problem
Would recommend being satisfied with this.

[Anonymous No.10122877]

Study is subordinate to intelligence, and intelligence is subordinate to intuition. And the thing is that no matter how much you study, or how high your intellect is, if you don't have the intuition you better dedicate yourself to something else.

[Anonymous No.10122886]

>>10122828
Ok. Thanks buddy.

[Anonymous No.10123049]

>>10122877
>not realizing that intuition is built by spending time on math

Shiggy

[Anonymous No.10123059]

>>10122638
Algebra by Gelfand and Shen
Functions and Graphs by Gelfand, Glagoleva, and Shnol
The Method of Coordinates by Gelfand, Glagoleva, and Kirillov
Trigonometry by Gelfand and Saul

[Anonymous No.10123060]

>>10122638
How to Solve It: A New Aspect of Mathematical Method by Polya
https://www.youtube.com/watch?v=h0gbw-Ur_do

[Anonymous No.10123130]

Do math and physics at the same time

[Anonymous No.10123147]

All you have to do is A C C E P T Pythagoras in3 your're heart bby uwu

[Anonymous No.10123151]

>>10123130
>physics

[Anonymous No.10123274]

>>10122638
Take a derivative for example. It's the difference between realizing the derivative is a notion for rate of change of the graph of the function, that is, it is a method of approximating tangent lines at points on the graph to arbitrary precision, and just memorizing derivative formulas. One is thinking about what the concepts are describing, the other is just using techniques and passing tests without giving it anymore thought.

[Anonymous No.10123309]

>>10123274
derivatives are where you subtract the exponent by 1 and then put the exponent at the front. If it gets more complicated than that I cant do it and im a software engineer for christ sake

[Anonymous No.10123338]

Try to see everything in as many ways as possible, e.g. find geometric analogies for algebraic and analytic concepts, etc. More often than not there are multiple approaches to a single problem, and in a single concept many branches of mathematics can come together. Like >>10123049 said, intuition in mathematics only comes with practice and you don't really have to be some sort of genius to do maths: https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/
If you haven't already, read Book of Proof: https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Don't listen to most people here, they're undergrad memesters and/or insecure brainlets projecting themselves.
>>10123130
That's not necessary at all. My uni makes math majors take obligatory physics courses and to most it's more of a burden than anything

[Anonymous No.10123344]

>>10122638
INSTABAN ALL FROG POSTERS

[Anonymous No.10123349]

>>10122638
Mathematical maturity comes from years of training; the aptitude to pass through those gates requires high iq. Both the intuition and the intelligence required are inborn traits generally, but you could probably hone your intuition just a bit with diligent practice even if you aren't intelligent enough for doing much of anything in the subject.
>>10123309
>>>/g/

[Anonymous No.10123401]

>>10123049
This, very very true

[Anonymous No.10123506]

>be biology student in russian university
>for 1st year higher math exam i must learn around 120 theorems, concepts and their respective demonstrations by memory because i'll get asked about 2 or 3 out of those 120 plus exercises
Normal mortals cheat, but i fucking suck at it and will definitely get caught. What the fuck do i do?

[Anonymous No.10123536]

>>10122824
what do you want him to say? You think there is some ritual that we're not telling you about that makes you good at math?

[Anonymous No.10123562]

>>10123506
>can't even memorize 120 theorems when you're told beforehand which ones you need to know
are you for real? you have months to memorize it, you can get it done easily in weeks

[Anonymous No.10123619]

>>10123506
The key is to develop a deep understanding of each theorem, concept, etc. While it might technically be possible to literally memorize the exact statements of 100+ such things, that's really a waste of time, and does not lend itself to you actually being able to solve problems.

First, you need to ensure that you have a good grasp of the basic definitions. You should be able to provide several examples of things that satisfy the definition, and also of things that dont satisfy it. You should look at various ways that something can fail to satisfy the definition--for example, if you are working in the domain of Calculus, being able to provide examples of removable discontinuities, jump discontinuities, and essential discontinuities will help you better understand what it means for a function to be continuous. You should also be able to work directly from the definition--again looking at Calculus, you should be able to differentiate using the limit definition of the derivative, even in cases where using a particular derivative rule might be easier.

For each theorem, you should make sure you understand clearly when it applies, and what it implies. You should try applying it to several different examples/situations, and also looking at situations where it doesn't apply. It is often helpful to consider what might happen if you remove/add conditions--what conclusions can you draw instead? Also, you should ideally completely understand and be able to explain the theorem's proof, this will give you a deeper understanding of the theorem.

More than anything else, thinking and working problems will help you understand. Do problems from the course, the textbook, other books, and talk to your professors if you have questions.

Now, to "put it all together", you need to separate the material into various topics. For each topic, identify the most important definitions and results, and focus your efforts there, then expand out into the more tangential material.

[Anonymous No.10124024]

There's a lot of people here talking about understanding the math as that is literally what OP asked for. But I just want to add that you should practise too. Just understanding them and moving on will make you forget them and fuck up. Practise will also make you understand everything better. But don't practise if you don't understand it in the first place. Just understanding or just practising is equally bad. A balance tends to be the solution.

[Anonymous No.10124038]

>>10123151
The greatest Physicist's of all time were also Mathematicians and vice versa.

[Anonymous No.10124265]

>>10122824
Brainlet

[Anonymous No.10124626]

OP, learn what math is about, what are the main problems of each area and how they approach to them, that'll make you familiar (and could make a huge difference) when you start studying a subject later on.

"Understanding" math is time consuming, and, un/like most subjects, it needs you to spend a lot of time asking yourself questions in order to get a deep understanding of the subject. Common questions after learning a new property of a mathematical element are
>Is there any other way to prove this property?
>How many elements satisfy this?
>Were all the conditions stated really necessary? Does the property hold if some of them were removed?
>What are some examples that satisfy this property? What are some examples in which the property does not hold? What are the differences between those two sets of mathematical elements?

As a rough example of this, real functions can be called continuous, uniformly continuous, Lipschitz continuous, differentiable, k-times differentiable, smooth, Riemann-integrable, etc. You can learn about these categories of functions by their definitions, but it creates a much richer experience to learn what makes a function being in "category1" and not in "category2", or if being in "category1" necessarily implies being in "category2". Algebraic examples, similarities in graphs and general properties of each category can help you understand even more of this.

And for the sake of it, here's some books that I really recommend for you
>Velleman's How to Prove It
>Morash's Bridge to Abstract Mathematics
>Hammack's Book of Proof
>Solow's The Keys to Abstract Mathematics

[Anonymous No.10124645]

>>10122638
study it for like a decade or just "get it"
>>10122828
brainlet