What is the best order to learn mathematics?
Is the order typically taught in elementary, middle, and high school, then college, the best order? Or is there an optimal order if we were to restart from scratch AND completely ignore practical applications?
That is, if the end goal were absolute knowledge of mathematics, not usefulness, what would be the best order to learn it all?
Other urls found in this thread:
sites.google.com
en.wikipedia.org
twitter.com
first step would be logic
It would be better if you used algebra, trig, arithmetic and calculus instead of grade levels.
>What is the best order to learn mathematics?
depends on what you plan on using math for
>end goal were absolute knowledge of mathematics
impossible nowadays
>impossible nowadays
Well then the main fundamentals
>It would be better if you used algebra, trig, arithmetic and calculus instead of grade levels.
That's what most schools do
read the stickies faggot
sites.google.com
the IDEAL way would be to start with sets and set theory as a child
this if they're even able to
my best advice is to finish out algebra, get familiar with graphs + graphical functions. Honestly calculus is just a framework built from algebra.
Go to the library and grab an algebra book, start from the beginning - work through each topic, skips ones that seem utterly pointless.
I say go learn(hopefully re-learn) trig after finishing with algebra. Trig identities and concepts are used throughout calculus to describe things that further learning.
I used to think that perhaps there was some special way to teach math that would help younger students. Now though, I think most people are just incapable of learning anything. With that said, I think that for those capable, there is a good route to learn the core of math. Here it is:
>Logic, Proof
>Number Theory
>Algebra of Groups, Fields, Rings.
>Linear Algebra
>Real Analysis
>Complex Analysis
>Topology
>Ordinary Differential Equations
>Partial Differential Equations
Algebra gives a good foundation for what math is as a subject. I was my experience as an undergraduate that upper division algebra courses became a strong source to lean on.
The point is to have a discussion, brainlet
>ode and pde after complex and topology
Why's this?
bruh you can't just tell someone to work through each topic then tell them to skip the ones that seem utterly pointless
how will they know if it's pointless? if they're autistic enough to *literally* do all of it, then let them. they'll become better mathematicians for it
start with The hardest mathematics field you with to study
once you learn that, everything else will be easy
...
just read Bourbaki
1. Plane and Solid Geometry
2. Arithmetic
3. Baby Algebra
4. Single Real Variable Calculus
5. Multi Real Variable Calculus
6. Single Complex Variable Calculus
7. Multi Complex Variable Calculus
8. Group Theory
9. Analytic Number Theory
10. Geometric Topology
11. Arithmetic Number Theory
12. Algebraic Topology
13. Homological Algebra
14. Universal Algebra
If you're a logical thinker, it technically is possible to "learn" any of these subjects without learning any of the others, as you would simply be applying definitions. I have experimented with this, but found it unsatisfactory. Advanced mathematics is much more satisfying when you have a larger background to draw analogies and build abstractions from.
Brainlet bump
Arithmetic
Algebra 1+2
Geometry
Trigonometry
Calculus 1 2 3
Differential Equations
Linear Algebra
???
Sky's the limit from here
We tried that. Didn't work.
Worked fine for the ruskies. American children just don't have a high enough IQ. Especially the niggers and spics.
>analytic number theory
>no complex analysis or introductory real analysis before hand
OH SHIT NIGGER WHAT R U DOIN
Is not linear algebra before differential equations?
It failed because there was mass confusion in how to implement it.
A lot of things in ode can be parameterized or thought of as curves on manifolds, and many solution sets have topological invariants.
Complex maybe because of Fourier series
>R U
>DOIN
>RUDOIN
>complaining about lack of analysis
Rudin-meme shill detected
>tfw niggers and spics have ruined the American education system for the sake of "equality"
This was incredible. Thank you very much user.