/sci/ - Science & Math

>>10360820
What, exactly, do you want to know?

>>10360826
For instance, how the underlying constructs map to the overlying equations.

Decide on what field of mathematics you wish to learn first

>>10360941
That's a hard one, considering how interesting most of them are.

>>10360820
https://4chan-science.wikia.com/wiki/Mathematics?oldid=4748#Survey_of_Real_Mathematics

Bump.

>>10360820

there is no mathematics without memorization. you have to memorize the definitions at the very least

>>10362358
As I said:
>... rather than just simply learning the mathematical methodology...
>... just...
As in, "alongside".

What do you mean by conceptual mechanics? When you say "underlying constructs" here >>10360885 which do you mean? In the mind or in the world?

I am interested in similar things but a bit fuzzy on what you mean exactly.

>>10362374
The reason I'm keeping the context ambiguous is so that the thread doesn't end up being stilted toward one field, or the other.
I want to be keep it broad, so the replies I get (hopefully) are all-encompassing.
Although, I haven't been very successful thus far.

>>10362393
That's a good idea I think, I just don't even understand what you mean enough to get off the ground thinking about it. I study the epistemology and ontology of mathematics but I don't know if what interests me would be of interest to you.

>>10360820
Definitions + rules/logic = Math
Applying those rules to the things which you define can lead to more complex rules
For example,In arithmetic I can "add" "numbers" to get another number 1 + 1 = 2
Now, what if I add a number x y times?
There you get multiplication.What if I multiply a b times? There you get exponents a^b
In algebra you now have equations and variables and you can do whatever you want as long as you follow the rules.Rules being whatever you do to one side of the equation you must also do to the other side.Rules lead to other rules which can lead to other definitions and yeah that's math its all about finding new rules and new definitions

>>10362445
Those rules and definitions are sometimes motivated by physical reality

>>10362445
I feel what you're lakcing is the connection from mathematics to the phenomenal world.
I'd like to understand how those concepts map to reality, enough that we can use them to form predictions.

>>10362401
>I study the epistemology and ontology of mathematics but I don't know if what interests me would be of interest to you.
It would.

>>10362458
That's why we have theories, we're trying to model the world through these rules and definitions in such a way that they make accurate predictions

>>10362480
That's physics not math

Also, aside from the rules and definitions, you also try to relate things. So, rules, definitions and relating things are what I'd say make up math

>>10360820
>carrying about mechanics
>not dynamics
how is the 20th century ?

>>10362622
That's a pretty stale joke, my friend.

Bump.

Anymore for anymore?

>>10360820
I unironically enjoy Wildberger's teaching style and minimalist perspective. Particularly his Math Foundations series on YouTube. It really forced me to think about the essence of mathematics in a more primitive way.

https://www.youtube.com/playlist?list=PL5A714C94D40392AB

https://www.youtube.com/watch?v=eNtJquRf-uk

>>10364637
>a=>b, b=>c implies a=>c
>Realizing that it wasn't all about the logic, but rather a creative process
>It's not about the tools, everyone knows the tools its about how you put them together

>>10364637
>What was keeping me from understanding these ideas wasn't the logic but its because these ideas were so different, so new

>>10364546
>Wildberger
I refuse to learn mathematics from this madman.

>>10364546
Wildberger is a crank, not even CS faggots are so retardedly ultrafinitist.
Best take on foundations is by Voevodsky.

>>10365392
You're missing out, bud. Wildberger is a great teacher.
>>10365530
Wildberger's ultrafinitist rules are excellent for computability. Means all quantities and operations are computable, no approximations needed. I love that shit.

>>10366475
>You're missing out, bud. Wildberger is a great teacher.
I can imagine he is, being passionate. However, I bet he evangelizes about his own theories, even when he's supposed to be teaching a subject, without offering his opinion. That's my issue.

>>10360885
You're being too broad to the point it's hard to give suggestions.

>>10366475
>Wildberger's ultrafinitist rules are excellent for computability
So is HoTT. Furthermore, it doesn't give up such tremendously powerful tools as axiom of choice. Simply put, univalent foundations are everything ultrafinitists want, but actually useful.
inb4 hurr HoTT no compute - CuTT

>>10365530
>CS
>ultrafinitist
I’d believe you if HoTT wasn’t a big push in TCS circles. CS =/= combinatorialist

>>10360820
Start with Euclid until you can re-write every proof on your own. Repeat with other mathematicians and their works

>>10366483
>I bet he evangelizes about his own theories.
Oh yeah, he totally does. I personally find it amusing, but others may find it off-putting and annoying. He's pretty good natured about it though.

>>10366525
>muh HoTT
I don't know much about HoTT and univalent foundations, to be honest. Seems pretty new. What's a good entry point?

I might be misinterpreting you, but you seem to take a hyperplatonic position on may. Pure math as taught in the mathematics department can (and arguably should) be entirely dissociated from "the world".
That said, the topics that were initially most studied are often tied to more physical and economical questions, simply because that's where outsiders come to mathematicans and ask for help, or where mathematicans with broader interest or capital interest will naturally get into.
But again, if you seek to tie math to logos in the work, then I think you're doing yourself a disfavour as far as the full scope (and thus the essence of) mathematics is concerned.

I might be misinterpreting you, but you seem to take a hyper-Platonic position on math. Pure math as taught in the mathematics department can (and arguably should) be entirely dissociated from "the world".

That said, the topics that were initially most studied are often tied to more physical and economical questions, simply because that's where outsiders come to mathematicans and ask for help, or where mathematicans with broader interest or capital interest will naturally get into.

