vault backup: 2025-06-06 14:43:51

.obsidian/app.json

@@ -2,7 +2,7 @@
   "vimMode": true,
   "promptDelete": false,
   "pdfExportSettings": {
-    "includeName": true,
+    "includeName": false,
     "pageSize": "Letter",
     "landscape": false,
     "margin": "0",

.obsidian/community-plugins.json

@@ -2,5 +2,6 @@
   "obsidian-git",
   "d2-obsidian",
   "execute-code",
-  "better-export-pdf"
+  "better-export-pdf",
+  "obsidian-excalidraw-plugin"
 ]

.obsidian/core-plugins.json

@@ -27,5 +27,6 @@
   "sync": false,
   "canvas": true,
   "bookmarks": true,
-  "properties": true
+  "properties": true,
+  "webviewer": false
 }

.obsidian/plugins/better-export-pdf/data.json

@@ -14,7 +14,7 @@
   "prevConfig": {
     "pageSize": "A4",
     "marginType": "1",
-    "showTitle": true,
+    "showTitle": false,
     "open": true,
     "scale": 100,
     "landscape": false,

.obsidian/plugins/obsidian-excalidraw-plugin/data.json

@@ -0,0 +1,799 @@
+{
+  "folder": "Excalidraw",
+  "cropFolder": "",
+  "annotateFolder": "",
+  "embedUseExcalidrawFolder": false,
+  "templateFilePath": "Excalidraw/Template.excalidraw",
+  "scriptFolderPath": "Excalidraw/Scripts",
+  "fontAssetsPath": "Excalidraw/CJK Fonts",
+  "loadChineseFonts": false,
+  "loadJapaneseFonts": false,
+  "loadKoreanFonts": false,
+  "compress": true,
+  "decompressForMDView": false,
+  "onceOffCompressFlagReset": true,
+  "onceOffGPTVersionReset": true,
+  "autosave": true,
+  "autosaveIntervalDesktop": 60000,
+  "autosaveIntervalMobile": 30000,
+  "drawingFilenamePrefix": "Drawing ",
+  "drawingEmbedPrefixWithFilename": true,
+  "drawingFilnameEmbedPostfix": " ",
+  "drawingFilenameDateTime": "YYYY-MM-DD HH.mm.ss",
+  "useExcalidrawExtension": true,
+  "cropPrefix": "cropped_",
+  "annotatePrefix": "annotated_",
+  "annotatePreserveSize": false,
+  "previewImageType": "SVGIMG",
+  "renderingConcurrency": 3,
+  "allowImageCache": true,
+  "allowImageCacheInScene": true,
+  "displayExportedImageIfAvailable": false,
+  "previewMatchObsidianTheme": false,
+  "width": "400",
+  "height": "",
+  "overrideObsidianFontSize": false,
+  "dynamicStyling": "colorful",
+  "isLeftHanded": false,
+  "iframeMatchExcalidrawTheme": true,
+  "matchTheme": false,
+  "matchThemeAlways": false,
+  "matchThemeTrigger": false,
+  "defaultMode": "normal",
+  "defaultPenMode": "never",
+  "penModeDoubleTapEraser": true,
+  "penModeSingleFingerPanning": true,
+  "penModeCrosshairVisible": true,
+  "renderImageInMarkdownReadingMode": false,
+  "renderImageInHoverPreviewForMDNotes": false,
+  "renderImageInMarkdownToPDF": false,
+  "allowPinchZoom": false,
+  "allowWheelZoom": false,
+  "zoomToFitOnOpen": true,
+  "zoomToFitOnResize": true,
+  "zoomToFitMaxLevel": 2,
+  "linkPrefix": "📍",
+  "urlPrefix": "🌐",
+  "parseTODO": false,
+  "todo": "☐",
+  "done": "🗹",
+  "hoverPreviewWithoutCTRL": false,
+  "linkOpacity": 1,
+  "openInAdjacentPane": true,
+  "showSecondOrderLinks": true,
+  "focusOnFileTab": true,
+  "openInMainWorkspace": true,
+  "showLinkBrackets": true,
+  "allowCtrlClick": true,
+  "forceWrap": false,
+  "pageTransclusionCharLimit": 200,
+  "wordWrappingDefault": 0,
+  "removeTransclusionQuoteSigns": true,
+  "iframelyAllowed": true,
+  "pngExportScale": 1,
+  "exportWithTheme": true,
+  "exportWithBackground": true,
+  "exportPaddingSVG": 10,
+  "exportEmbedScene": false,
+  "keepInSync": false,
+  "autoexportSVG": false,
+  "autoexportPNG": false,
+  "autoExportLightAndDark": false,
+  "autoexportExcalidraw": false,
+  "embedType": "excalidraw",
+  "embedMarkdownCommentLinks": true,
+  "embedWikiLink": true,
+  "syncExcalidraw": false,
+  "experimentalFileType": false,
+  "experimentalFileTag": "✏️",
+  "experimentalLivePreview": true,
+  "fadeOutExcalidrawMarkup": false,
+  "loadPropertySuggestions": true,
+  "experimentalEnableFourthFont": false,
+  "experimantalFourthFont": "Virgil",
+  "addDummyTextElement": false,
+  "zoteroCompatibility": false,
+  "fieldSuggester": true,
+  "compatibilityMode": false,
+  "drawingOpenCount": 0,
+  "library": "deprecated",
+  "library2": {
+    "type": "excalidrawlib",
+    "version": 2,
+    "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.8.3",
+    "libraryItems": []
+  },
+  "imageElementNotice": true,
+  "mdSVGwidth": 500,
+  "mdSVGmaxHeight": 800,
+  "mdFont": "Virgil",
+  "mdFontColor": "Black",
+  "mdBorderColor": "Black",
+  "mdCSS": "",
+  "scriptEngineSettings": {},
+  "defaultTrayMode": true,
+  "previousRelease": "2.8.3",
+  "showReleaseNotes": true,
+  "showNewVersionNotification": true,
+  "latexBoilerplate": "\\color{blue}",
+  "latexPreambleLocation": "preamble.sty",
+  "taskboneEnabled": false,
+  "taskboneAPIkey": "",
+  "pinnedScripts": [],
+  "customPens": [
+    {
+      "type": "default",
+      "freedrawOnly": false,
+      "strokeColor": "#000000",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
+      "strokeWidth": 0,
+      "roughness": 0,
+      "penOptions": {
+        "highlighter": false,
+        "constantPressure": false,
+        "hasOutline": false,
+        "outlineWidth": 1,
+        "options": {
+          "thinning": 0.6,
+          "smoothing": 0.5,
+          "streamline": 0.5,
+          "easing": "easeOutSine",
+          "start": {
+            "cap": true,
+            "taper": 0,
+            "easing": "linear"
+          },
+          "end": {
+            "cap": true,
+            "taper": 0,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
+      "type": "highlighter",
+      "freedrawOnly": true,
+      "strokeColor": "#FFC47C",
+      "backgroundColor": "#FFC47C",
+      "fillStyle": "solid",
+      "strokeWidth": 2,
+      "roughness": null,
+      "penOptions": {
+        "highlighter": true,
+        "constantPressure": true,
+        "hasOutline": true,
+        "outlineWidth": 4,
+        "options": {
