Software tools, math

- LaTeX, yabai, gdb
- Small cleanup to media folder

docs/Public/Math/Analysis/analysis.md

@@ -0,0 +1,5 @@
+*See:* [[real analysis]], [[complex analysis]]
+
+*Analysis* is like the formal, rigorous version of [[calculus]]. It takes the aspect taught in calculus classes and examines them more closely, seeking to generalize the rules of calculus and derive them from [[axioms]], or logically prove them. [^1]
+
+[^1]: https://www.reddit.com/r/explainlikeimfive/comments/g4b4wd/eli5_what_is_real_analysis/

docs/Public/Math/Analysis/real analysis.md

@@ -0,0 +1,3 @@
+*Real analysis* deals with [[analysis]] of the functions of the [[real numbers]].
+
+Topics include [[continuous]] functions, [[differentiation]], [[integral]], [[limit]], [[sequence]], and [[series]]. 

docs/Public/Math/LaTeX cheat sheet.md

@@ -0,0 +1,44 @@
+`a_b`: $a_b$
+
+`\mathbf{R}`: $\mathbf{R}$
+
+`\mathbb{R}`: $\mathbb{R}$
+
+`\frac{a}{b}`: $\frac{a}{b}$
+
+`\{x\}`: $\{x\}$
+
+`\cdot`: $\cdot$
+
+`\in`: $\in$
+
+`\subset`: $\subset$
+
+`\cap`: $\cap$
+
+`\cup`: $\cup$
+
+`\emptyset`: $\emptyset$
+
+`\begin{enumerate}`: Creates a numerated list
+
+![[enumerate.png]]
+
+`\exists`: $\exists$
+
+`\forall`: $\forall$
+
+`\therefore`: $\therefore$
+
+`\x_{a}^{b}`: $x_{a}^{b}$
+
+`\text{Hello World}`: $\text{Hello World}$
+
+`\implies`: $\implies$
+
+
+
+
+
+
+

docs/Public/Math/Logic/and.md

@@ -11,5 +11,5 @@ An *AND* of two or more [[literal]] is called a [[product]].
 | 1 | 0 | 0 |
 | 1 | 1 | 1 |
 
-![[and.png.png]]
+![[and.png]]
 

docs/Public/Math/Logic/not.md

@@ -7,6 +7,6 @@ $!n$
 | 0 | 1 |
 | 1 | 0 |
 
-![[not.png.png]]
-
 ![[not.png]]
+
+![[not_transistor.png]]

docs/Public/Math/Logic/or.md

@@ -15,4 +15,4 @@ Truth table:
 
 Logical circuit:
 
-![[or.png.png]]
+![[or.png]]

docs/Public/Math/Proofs/principle of mathematical induction.md

@@ -0,0 +1,10 @@
+*Principle of mathematical induction*, sometimes referred to as *strong mathematical induction*, is as follows:
+
+Let $S$ be a subset of $\mathbb{N}$ with these two properties:
+1. $1\in S$, and
+2. for all $n\in \mathbb{N}$, if $n\in S$, then $n+1\in S$
+Then $S = \mathbb{N}$.
+
+In other words, to prove the statement: $p(n)$ is true for all $n\in \mathbb{N}$
+- $p(1)$ is true (base)
+- If $p(j)$ is true for all integers $1\le j \le m$, then $p(m+1)$ is true

docs/Public/Math/Sets/real numbers.md

@@ -0,0 +1 @@
+*Real numbers* contain the set of [[rational numbers]] and [[irrational numbers]]. 

docs/Public/Software/Computer Architecture/xor.md

@@ -9,4 +9,4 @@ $a$ ^ $b$
 | 1 | 0 | 1 |
 | 1 | 1 | 0 |
 
-![[xor.png.png]]
+![[xor.png]]

docs/Public/Software/Engineering/debugging.md

@@ -17,6 +17,9 @@ The MINS problem solving model works like this:
 - Solve
 	- After locating the bug, generate a solution and test it
 
+- For production, probably better to disable the debug support and activate all possible optimization support
+	- Reduce size, increase performance
+
 