But again, if you seek to tie math to logos in the world, then I think you're doing yourself a disfavour as far as the full scope (and thus the essence of) mathematics is concerned.

>>10362534
Yes because physics is the only field that uses mathematics to make predictions.

>>10366706
>Oh yeah, he totally does.
Imagine him being your professor.

>>10360820
Just study the evolution of the concepts of physics aka history of physics and math. You know, start wiht egiptian and sumerian math and Thales of Miletus proto-science, don't forget about Aristotle, Euclid, Hipparchus and y Claudius Ptolemy before you know about al-Khwarizmi and the other indians an arabs. Then you have Cardan, Tartaglia, the Bernoulli family, Fermat, Descartes, Huygens, Newton, Leibniz, Euler, Gauss, Maxwell, Cauchy, Riemann, etc.

There is a lot of books concerning this topic, and maybe you could learn the ""conceptual mechanics" by learning how the concepts were develop form nothing, how there were many incredible discoveries and how natural philosophy changed, evolved, nourished and grew since the ancients untill now.

>>10366640
Most of the ultrafinitists i know have CS background and own a copy of Gödel, Escher, Bach.
Luckily some CS people aren't completely braindead and understand the importance of HoTT, but progress is still pretty much exclusive to mathematicians.
>>10366706
>What's a good entry point?
HoTT book, it's self-contained. But you should probably watch the IAS talks too.

>>10366904
>>10360820
Or maybe you don't only want history but also want the construction of math. On the one hand you have pictography, ideography, logograms, on the second one you have ways of abstracting objects and relations of the world and posability to think about things that have almost no basis it, on the third hand you have a natural language but there is an emerging need and formal languages and on the fourth hand (suppose you are Ganesha) you have simple and common, recurrent ideas, you have some problems on thinking about certain things, or some practical difficulties in you enviroment and finally you have specific concepts that can be generalized.

What you have in your hands is something very interesting, you could start with linguistics and a dictionary, but lets say you start with semiotics studies to handle all the symbolic problem and come up with calculi, symbol systems with transfromation rules in order to arrive to what logic could be, finally understanding what is this thing of formal languejes and arriving to certain structure or model, you know, something like starting with intuitions, paioms, postulates and using calculi and logic to finally develop the mathematics as such and relate these four aspects of reason, of thinking and of the world. What you didn't know is how this humble activity will help you a lot to improve your way of think about the world and the big, ancient, fundamental problems and questions of life and universe.

I mean, maybe what you want is hardcore foundations of math.

>>10367009
Someday you will use set theory, analysis, geometry and topology to understand what numbers are and how to use and improve (to improve arithmetic? basic algebra. To improve basic algebra? linear algebra and calculus, and so on) them, what is infinity, what is to demonstrate something, what is abstraction, what is truth... with the plus of also aproaching to the questions about the natural world.

What is the man, where does the world came from, why do we reason and what can we do with reason? How and what to live for? Maybe this are the motivations that >>10360820
(you), OP, to beat this boring view of "simply learning the mathematical methodology by rote memorization".

Just study the evolution of the concepts of physics aka history of physics and math. You know, start with Egyptian and Sumerian math and Thales of Miletus proto-science, don't forget about Aristotle, Euclid, Hipparchus, and y Claudius Ptolemy before you know about al-Khwarizmi and the other Indians an Arabs. Then you have Cardan, Tartaglia, the Bernoulli family, Fermat, Descartes, Huygens, Newton, Leibniz, Euler, Gauss, Maxwell, Cauchy, Riemann, etc.

There is a lot of books concerning this topic, and maybe you could learn the "conceptual mechanics" by learning how the concepts were developed from nothing, how there were many incredible discoveries and how natural philosophy changed, evolved, nourished and grew since the ancients until now.

Or maybe you don't only want history but also want the construction of math. On the one hand you have photography, ideography, logograms, on the second one you have ways of abstracting objects and relations of the world and possibility to think about things that have almost no basis it, on the third hand you have a natural language but there are an emerging need and formal languages and on the fourth hand (suppose you are Ganesha) you have simple and common, recurrent ideas, you have some problems on thinking about certain things or some practical difficulties in your environment and finally you have specific concepts that can be generalized.

>>10367062
What you have in your hands is something very interesting, you could start with linguistics and a dictionary, but lets say you start with semiotics studies to handle all the symbolic problem and come up with calculi, symbol systems with transformation rules in order to arrive to what logic could be, finally understanding what is this thing of formal languages and arriving to certain structure or model, you know, something like starting with intuitions, axioms, postulates and using calculi and logic to finally develop the mathematics as such and relate these four aspects of reason, of thinking and of the world. What you didn't know is how this humble activity will help you a lot to improve your way of think about the world and the big, ancient, fundamental problems and questions of life and universe.

I mean, maybe what you want is hardcore foundations of math.

Someday you will use set theory, analysis, geometry and topology to understand what numbers are and how to use and improve (to improve arithmetic? basic algebra. To improve basic algebra? linear algebra and calculus, and so on) them, what is infinity, what is to demonstrate something, what is abstraction, what is truth... with the plus of also approaching to the questions about the natural world.

What is the man, where does the world came from, why do we reason and what can we do with reason? How and what to live for? Maybe this is the motivations that >>10360820 (OP)
(you), OP, to beat this boring view of "simply learning the mathematical methodology by rote memorization".

Bump.

>>10362610
Consider Analytic Geometry relating Algebra and Geometry via the coordinate plane

Educated bump.

>>10370470
Thanks. OP here, I forgot I had to keep this alive.