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+          "easing": "linear",
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+            "cap": true,
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+          "end": {
+            "taper": 0,
+            "cap": true,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
+      "type": "finetip",
+      "freedrawOnly": false,
+      "strokeColor": "#3E6F8D",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
+      "strokeWidth": 0.5,
+      "roughness": 0,
+      "penOptions": {
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+        "hasOutline": false,
+        "outlineWidth": 1,
+        "constantPressure": true,
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+            "cap": false,
+            "easing": "linear"
+          }
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+      }
+    },
+    {
+      "type": "fountain",
+      "freedrawOnly": false,
+      "strokeColor": "#000000",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
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+      "roughness": 0,
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+        "options": {
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+          "easing": "easeInOutSine",
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+            "taper": 150,
+            "cap": true,
+            "easing": "linear"
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+            "taper": 1,
+            "cap": true,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
+      "type": "marker",
+      "freedrawOnly": true,
+      "strokeColor": "#B83E3E",
+      "backgroundColor": "#FF7C7C",
+      "fillStyle": "dashed",
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+      "roughness": 3,
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+          }
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+  "pdfScale": 4,
+  "pdfBorderBox": true,
+  "pdfFrame": false,
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+  "pdfGroupPages": false,
+  "pdfLockAfterImport": true,
+  "pdfNumColumns": 1,
+  "pdfNumRows": 1,
+  "pdfDirection": "right",
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+  "gridSettings": {
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+    "COLOR": "#000000",
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+    "DECAY_TIME": 1000,
+    "COLOR": "#ff0000"
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+    "backgroundMatchCanvas": false,
+    "backgroundMatchElement": true,
+    "backgroundColor": "#fff",
+    "backgroundOpacity": 60,
+    "borderMatchElement": true,
+    "borderColor": "#fff",
+    "borderOpacity": 0,
+    "filenameVisible": false
+  },
+  "markdownNodeOneClickEditing": false,
+  "canvasImmersiveEmbed": true,
+  "startupScriptPath": "",
+  "openAIAPIToken": "",
+  "openAIDefaultTextModel": "gpt-3.5-turbo-1106",
+  "openAIDefaultVisionModel": "gpt-4o",
+  "openAIDefaultImageGenerationModel": "dall-e-3",
+  "openAIURL": "https://api.openai.com/v1/chat/completions",
+  "openAIImageGenerationURL": "https://api.openai.com/v1/images/generations",
+  "openAIImageEditsURL": "https://api.openai.com/v1/images/edits",
+  "openAIImageVariationURL": "https://api.openai.com/v1/images/variations",
+  "modifierKeyConfig": {
+    "Mac": {
+      "LocalFileDragAction": {
+        "defaultAction": "image-import",
+        "rules": [
+          {
+            "shift": false,
+            "ctrl_cmd": false,
+            "alt_opt": false,
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+            "result": "image-import"
+          },
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+            "result": "embeddable"
+          }
+        ]
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+            "result": "embeddable"
+          },
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+            "result": "image-import"
+          }
+        ]
+      },
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+          },
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+            "ctrl_cmd": false,
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+            "meta_ctrl": true,
+            "result": "image-fullsize"
+          }
+        ]
+      },
+      "LinkClickAction": {
+        "defaultAction": "new-tab",
+        "rules": [
+          {
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+            "ctrl_cmd": false,
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+            "meta_ctrl": false,
+            "result": "active-pane"
+          },
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+            "result": "new-tab"
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+            "result": "new-pane"
+          },
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+          },
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+            "result": "md-properties"
+          }
+        ]
+      }
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+            "result": "embeddable"
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+        ]
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+  "areaZoomLimit": 1,
+  "longPressDesktop": 500,
+  "longPressMobile": 500,
+  "doubleClickLinkOpenViewMode": true,
+  "isDebugMode": false,
+  "rank": "Bronze",
+  "modifierKeyOverrides": [
+    {
+      "modifiers": [
+        "Mod"
+      ],
+      "key": "Enter"
+    },
+    {
+      "modifiers": [
+        "Mod"
+      ],
+      "key": "k"
+    },
+    {
+      "modifiers": [
+        "Mod"
+      ],
+      "key": "G"
+    }
+  ],
+  "showSplashscreen": true,
+  "pdfSettings": {
+    "pageSize": "A4",
+    "pageOrientation": "portrait",
+    "fitToPage": 1,
+    "paperColor": "white",
+    "customPaperColor": "#ffffff",
+    "alignment": "center",
+    "margin": "normal"
+  }
+}

