Difference between revisions of "User:Johnxyz1"

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<math>\huge\mathcal{JOHN}</math>
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==Major Contributions==
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*''[[Tree (graph theory)]]''
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*''[[Reverse Polish notation]]''
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*''[[LaTeX:Packages]]''
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*''[[Basic Programming With Python]]''
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==Favorites==
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Favorite topic: <cmath>\text{Counting \& Probability}</cmath>for which I am reading AOPS intermediate book on
 
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 color: <cmath>\text{\textcolor{green}{Green}}</cmath>
  
Favorite software: <cmath>MS\ \text{Excel}</cmath>
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Favorite software: <cmath>\mathit{Microsoft}\ \text{Excel}</cmath>
  
 
Favorite Typesetting Software: <cmath>\text{\LaTeX}</cmath>
 
Favorite Typesetting Software: <cmath>\text{\LaTeX}</cmath>
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<math>\textit{Remark.}</math>
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<cmath>\text\LaTeX>\text{Word}>\text{Canva}</cmath>
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<cmath>\text{\LaTeX}+\textsf{beamer}>\text{Powerpoint}>\text{Canva}</cmath>
 +
  
 
Favorite Operating System: Linux (although I am rarely on one)
 
Favorite Operating System: Linux (although I am rarely on one)
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 +
==<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)
 
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)
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==Personal==
Asymptote test (with autoGraph):
 
 
 
<asy>/* AUTO-GRAPH V-4 beta by PythonNut*/
 
 
 
/* Customizations: feel free to edit */
 
import math;
 
import graph;
 
/* x maximum and minimum */
 
int X_max = 10;
 
int X_min =-10;
 
/* y maximum and minimum */
 
int Y_max = 10;
 
int Y_min = -10;
 
/* linewidth */
 
real line_width = 0.75;
 
/* graph color */
 
pen graph_color = magenta;
 
/* special */
 
bool mark_lattice = false;
 
bool show_grid = true;
 
real X_tick_density = 1;
 
real Y_tick_density = 1;
 
real ratio = 1;
 
real resolution = 0.0001;
 
int size = 300;
 
/* graph function */
 
real f(real x)
 
  {
 
  return sin(x)*sin(x); /* type function to be graphed here */
 
}
 
 
 
/* The Code. Do not disturb unless you know what you are doing */
 
bool ib(real t){ return (Y_min <= f(t) && f(t) <= Y_max); }
 
 
 
size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6);
 
xaxis("$x$",X_min,X_max,Ticks(l,X_tick_density,(X_tick_density/2),NoZero),Arrows);
 
yaxis("$y$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);//
 
if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));}
 
 
 
real t, T1, T2;
 
 
 
for (T1 = X_min ; T1 <= X_max ; T1 += resolution){
 
    while (! ib(T1) && T1 <= X_max){T1 += resolution;}
 
    if(T1 > X_max){break;}
 
    T2 = T1;
 
    while (  ib(T1) && T1 <= X_max){T1 += resolution;}
 
    T1 -= resolution;
 
    draw(graph(f,T2,T1,n=2400),graph_color+linewidth(line_width),Arrows);
 
}
 
 
 
if (mark_lattice){
 
    for (t = X_min; t <= X_max; ++t){
 
        if (f(t)%1==0 && ib(t)){
 
            dot((t,f(t)),graph_color+linewidth(line_width*4));
 
        }
 
    }
 
}
 
dot((0,0));</asy>
 
 
 
 
 
If you want to typeset your own LaTeX equation in a STANDALONE PDF like AOPS does (although they do images), use the standalone documentclass.
 
 
 
 
 
==Miscellaneous==
 
On an AMC 8, you can use a ruler to measure things out. Sometimes that works!
 
 
 
 
Complementary casework example: https://artofproblemsolving.com/wiki/index.php/2024_AMC_8_Problems/Problem_25
 
Complementary casework example: https://artofproblemsolving.com/wiki/index.php/2024_AMC_8_Problems/Problem_25
  
==Representing Actions as Permutations==
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===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 4×6 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
 
''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 4×6 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
 
     UUUURRRRRR
 
which simplifies the problem.
 
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.
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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.

Latest revision as of 14:32, 21 September 2024

$\huge\mathcal{JOHN}$

Major Contributions

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: \[\text{\LaTeX}\]

$\textit{Remark.}$ \[\text\LaTeX>\text{Word}>\text{Canva}\] \[\text{\LaTeX}+\textsf{beamer}>\text{Powerpoint}>\text{Canva}\]


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


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 4×6 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.