 
 

docs/Public/Software/Networks/SSH cheat sheet.md

@@ -0,0 +1,20 @@
+Log into UC Davis CSIF computers:
+```bash
+ssh [email protected]
+```
+
+Referencing files on the host:
+```
+host:[/path]
+```
+Transferring files from local to CSIF:
+```bash
+scp 
+```
+
+Transfer files from CSIF to local:
+```bash
+
+```
+
+

docs/Public/Software/Operating Systems/GDB.md

@@ -0,0 +1,75 @@
+*GDB* stands for the [[GNU]] debugger, which helps finds errors like segmentation faults. 
+
+Canonical complication command line: 
+```bash
+gcc [cflags] -o <output> <input
+``` 
+
+Optimize for speed: (-O2)
+
+```bash
+gcc -Wall -Werror -O2 -o myprogram main.c
+```
+
+Enable debugging support (-g):
+```bash
+gcc -Wall -Error -g myprogram main.c
+```
+- To balance performance with debugging experience use `-Og`
+- Not recommended to use debugging along with other optimizations
+	- No optimization option is equivalent to `-O8`
+
+Start GDB with the program to debug as an argument:
+```bash
+gdb myprogram
+```
+
+Running the program:
+- Without any argument: `gdb run`
+- With arguments: `gdb run argv1, argv2... `
+
+GDB offers an interactive shell:
+- Can ask `gdb help <argument>`
+
+Possible scenarios:
+1. Program doesn't have bugs
+2. Best-case scenario: Segmentation fault
+3. Worst-case scenario: Doesn't crash, but wrong output
+
+Backtrace:
+- First thing to do when getting a segfault
+	- Understand what is the sequence of calls that brought us there
+```bash
+gdb backtrace
+```
+Breakpoints:
+- Stop the program during the execution at a designated point
+- At a line:
+```bash
+gdb break string-test.c.:13
+Breakpoint 1 at 0x4005ef: file string-test.c, line 13.
+```
+- At a function:
+```bash
+gdb b main
+Breakpoint 1 at 0x40059f: file string-test.c, line 8
+```
+- At a condition:
+```bash
+gdb b string-test.c:13 if i == 5
+```
+- Show info of all declared breakpoints:
+```
+gdb info b
+```
+
+Dealing with Breakpoints:
+- Once the program has stopped and the gdb shell is available, you can:
+	1. Continue the execution until the next breakpoint: `gdb continue` or `gdb c`
+	2. Execute only the next line of code and break again: `gdb step` or `gdb s`
+	3. Jump over function calls: `gdb next` or `gdb n`
+- Tip: Typing `<enter>` in the interactive gdb shell repeats the last command
+
+
+
+

docs/Public/Software/Operating Systems/segmentation fault.md

@@ -0,0 +1,3 @@
+A *segmentation fault* occurs when a program attempts to access a memory location it is not allowed to access. [^1]
+
+[^1]: https://en.wikipedia.org/wiki/Segmentation_fault

docs/Public/Software/Tools/flowchart.md

@@ -5,6 +5,6 @@ Some building blocks are:
 - Decision: Represents a question with a finite number of answers
 - Terminal: Represents the beginning or ending of a chart
 
-![[flowchart.png.png]]
+![[flowchart.png]]
 
 Think about what the program should accomplish in terms of inputs and outputs. 

docs/Public/Software/Tools/yabai cheat sheet.md

@@ -0,0 +1,17 @@
+Change window focus within space:
+- `alt` + `j/k/h/l`
+
+Swap windows:
+- `shift` + `alt` + `j/k/h/l`
+
+Change focus between external displays:
+- `alt` + `s/g`
+
+Maximize a window:
+- `shift` + `alt` + `m`
+
+Balance windows:
+- `shift` + `alt` + `e`
+
+Start / stop / restart yabai:
+- `ctrl` + `alt` + `q/s/r`

docs/Public/Software/Tools/yabai.md

@@ -0,0 +1,5 @@
+*See:* [[yabai cheat sheet]]
+
+*yabai* is a window tiling manager. 
+
+It is used with skhd to map keybinds to tiling functions.