.obsidian/plugins/obsidian-excalidraw-plugin/manifest.json

@@ -0,0 +1,12 @@
+{
+  "id": "obsidian-excalidraw-plugin",
+  "name": "Excalidraw",
+  "version": "2.8.3",
+  "minAppVersion": "1.1.6",
+  "description": "An Obsidian plugin to edit and view Excalidraw drawings",
+  "author": "Zsolt Viczian",
+  "authorUrl": "https://www.zsolt.blog",
+  "fundingUrl": "https://ko-fi.com/zsolt",
+  "helpUrl": "https://github.com/zsviczian/obsidian-excalidraw-plugin#readme",
+  "isDesktopOnly": false
+}

.obsidian/plugins/obsidian-git/data.json

@@ -5,7 +5,7 @@
   "autoSaveInterval": 5,
   "autoPushInterval": 0,
   "autoPullInterval": 5,
-  "autoPullOnBoot": true,
+  "autoPullOnBoot": false,
   "disablePush": false,
   "pullBeforePush": true,
   "disablePopups": false,

.obsidian/types.json

@@ -0,0 +1,27 @@
+{
+  "types": {
+    "aliases": "aliases",
+    "cssclasses": "multitext",
+    "tags": "tags",
+    "excalidraw-plugin": "text",
+    "excalidraw-export-transparent": "checkbox",
+    "excalidraw-mask": "checkbox",
+    "excalidraw-export-dark": "checkbox",
+    "excalidraw-export-padding": "number",
+    "excalidraw-export-pngscale": "number",
+    "excalidraw-export-embed-scene": "checkbox",
+    "excalidraw-link-prefix": "text",
+    "excalidraw-url-prefix": "text",
+    "excalidraw-link-brackets": "checkbox",
+    "excalidraw-onload-script": "text",
+    "excalidraw-linkbutton-opacity": "number",
+    "excalidraw-default-mode": "text",
+    "excalidraw-font": "text",
+    "excalidraw-font-color": "text",
+    "excalidraw-border-color": "text",
+    "excalidraw-css": "text",
+    "excalidraw-autoexport": "text",
+    "excalidraw-embeddable-theme": "text",
+    "excalidraw-open-md": "checkbox"
+  }
+}

education/calculus/precalculus/Composing Functions.md

@@ -0,0 +1,3 @@
+- To compose a function is to create a new function from multiple smaller functions.
+- They can be solved from the inside out
+- 

education/computer engineering/ECE2700/Adders.md

@@ -1,7 +1,15 @@
+# Half Adder
+
+# Full Adder
+
+# Ripple Carry Adder
+
 # Carry-Select Adder
 A carry select adder is built using two ripple carry adders, and multiplexing them together based off of the value of $c_{in}$. This is done for performance reasons, because when adding two numbers $x$ and $y$, we know $x$ and $y$ *before* we know the value of $c_{in}$. This means we can compute what the output of $x + y + c_{in}$ would be for $c_{in} = 0$ and $c_{in} = 1$ at the same time, then just toggle between the two possible values given the *actual* value of $c_{in}$.
 
 The delay is calculated like so:
 1. Given the delay of a full adder is $k$, and the delay of a 2 to 1 mux is $\frac{1}{m}k$,
 2. then the delay of a 4 bit ripple carry adder is $4k$, because it's 4 full adders chained together, running sequentially.
-3. This means that the delay of a 4 bit carry select adder is $4k + \frac{k}{m}$ 
+3. This means that the delay of a 4 bit carry select adder is $4k + \frac{k}{m}$ 
+
+# Carry-lookahead adder

education/computer engineering/ECE2700/Karnaugh Maps.md

@@ -0,0 +1,37 @@
+A Karnaugh map is an alternative to a truth table for representing a function in boolean algebra, and serve as a way to derive minimum cost circuits for a truth table.
+
+![[karnaugh-maps.png]]
+
+Given the above truth table, the columns are labelled with $x_1$, and the rows are labelled with $x_2$.
+
+To find a minimal boolean expression with a Karnaugh map, we need to find the smallest number of product terms  ($x_1$, $x_2$) that should produce a 1 for all instances where the cell in a table is $1$. 
+
+# Two Variable Maps
+
+![[Pasted image 20250224104850.png]]
+
+- Given the map described in the above image, the output is $1$ for the row where $x_2$ is equal to 1.
+- Similarly, the output is $1$ for the column where $x_1$ is equal to zero.
+- By ORing the condition where $x_1$ is zero ($\overline{x_1}$), and the condition where $x_2$ is one ($x_1$), we can find a minimal expression for the truth table.
+
+# Three Variable Maps
+![[Pasted image 20250224105753.png]]
+
+A three variable Karnaugh map is constructed by placing 2 two-variable maps side by side. The values of $x_1$ and $x_2$ distinguish columns in the map, and the value of $x_3$ distinguishes rows in the map.
+
+To convert a 3 variable Karnaugh map to a minimal boolean expression, start by looking for places in the map that contain 1s next to each other (by row, or by column).
+
+![[Pasted image 20250224110124.png]]
+
+From there, describe the pair of 1s using boolean algebra.
+
+In the above example, the top pair of 1s is in the column where $x_3$ is equal to zero ($\overline{x_3}$), and $x_1$ is equal to $1$ ($x_1$). This describes a single term in the resulting equation ($x_1\overline{x_3}$).
+
+
+![[Pasted image 20250224110632.png]]
+> Similar logic can be employed using more than just a *pair* of ones.
+
+
+# Four Variable Maps
+![[Pasted image 20250224111117.png]]
+![[Pasted image 20250224110819.png]]

education/computer engineering/ECE2700/Sequential Circuits.md

@@ -0,0 +1,50 @@
+- Output depends on input and past behavior
+- Requires use of storage elements
+
+# Latches
+## SR Latch
+SR stands for *Set*/*Reset*, and functions like so:
+- When a signal comes into $S$, $Q_a$ is **set** on and stays on until a signal comes into $R$, at which point the output ($Q_a$) is **reset**, back to zero.
+- $S$ and $R$ are interchangeable, it just impacts whether $Q_a$ or $Q_b$ is set/reset. 
+Truth table:
+
+| $S$ | $R$ | $Q_a$ | $Q_b$ |
+| --- | --- | ----- | ----- |
+| 0   | 0   | 0/1   | 1/0   |
+| 0   | 1   | 0     | 1     |
+| 1   | 0   | 1     | 0     |
+| 1   | 1   | 0     | 0     |
+![[Pasted image 20250303095542.png]]
+
+
+## Gated Latch
+A gated latch is similar to a basic latch,  but the output only changes when $clk = 1$. 
+## D Latch
+A D latch has two inputs, $clk$ and $data$. When $clk$ is high, $data$ is stored. 
+# Flip Flops
+A latch, but the output only changes on one of the clock edges
+- Can be a rising edge latch or a falling edge latch
+## JK Flip Flop
+Similar to an SR flip flop, a JK flip flop has set/reset inputs, but when *both* inputs are high, then the output is toggled.
+## T Flip Flop
+A T Flip Flip, or a toggle flip flop has two inputs:
+- $clk$ - Clock input
+- $T$ - Whenever $T$ goes from low to high, the output toggles its state
+
+# Registers
+## Shift Register
+![[Pasted image 20250317101146.png]]
+Above is a simple shift register.
+
+## Parallel Shift Register
+A parallel shift register has 4 inputs, 4 outputs, a serial input, and a shift/load input.
+
+When the *load* input is high, the input is stored into the register. When the *shift* input is high, the registers are shifted and the serial input is read into the new space.
+
+# Counters
+## A 3-bit Up-counter
+![[Pasted image 20250317102911.png]]
+
+# Synchronous Sequential Circuits
+- A synchronous circuit is clock driven, while an asynchronous circuit is not.
+

