/sci/ - Science & Math

[Anonymous No.11383245]

relearning math from the ground up. I want to better my own intuition. Does anyone have any recommendations?

[Anonymous No.11383260]

Yes, don't relearn math from the ground up. Move on to new topics and stop being a coward wallowing in high school math. I understand the allure of "perfecting" your understanding before moving on, but evidence suggests (and I have personally experienced this, too) that only by moving on do you acquire a better understanding of preceding material.

[Anonymous No.11383270]

[Anonymous No.11383289]

>>11383260
Pretty much this. I didn't understand vector calculus despite getting an A in calc 3. It was all cookie cutter problems and mechanical symbol pushing that didn't require deep understanding. It wasn't until I had intermediate physics courses which required me to actually use vector calculus to solve a variety of problems that I gained a deep understanding.

[Anonymous No.11383297]

>>11383289
>>11383270
>>11383260
So if I don't immediately understand how Lagrange created a general formula for polynomial interpolation, then it's no big deal?

[Anonymous No.11383309]

>>11383297
Deep mathematical understanding develops like a polaroid picture. As you progress your understanding of the whole becomes clearer and more defined. One part of the picture doesn't need to come into perfect focus for you to move on to another part.

[Anonymous No.11383327]

>>11383297
Lagrange interpolation formula is simple. You build up the function from indicator functions: f_i(x_i)=1 and f_i(x_j)=1 for all i!=j. Because F_i has roots x_j, you can write f_i(x)=Prod{i!=j}(x_x_j)K
Then K is determined by the condition f_i(x_i)=1
Then adding up the indicator functions with appropriate multiplicative constants you get your interpolating polynomial :)

[Aeris Turtle No.11383336]

>>11383245
start with the basics:

https://www.openlearning.com/courses/algebraic-calculus-one/

:))

[Anonymous No.11383342]

>>11383245
rush through basic material and only stop on parts you don't fully understand

[Anonymous No.11383519]

>>11383245
>Does anyone have any recommendations?