Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "User:Johnxyz1"

(→‎My Contributions)
(→‎My Contributions)
Line 62: Line 62:
 
*[[2024 AMC 8 Problems/Problem 13]]
 
*[[2024 AMC 8 Problems/Problem 13]]
 
*[[1988 AHSME Problems/Problem 16]] (not-so-trival edit)
 
*[[1988 AHSME Problems/Problem 16]] (not-so-trival edit)
 +
*[[Texas mathematics competitions]]

Revision as of 21:17, 17 September 2024

$\huge\mathcal{JOHN}$

Favorites

Favorite topic: \[\text{Counting \& Probability}\]for which I am reading AOPS intermediate book on

Favorite color: \[\text{\textcolor{green}{Green}}\]

Favorite software: \[\mathit{Microsoft}\ \text{Excel}\]

Favorite Typesetting Software: \[\text{\LaTeX}\]

Favorite Operating System: Linux (although I am rarely on one)

$\Large\text{\bfseries\LaTeX}$ typesetting

Below are some stuff I am doing to practice $\text{\LaTeX}$. That does not mean I know all of it (actually the only ones I do not know yet is the cubic one and the $e^{i\pi}$ one)

\[\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\] \[e^{i\pi}+1=0\] \[\sum_{x=1}^{\infty} \frac{1}{x}=2\] \begin{align*} x &= \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) + \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} \\ & + \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) - \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} - \frac{b}{3a} \\ &\text{(I copied it from another website but I typeset it myself;}\\ &\text{I am pretty sure those are not copyrightable. I still need \textit{years} to even understand this.)}\\ &\text{This is the cubic formula, although it is \textit{rarely} actually used and memorized a lot. The equation is}\\ &ax^3+bx^2+cx+d=0 \end{align*}


Source code for equations:

https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm


Math Stuff (for my own)

Complementary casework example: https://artofproblemsolving.com/wiki/index.php/2024_AMC_8_Problems/Problem_25

Representing Actions as Permutations

The idea is that if you must do a fixed number of operations of multiple types, you can make those operations letters, and permutate them. For example, if you have a grid of \(4\times 6\) and you want to walk from one corner to the opposite one, WLOG you need to go up \(4\) times and right \(6\) times. You can do that in any order, so basically you are arranging 

   UUUURRRRRR

which simplifies the problem.

Example: 2024 AMC 8 Problems/Problem 13. In this problem you can treat going up as \(U\) and going down as \(D\). Since you have to end up on the ground in \(6\) steps you have \(3\) U's and \(3\) D's; same as above. There are some special cases --- begin with U end with D and invalid stuff.

My Contributions

Redirect creation, this page, talk pages, reverts, and undoing vandalism are excluded. Most edits are very minor.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=User:Johnxyz1&oldid=227454"