education/computer engineering/ECE2700/Verilog/Modules.md

@@ -0,0 +1,135 @@
+Modules are the building block through which Verilog is built.
+
+Each module can be thought of as a black box with a series of inputs, and a series of outputs. Changing the input changes the outputs.
+
+Module definitions are started with the `module` keyword, and closed with the `endmodule` keyword.
+
+## Syntax
+The general syntax of a module is as follows:
+```verilog
+// This line is referred to as the *module header*
+module <name> ([port_list]);
+	// Contents of the module
+endmodule
+
+// The port list is optional
+module <name>;
+	// Contents
+endmodule
+```
+
+Below is an example of the structure of a half adder module:
+```verilog
+module half_adder(
+	input a,
+	input b,
+	output sum_bit,
+	output carry_bit
+	);
+	// ------- snip ------------
+endmodule
+```
+
+## Ports
+Ports are a set of signals that act as input and outputs for a particular module. 
+
+There are 3 kinds of ports:
+- `input`: Input ports can only receive values from the outside. `input` ports cannot be written to.
+- `output`: Output ports can be written to, but not read from.
+- `inout`: Inout ports can send *and* receive values.
+
+Ports can be declared in the port list, or in the module body. Ports declared in the port list can optionally omit their type and only declare a name, to be specified within the body of the module:
+```verilog
+module half_adder(
+	a,
+	b,
+	sum_bit,
+	carry_bit
+	);
+	input a;
+	input b;
+	output sum_bit;
+	output carry_bit;
+	// ----------- snip -----------
+endmodule
+```
+
+The full type of a port can also be defined within the portlist:
+```verilog
+```verilog
+module half_adder(
+	input wire a,
+	input wire b,
+	output wire sum_bit,
+	output wire carry_bit
+	);
+	input a;
+	input b;
+	output sum_bit;
+	output carry_bit;
+	// ----------- snip -----------
+endmodule
+```
+
+### Port types
+If no type is defined, ports are implicitly defined as *nets* of type `wire`.
+
+> In verilog, the term *net* refers to network, and it refers to a connection that joins two or more devices together.
+
+Ports can be a vector type:
+```verilog
+module test(a, b, c);
+	input [7:0] a;
+	input [7:0] b;
+	output [7:0] c;
+	// -------- snip ---------
+endmodule
+```
+
+# Instantiation
+Larger designs can be built by using multiple smaller modules.
+
+Modules can be *instantiated* within other modules and ports, and these *instances* can be connected with other signals.
+
+These port connections can be defined by an *ordered list*, or by *name*.
+
+### By Ordered List
+```verilog
+module submodule (input x, y, z, output o);
+	// ------- snip -------
+endmodule
+
+module parent;
+	wire a, b, c;
+	wire o;
+	// Similar to C, the type of the module is first, followed by
+	// the name of the module instance.
+	submodule foo (a, b, c, o);
+endmodule
+```
+
+### By Name
+Ports can also be joined by explicitly defining the name.
+
+Syntactically, this is done with a dot (`.`), followed by the port name defined by the design, followed by the signal name to connect, wrapped in parenthesis (`.x(a)`).
+```verilog
+module submodule (input x, y, z, output o);
+	// ------------snip-----------------
+endmodule
+
+module parent;
+	wire a, b, c;
+	wire o;
+	submodule foo (
+		.x(a),
+		.y(b),
+		.z(c),
+		.o(o)
+	);
+```
+
+Because association is done by name, the order of definition does not matter.
+
+### Unconnected ports
+Ports that are not connected to any wire by the parent module will have a value of high impedance, and is considered unknown/undefined.
+

education/computer engineering/ECE2700/Verilog/Types.md

@@ -0,0 +1,88 @@
+There are two main categories of data types in Verilog. These categories differ in the underlying hardware structure they represent, and they differ in the way they are assigned and retain values.
+# Nets
+A *net* refers to a *network* of connections that join two or more devices together.
+
+Nets connect different hardware entities and *do not store values*. 
+## Wire
+A `wire` is the most commonly used type of net. When a port is declared in Verilog, it is implicitly given a type of `wire`.
+
+It is illegal to re-declare a name already in use by a net:
+```verilog
+module foo;
+	wire abc;
+	wire a;
+	wire b;
+	wire c;
+
+	wire abc; // ILLEGAL: The wire `abc` is already defined
+
+```
+
+# Variables
+A variable is a data storage element. They retain the last input given.
+```verilog
+```verilog
+module testbench;
+  integer  	int_a; 				// Integer variable
+  real 		real_b; 			// Real variable
+  time 		time_c; 			// Time variable
+
+  initial begin
+    int_a 	= 32'hfacd_1b34; 	// Assign an integer value
+    real_b 	= 0.1234567; 		// Assign a floating point value
+
+    #20; 						// Advance simulation time by 20 units
+    time_c 	= $time; 			// Assign current simulation time
+
+    // Now print all variables using $display system task
+    $display ("int_a 	= 0x%0h", int_a);
+    $display ("real_b 	= %0.5f", real_b);
+    $display ("time_c 	= %0t", time_c);
+  end
+endmodule
+```
+```
+## Registers
+A `reg` can be used to model hardware registers because it stores a value until the next assignment.
+
+### Integer
+A Verilog `integer` type is a 32 bit wide storage value. It does not *need* to store integers, it can be used for other purposes.
+```verilog
+	integer   count;
+```
+### Time
+A `time` variable is unsigned, 64 bits wide, and can be used to store time duration for debugging purposes. `realtime` is similar, but time is stored as a floating bit value.
+
+## Real
+The `real` type denotes a floating point value.
+
+## Strings
+Strings are stored in a vector of `reg`s. The width of the `reg` *must* be large enough to hold the string.
+
+Each character in a string represents a one byte ASCII value. If the size of the variable is smaller than the string, the string is truncated.
+# Scalar and Vector Types
+By default, declarations of a net or `reg` value is 1 bit wide, referred to as a *scalar* value (only a single value).
+
+```verilog
+// Scalar declaration
+wire foo;
+// Vector declaration, with 8 bits.
+wire [7:0] bar;
+```
+
+Individual bits in a vector can be accessed using array operators, eg `[i]`.
+
+```verilog
+reg [7:0] foo;
+
+// Write to bit 0
+foo [0] = 1;
+```
+
+## Part selects
+A range of contiguous bits from within another vector can be selected, referred to as a part select. This range can then be treated as a vector.
+```verilog
+reg [31:0] foo;
+// Select bits 23 through 16 (inclusive), and assign the 8 bit hex value `0xff` to them.
+foo [23:16] = 8'hff;
+```

education/computer engineering/ECE2700/Verilog/Verilog.md

@@ -17,8 +17,11 @@
 - Put in public domain in 1990
 - Standardized in 1995
 - Originally intended for simulation of logic networks, later adapted to synthesis
+- Structural Verilog describes how things are laid out at a logic level.
 
