Difference between revisions of "User:Johnxyz1"
(Created page with "Below are some stuff I am doing to practice <math>\LaTeX</math> (that logo typeset by <code>\LaTeX</code> looks a bit off). <cmath>\text{If }ax^2+bx+c=0\text{, then }x=\frac{...") |
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− | Below are some stuff I am doing to practice <math>\LaTeX</math> ( | + | <math>\huge\mathcal{JOHN}</math> |
+ | |||
+ | ==Major Contributions== | ||
+ | *''[[Tree (graph theory)]]'' | ||
+ | *''[[Reverse Polish notation]]'' | ||
+ | *''[[LaTeX:Packages]]'' | ||
+ | *''[[Basic Programming With Python]]'' | ||
+ | |||
+ | ==Favorites== | ||
+ | |||
+ | Favorite topic: <cmath>\text{Counting \& Probability}</cmath>for which I am reading AOPS intermediate book on | ||
+ | |||
+ | Favorite color: <cmath>\text{\textcolor{green}{Green}}</cmath> | ||
+ | |||
+ | Favorite software: <cmath>\mathit{Microsoft}\ \text{Excel}</cmath> | ||
+ | |||
+ | Favorite Typesetting Software: <cmath>\text{\LaTeX}</cmath> | ||
+ | |||
+ | <math>\textit{Remark.}</math> | ||
+ | <cmath>\text\LaTeX>\text{Word}>\text{Canva}</cmath> | ||
+ | <cmath>\text{\LaTeX}+\textsf{beamer}>\text{Powerpoint}>\text{Canva}</cmath> | ||
+ | |||
+ | |||
+ | Favorite Operating System: Linux (although I am rarely on one) | ||
+ | |||
+ | ==<math>\Large\text{\bfseries\LaTeX}</math> typesetting== | ||
+ | |||
+ | Below are some stuff I am doing to practice <math>\text{\LaTeX}</math>. That does not mean I know all of it (actually the only ones I do not know yet is the cubic one and the <math>e^{i\pi}</math> one) | ||
<cmath>\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</cmath> | <cmath>\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</cmath> | ||
<cmath>e^{i\pi}+1=0</cmath> | <cmath>e^{i\pi}+1=0</cmath> | ||
+ | <cmath>\sum_{x=1}^{\infty} \frac{1}{x}=2</cmath> | ||
+ | <cmath>\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*} | ||
+ | </cmath> | ||
+ | |||
+ | |||
+ | Source code for equations: | ||
+ | |||
+ | https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm | ||
+ | |||
+ | |||
+ | |||
+ | ==Personal== | ||
+ | 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 | ||
+ | UUUURRRRRR | ||
+ | which simplifies the problem. | ||
+ | |||
+ | Example: 2024 AMC 8 Problems/Problem 13. In this problem you can treat going up as |
Latest revision as of 14:32, 21 September 2024
Contents
[hide]Major Contributions
Favorites
Favorite topic: for which I am reading AOPS intermediate book on
Favorite color:
Favorite software:
Favorite Typesetting Software:
Favorite Operating System: Linux (although I am rarely on one)
typesetting
Below are some stuff I am doing to practice . That does not mean I know all of it (actually the only ones I do not know yet is the cubic one and the one)
Source code for equations:
https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm
Personal
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
UUUURRRRRR
which simplifies the problem.
Example: 2024 AMC 8 Problems/Problem 13. In this problem you can treat going up as