-- Behavioral Verilog describes broader behavior, at a higher level
+## Structural Verilog
+Structural Verilog describes things at a logic level.
+- The use of logic gates and continuous assignment are markers of structural Verilog.
 ```verilog
 //              V---V---v--v-----portlist (not ordered)
 module example1(x1, x2, s, f);
@@ -32,24 +35,24 @@ module example1(x1, x2, s, f);
 	and(g, k, x1);
 	and(h, s, x2);
 	or(f, g, h);
+	// You can also do this
+	assign f = (~s & x1) | (s & x2);
 endmodule	
 ```
-
+## Behavioral Verilog
+Behavioral Verilog describes broader behavior, at a higher level
+- The use of `reg`s, time delays, arithmetic expressions, procedural assignment, and other control flow constructs are markers of behavioral Verilog.
 ```verilog
 //              V---V---v--v-----portlist (not ordered)
 module example1(x1, x2, s, f);
 	// Defining the types of the various ports
 	input x1, x2, s;
 	output f;
-	// You can also do this
-	assign f = (~s & x1) | (s & x2);
-	// Or this
 	always @(a, b)
 	// always @(....) says "do this stuff whenever any of the values inside of @(...) change"
 		{s1, s0} = a + b;
 endmodule	
 ```
-- Structural Verilog describes how things are laid out at a logic level
 
 ## Testbench Layout
 - Define UUT module

education/humanities/Introduction.md

@@ -1,85 +0,0 @@
-## What is art?
-**Art**: the expression or application of human creative skill.
-art must:
-- be made with the intent to convey emotion
-- should "satisfy the senses"
-- be made with intent
-- have attention to feeling and emotion
-art may:
-- be a relay of experience or emotion from one person to another
-
-## Medium
-A particular material, along with an accompanying technique (plural: media). Example include:
-- Acrylic, enamel, gesso, glaze, ink, oil
-
-## History
-1. The branch of knowledge dealing with past events
-## How do you look at art?
-Purposes and functions of art include:
-- Communicating information:
-	- In non-literate societies, art was used to teach.
-	- Today, film and television are used to disseminate information.
-- Spirituality and Religion
-	- All of the world's major religions have used art to inspire and instruct the faithful
-- Personal and cultural expression
-- Social and political ends
-	  - Artists have criticized or influenced values or public opinion
-	  - Often it is clear and direct
-	  - Other times, however, it is less obvious
-		  - Monarchs who commissioned projects to symbolize their strength and power
-
-Generally, art can be broken down into two parts, *form*, and *content*. 
-- Form relates to the "formal" aspects of art, composition or medium.
-- Content relates to the subject. What's being portrayed, how are they portraying it?
-- The distinction should be made between fact and opinion/guessing.
-
-Parts of form:
-1. Line and Shape
-	- Lines define space and may create an outline or contour, as style called "linear"
-	- They can be *visible* or *implied*, and may be a part of composition
-	- It may be 2 dimensional, 3 dimensional, suggested, or implied.
-	- *Wherever there is an edge
-2. Color
-	- Hue: The name of the color (red, blue, yellow)
-	- Saturation: The quality or vibrancy of those values
-	- Value: The addition of white, black, or grey to the value
-		- Tint: pure hue + white
-		- Tone: pure hue + grey
-		- Shade: pure hue + black
-3. Texture
-	- Texture is an element of art pertaining to the surface quality or "feel" of the work of art
-	- Texture can be described as smooth, rough, soft, etc. Some textures are real, and others are simulated
-	- Textures that can be *felt* are ones that fingers can actually touch.
-4. Space and Mass
-	- Space references to what contains objects: may be 2D or 3D.
-	- Mass refers to the effect and degree of the bulk, density, and weight of matter in space.
-	- In architecture or sculpture, it is the area occupied by a form.
-	- Perspective: Foreshortening is a way of representing an object so that it conveys the illusion of depth; an object appears to be thrust forward or backward in space.
-5. Composition
-	- How are items arranged or organized in art
-	- Symmetrical, asymmetrical
-	- Static or dynamic
-	- Picture space is comprised of foreground, middle ground, and background.
-6. Scale
-	- As an art history term, scale refers to the size of an object or object represented
-	- Size of things, conveyed or literal
-
-Parts of style:
-- Cultural style
-	- Societies develop their own beliefs and style of material forms
-	- Artists are a product of their culture
-- Period style
-	- Style changes over time
-	- Art changes because of economic and political changes
-- Regional style
-	- Geography leads to diverse styles
-- Personal style
-	- Individual artists often have distinct styles
-
-Two basic forms of style:
-- Representational: Seeks to create recognizable subject matter (this is a picture of a dog)
-- Abstract: Seeks to capture the essence of a form, not the literal representation (this picture captures the feeling of a dog)
-
-| Phrase | Definition |
-| ---- | ---- |
-|  |  |

education/humanities/Test 2.md

@@ -1,37 +0,0 @@
-| Piece                                            | Place                         | Artist                               | Medium                            | Stuff                                                                                                                                                                                                                                                                                          |
-| ------------------------------------------------ | ----------------------------- | ------------------------------------ | --------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
-| Treasury Of Atreus                               | Ancient Greece: Helladic      | Unknown                              | Limestone                         | Largest dome for over 1000 years<br>Largest monolithic lintel<br>Ashlar masonry and cyclopic masonry<br>Thought to be Atreus, he abdicated (possibly a tomb)<br>post and lintel and corbelled arch<br>                                                                                         |
-| Snake Goddess                                    | Ancient Greece: Minoan        | Unknown                              | Faience                           | Hierarchy of Scale; Exposed breasts - power<br>victory pose<br>rosettes<br>sideways dress - otherworldly<br>We don't know much about this work                                                                                                                                                 |
-| Bull-leaping, from the palace at Knossos         | Ancient Greece: Minoan        | Unknown                              | Fresco                            | Different people with different colors<br>Elongation of bull shows motion<br>Aquatic pattern on border<br>Connection to sea                                                                                                                                                                    |
-| Doryphoros (Spear Bearer) or *Canon*             | Classical Greece: Classical   | Polykleitos                          | Marble copy after bronze original | Called Canon because it's the standard of beauty for sculptures<br>Used golden ratio<br>Polykleitos was in the cult of pythagoreans<br>Contraposto - counter posture<br>Well preserved because of Pompeii<br>                                                                                  |
-| Dying Gaul                                       | Classical Greece: Hellenistic | Epigonos                             | Marble copy after bronze original | Representational hair<br>Objects on ground give sense of place<br>Shows blood and sweat<br>Doesn't portray a greek man (less jacked, less hot), shows a frenchman<br>Choker shows he's a gaul<br>Defeat: Broken sword, no attempt to call for help (horn), sitting on shield                   |
-| Aphrodite (Venus de Milo)                        | Classical Greece: Hellenstic  | Alexandros of Antioch-on-the-Meander | Marble                            | Individualized<br>Lot of detail compared to aphrodite of knidos<br>Dry drapery<br>Contrasting textures<br>Contraposto<br>Has musculature and feminine form<br>More intimate, sensual                                                                                                           |
-| Nike alighting on a warship (Nike of Samothrace) | Classical Greece: Hellenistic | Unknown                              | Marble                            | Rhodes probably had a successful naval victory<br>Where Nike got it's logo<br>Wet drapery, would have been in fountain<br>lot of contrasting texture<br>Dynamic<br>                                                                                                                            |
-| Pont-du-Gard                                     | Rome: Empire                  | Unknown                              | Shelly Limestone                  | Arches create space<br>Aquaduct helped city<br>columns aligned vertically<br>Ashlar Masonry<br>Used as major bridge<br>Use of Roman arch                                                                                                                                                       |
-| Portrait of Augustus as General                  | Rome: Empire                  | Unknown                              | Marble Copy, Bronze Original      | Three powers (ishtar gate):<br>- Curass - Military<br>- Toga - Wealth and political power<br>- Eros - Supernatural power<br>Harkening pose: asking for cooperation, contraposto<br>Idealized proportions<br>                                                                                   |
-| The Pantheon                                     | Roman: Empire                 | Patron: Hadrean                      | Concrete                          | First pantheon built out of wood, burned down<br>Rebuilt out of concrete<br>Originally built on a hill, now sunk by detrius of time<br>Monolithic columns from egypt in portico(front porch)<br>Had rosettes in ceiling squares<br>Biggest dome in the world<br>Squares and circles everywhere |
-| Arch of Titus                                    | Rome: Empire                  | Patron: Titus                        | Concrete faced with marble        | Commemorates when Rome defeats Jerusalem<br>Triumphal Arch <br>Depicts jewish temple being raided, money used to fund colosseum<br>Original historian was jewish (Josephus)                                                                                                                    |
-| Portrait of a Husband and Wife                   | Rome: Empire                  | Unknown                              | Fresco                            | His skin is darker<br>Preserved because of Pompeii<br>She's holding beeswax tablet and stylus<br>They're flexing literacy<br>Literacy was only for the rich<br>                                                                                                                                |
-|                                                  |                               |                                      |                                   |                                                                                                                                                                                                                                                                                                |
-
-| Term                       | Definition                                                                                           |
-| -------------------------- | ---------------------------------------------------------------------------------------------------- |
-| Faience                    | Metal Glaze, Colder                                                                                  |
-| Verism                     | Exaggerated age, wrinkles. Counterpart to hellenism but with emphasis on age instead of muscles      |
-| Chryselephantine           | Ivory veneer with gold                                                                               |
-| Archaizing                 | Make something look older in content and style - Fonseca Bust                                        |
-| Harkening Pose             | Asking for cooperatinon                                                                              |
-| Patron                     | Person that paid for it                                                                              |
-| Incrustacean               | Cut rock in half and flip to show vein - Pantheon                                                    |
-| Portico                    | Fancy front porch - Pantheon                                                                         |
-| Trumphal Arch              | Winning army walks through on return home                                                            |
-| Contraposto                | The Italian word for counter posture, natural stance, more weight on one foot, body makes an S shape |
-| Ungrounded                 | No historical record                                                                                 |
-| Doric                      | Masculine, beefy, the simplest, oldest style                                                         |
-| Ionic                      | Feminine, slender, medium old                                                                        |
-| Corinthian                 | Fancy top, planty shape around the base of the top, latest style                                     |
-| Corbelled Arch             | Rocks that go in gradually, like two wedges                                                          |
-| Post and Lintel            | Two posts and a lintel across the top                                                                |
-| Roman arch (with keystone) | Normal vault                                                                                         |
-| Groin vault                | 4 way intersection                                                                                   |
-|                            |                                                                                                      |

education/math/MATH1210 (calc 1)/Derivatives.md

@@ -1,4 +1,4 @@
-A derivative can be used to describe the rate of change at a single point, or the *instantaneous velocity*.
+SA derivative can be used to describe the rate of change at a single point, or the *instantaneous velocity*.
 
 The formula used to calculate the average rate of change looks like this:
 $$ \dfrac{f(b) - f(a)}{b - a} $$
@@ -14,6 +14,27 @@ If we have the coordinate pair $(a, f(a))$, and the value $h$ is the distance be
 - The slope of the *tangent line* or the *instantaneous velocity* can be found by taking the limit of the above function as the distance ($h$) approaches zero:
 $$\lim_{h \to 0}\dfrac{f(a + h) - f(a)}{h}$$
 The above formula can be used to find the *derivative*. This may also be referred to as the *instantaneous velocity*, or the *instantaneous rate of change*.
+
+## Examples
+
+> Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$ 
+
+1. $f(x) = 4\sqrt[3]{x} = \dfrac{1}{x^6}$
+2. $= 4x^\frac{1}{3} - x^{-6}$  
+3. $f'(x) = \dfrac{1}{3} * 4x^{-\frac{2}{3}} -(-6)(x^{-6-1})$ 
+4. $= 4x^{-2-\frac{2}{3}} + 6x^{-7}$
+5. $= \dfrac{4}{3\sqrt[3]{x^2}} + \dfrac{6}{x^7}$
+# Point Slope Formula (Review)
+$$  y - y_1 = m(x-x_1) $$
+Given that $m = f'(a)$ and that $(x_1, y_1) = (a, f(a))$, you get the equation:
+ $$ y - f(a) = f'(a)(x - a) $$
+As a more practical example, given an equation with a slope of $6$ at the point $(-2, -4)$:
+$$ y - (-4) = 6(x - -2)$$
+Solving for $y$ looks like this:
+1. $y + 4 = 6(x + 2)$
+2. $y = 6(x + 2) - 4$ 
+3. $y = 6x + 12 - 4$
+4. $y = 6x + 8$ 
 # Line Types
 ## Secant Line
 A **Secant Line** connects two points on a graph.
@@ -37,6 +58,15 @@ Given the equation $y = f(x)$, the following are all notations used to represent
 # Higher Order Derivatives
 - Take the derivative of a derivative
 
+# Constant Rule
+The derivative of a constant is always zero.
+$$ \dfrac{d}{dx}[c] = 0$$
+For example, the derivative of the equation $f(x) = 3$ is $0$. 
+# Derivative of $x$
+The derivative of $x$ is one.
+
+For example, the derivative of the equation $f(x) = x$ is $1$, and the derivative of the equation $f(x) = 3x$ is $3$. 
+
 # Exponential Derivative Formula
 Using the definition of a derivative to determine the derivative of $f(x) = x^n$, where $n$ is any natural number.
 
@@ -91,4 +121,93 @@ $$ \dfrac{d}{dx}(\dfrac{f(x)}{g(x)}) = \dfrac{f'(x)g(x) -f(x)g'(x)}{(g(x))^2}  $
 # Exponential Rule
 $$ \dfrac{d}{dx} e^x = e^x $$
 $$ \dfrac{d}{dx}a^x = a^x*(\ln(a)) $$
-for all $a > 0$
+for all $a > 0$
+
+
+# Logarithms
+
+For natural logarithms:
+$$ \dfrac{d}{dx} \ln |x| = \dfrac{1}{x} $$
+
+For other logarithms:
+$$ \dfrac{d}{dx} \log_a x = \dfrac{1}{(\ln a) x}$$
+When solving problems that make use of logarithms, consider making use of logarithmic properties to make life easier:
+$$ \ln(\dfrac{x}{y}) = \ln(x) - \ln(y) $$
+$$ \ln(a^b) = b\ln(a) $$
+## Logarithmic Differentiation
+This is used when you want to take the derivative of a function raised to a function ($f(x)^{g(x)})$
+
+1. $\dfrac{d}{dx} x^x$
+2. $y = x^x$
+3. Take the natural log of both sides: $\ln y = \ln x^x$
+4. $\ln(y) = x*\ln(x)$
+5. Use implicit differentiation: $\dfrac{d}{dx} \ln y = \dfrac{d}{dx} x \ln x$
+6. Solve for $\dfrac{dy}{dx}$: $\dfrac{1}{y} \dfrac{dy}{dx} = 1 * \ln x + x * \dfrac{1}{x}$ 
+7. $\dfrac{dy}{dx} = (\ln x + 1) * y$
+8. Referring back to step 2, $y = x^x$, so the final form is:
+9. $\dfrac{dy}{dx} = (\ln(x) + 1)x^x$
+
+### Examples
+> Find the derivative of $(7x + 2)^x$
+
+1. $\ln y = \ln((7x+2)^x)$
+2. $\ln y = x*\ln(7x + 2)$ 
+3. $\dfrac{dy}{dx} \dfrac{1}{y} =  \dfrac{7x}{7x + 2} * \ln(7x+2)$ 
+4. $\dfrac{dy}{dx} = (\dfrac{7x}{7x+2} * \ln(7x+2))(7x+2)^x$
+
+> Find the derivative of the function $y = (2x \sin x)^{3x}$
+
+5. $\ln y = \ln (3x \sin x)^{3x}$ 
+6. $\ln y = 3x * \ln(2x \sin x)$
+7. $\dfrac{d}{dx} \ln(y) = \dfrac{d}{dx} 3x(\ln 2 + \ln x + \ln(sinx))$ 
+8. $\dfrac{1}{y} \dfrac{dy}{dx} = 3(\ln 2 + \ln x + \ln(\sin(x))) + 3x (0 + \dfrac{1}{x} + \dfrac{1}{\sin x} * \cos x)$
+9. $\dfrac{dy}{dx} = (3\ln 2 + 3 \ln x + 3\ln \sin(x) + 3\ln(\sin(x) + 3x\cot(x))(2x\sin x)^{3x}$ 
+# Chain Rule
+$$ \dfrac{d}{dx} f(g(x)) = f'(g(x))*g'(x) $$
+## Examples
+> Given the function $(x^2+3)^4$, find the derivative.
+
+Using the chain rule, the above function might be described as $f(g(x))$, where $f(x) = x^4$, and $g(x) = x^2 + 3)$.
+10. First find the derivative of the outside function function ($f(x) = x^4$):
+$$ \dfrac{d}{dx} (x^2 +3)^4 = 4(g(x))^3 ...$$
+11. Multiply that by the derivative of the inside function, $g(x)$, or $x^2 + 3$. 
+$$ \dfrac{d}{dx} (x^2 + 3)^4 = 4(x^2 + 3)^3 * (2x)$$ 
+> Apply the chain rule to $x^4$
+
+If we treat the above as a function along the lines of $f(x) = (x)^4$, and $g(x) = x$, then the chain rule can be used like so:
+$$ 4(x)^3 * (1) $$
+# Trig Functions
+$$ \lim_{x \to 0} \dfrac{\sin x}{x} = 1 $$
+$$ \lim_{x \to 0} \dfrac{\cos x - 1}{x} = 0 $$
+## Sine
+$$ f'(x) = \lim_{h \to 0} \dfrac{\sin(x + h) - sin(x)}{h} $$
+Using the sum trig identity, $\sin(x + h)$ can be rewritten as $\sin x \cos h + \cos x \sin h$.
+
+This allows us to simplify, ultimately leading to:
+$$ \dfrac{d}{dx} \sin x = \cos x$$
+## Cosine
+$$ \dfrac{d}{dx} \cos x = -\sin x $$
+
+## Tangent
+$$ \dfrac{d}{dx} \tan x = \sec^2x $$
+## Secant
+$$ \dfrac{d}{dx} \sec x = \sec x * \tan x $$
+
+## Cosecant
+$$ \dfrac{d}{dx} \csc x = -\csc x \cot x $$
+## Cotangent
+$$ \dfrac{d}{dx} \cot x = -\csc^2 x $$
+## Arcsin
+$$ \dfrac{d}{dx}(\arcsin(x) = \dfrac{1}{\sqrt{1-x^2}}$$
+# Implicit Differentiation
+- There's a reason differentials are written like a fraction
+- $\dfrac{d}{dx} x^2 = \dfrac{d(x^2)}{dx}$, or, "the derivative of $x^2$ with respect to $x$"
+- $\dfrac{d}{dx} x = \dfrac{dx}{dx} = 1$ : The derivative of $x$ with respect to $x$ is one
+- $\dfrac{d}{dx} y = \dfrac{dy}{dx} = y'$ 
+- Given the equation $y = x^2$, $\dfrac{d}{dx} y = \dfrac{dy}{dx} = 2x$.
+
+Given these facts:
+12. Let $y$ be some function of $x$
+13. $\dfrac{d}{dx} x = 1$
+14. $\dfrac{d}{dx} y = \dfrac{dy}{dx}$
+

education/math/MATH1210 (calc 1)/Integrals.md

@@ -0,0 +1,229 @@
+# Antiderivatives
+An antiderivative is useful when you know the rate of change, and you want to find a point from that rate of change
+
+> A function $F$ is said to be an *antiderivative* of $f$ if $F'(x) = f(x)$ 
+## Notation
+The collection of all antiderivatives of a function $f$ is referred to as the *indefinite integral of $f$ with respect to $x$*, and is denoted by:
+$$ \int f(x) dx $$
+## Examples
+> Find the antiderivative of the function $y = x^2$
+
+1. We know that to find the derivative of the above function, you'd multiply by the exponent ($2$), and subtract 1 from the exponent.
+2. To perform this operation in reverse:
+	1. Add 1 to the exponent
+	2. Multiply by $\dfrac{1}{n + 1}$
+3. This gives us an antiderivative of $\dfrac{1}{3}x^3$ 
+4. To check our work, work backwards.
+5. The derivative of $\dfrac{1}{3}x^3$ is $\dfrac{1}{3} (3x^2)$
+6. $= \dfrac{3}{3} x^2$
+
+
+## Formulas
+
+| Differentiation Formula                               | Integration Formula                                      |
+| ----------------------------------------------------- | -------------------------------------------------------- |
+| $\dfrac{d}{dx} x^n = nx^{x-1}$                        | $\int x^n dx = \dfrac{1}{n+1}x^{n+1}+ C$ for $n \ne -1$  |
+| $\dfrac{d}{dx} kx = k$                                | $\int k \space dx = kx + C$                              |
+| $\dfrac{d}{dx} \ln \|x\| = \dfrac{1}{x}$              | <br>$\int \dfrac{1}{x}dx = \ln \|x\| + C$                |
+| $\dfrac{d}{dx} e^x = e^x$                             | <br>$\int e^x dx = e^x + C$                              |
+| $\dfrac{d}{dx} a^x = (\ln{a}) a^x$                    | $\int a^xdx = \ln \|x\| + C$                             |
+| $\dfrac{d}{dx} \sin x = \cos x$                       | $\int \cos(x) dx  = \sin (x) + C$                        |
+| $\dfrac{d}{dx} \cos x = -\sin x$                      | $\int \sin(x)dx = \sin x + C$                            |
+| $\dfrac{d}{dx} \tan{x} = \sec^2 x$                    | $\int \sec^2(x)dx = \tan(x) + C$                         |
+| $\dfrac{d}{dx} \sec x = \sec x \tan x$                | $\int sec^2(x) dx = \sec(x) + C$                         |
+| $\dfrac{d}{dx} \sin^{-1} x = \dfrac{1}{\sqrt{1-x^2}}$ | $\int \sec(x) \tan(x) dx = \sec x + C$                   |
+| $\dfrac{d}{dx} \tan^{-1} x = \dfrac{1}{1+x^2}$        | $\int \dfrac{1}{\sqrt{1+x^2}}dx = \tan^{-1}x + C$        |
+| $\dfrac{d}{dx} k f(x) = k f'(x)$                      | $\int k*f(x)dx = k\int f(x)dx$                           |
+| $\dfrac{d}{dx} f(x) \pm g(x) = f'(x) \pm g'(x)$       | $\int (f(x) \pm g(x))dx = \int f(x) dx \pm \int g(x) dx$ |
+# Area Under a Curve
+The area under the curve $y = f(x)$ can be approximated by the equation $\sum_{i = 1}^n f(\hat{x_i})\Delta x$ where $\hat{x_i}$ is any point on the interval $[x_{i - 1}, x_i]$, and the curve is divided into $n$ equal parts of width $\Delta x$
+
+Any sum of this form is referred to as a Reimann Sum.
+
+To summarize:
+- The area under a curve is equal to the sum of the area of $n$ rectangular subdivisions where each rectangle has a width of $\Delta x$ and a height of $f(x)$.
+# Definite Integrals
+Let $f$ be a continuous function on the interval $[a, b]$. Divide $[a, b]$ into $n$ equal parts of width $\Delta x = \dfrac{b - a}{n}$ . Let $x_0, x_1, x_2, \cdots, x_3$ be the endpoints of the subdivision.
+
+The definite integral of $f(x)$ with respect to $x$ from $x = a$ to $x = b$ can be denoted:
+$$ \int_{a}^b f(x) dx $$
+
+And __can__ be defined as:
+$$ \int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i = 1}^n f(x_i)\Delta x$$
+
+$f(x_i)$ is the *height* of each sub-interval, and $\Delta x$ is the change in the *x* interval, so $f(x_i) \Delta x$ is solving for the area of each sub-interval.
+
+- If your function is always positive, then the value of a definite integral is the area under the curve.
+- If the function is always negative, then the value of a definite integral is the area above the curve to zero.
+- If the function has both positive and negative values, the output is equal to the area above the curve minus the area below the curve.
+
+## Examples
+> Find the exact value of the integral $\int_0^1 5x \space dx$ 
+
+Relevant formulas:
+$$ \sum_{i = 1}^n = \dfrac{(n)(n + 1)}{2} $$
+$$ \Delta x = \dfrac{1 - 0}{n} = \dfrac{1}{n}$$$$ x_i = 0 + \Delta xi + \dfrac{1}{n} \cdot i$$
+1. $\int_0^1 5x \space dx = \lim_{n \to \infty} \sum_{i=1}^n 5(x_i) \cdot \Delta x$
+2. $= \lim_{n \to \infty} \sum_{i=1}^n 5(\frac{1}{n} \cdot i) \cdot \frac{1}{n}$ 
+3. $= \lim_{n \to \infty} \sum_{i = 1}^n \dfrac{5}{n^2}\cdot i$ 
+4. $= \lim_{n \to \infty} \dfrac{5}{n^2} \sum_{i = 1}^n i$
+5. $= \lim_{x \to \infty} \dfrac{5}{n^2} \cdot \dfrac{n(n + 1)}{2}$ 
+6. $= \lim_{n \to \infty} \dfrac{5n^2 + 5n}{2n^2}$
+7. $= \dfrac{5}{2}$ 
+
+# Properties of Integrals
+1. $\int_a^a f(x)dx = 0$ - An integral with a domain of zero will always evaluate to zero.
+2. $\int_b^a f(x)dx = -\int_a^b f(x) dx$  - The integral from $a \to b$ is equal to the integral from $-(b\to a)$ 
+3. $\int_a^b cf(x) dx = c \int_a^b f(x) dx$ - A constant from inside of an integral can be moved outside of an integral
+4. $\int_a^b f(x) \pm g(x) dx = \int_a^b f(x) dx \pm \int_a^b g(x)dx$  - Integrals can be distributed
+5. $\int_a^c f(x)dx = \int_a^b f(x)dx + \int_b^c f(x)dx$  - An integral can be split into two smaller integrals covering the same domain, added together.
+
+# Averages
+To find the average value of $f(x)$ on the interval $[a, b]$ is given by the formula:
+
+Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ 
+
+# The Fundamental Theorem of Calculus
+1. Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then:
+$$\int_a^b f(x) dx = F(b) - F(a)$$
+2. Let $f$ be a continuous function on $[a, b]$ and let $x$ be a point in $[a, b]$.
+$$ F(x) = \int_a^x f(t)dt \Rightarrow F'(x) = f(x) $$
+This basically says that cancelling out the derivative from $a$ to $x$ can be done by taking the derivative of that equation. with respect to $x$.
+$$ \dfrac{d}{dx} \int_a^{g(x)} f(t) dt = f(g(x)) * g'(x)* $$
+## Examples
+> Finding the derivative of an integral
+$$ \dfrac{d}{dx} \int_2^{7x} \cos(t^2) dt = cos((7x)^2) * 7 = 7\cos(49x^2)$$
+> Finding the derivative of an integral
+$$ \dfrac{d}{dx}\int_0^{\ln{x}}\tan(t) = \tan(\ln(x))*\dfrac{1}{x} $$
+> $x$ and $t$ notation *(note: the bar notation is referred to as "evaluated at")*
+$$ F(x) = \int_4^x 2t \space dt = t^2 \Big|_4^x  = x^2 - 16$$
+> $x$ in top and bottom
+$$ \dfrac{d}{dx} \int_{2x}^{3x} \sin(t) dt = \dfrac{d}{dx} -\cos(t)\Big|_{2x}^{3x} = \dfrac{d}{dx} (-\cos(3x) + cos(2x) = 3\sin(3x) - 2\sin(2x) $$
+
+# The Mean Value Theorem for Integrals
+If $f(x)$ is continuous over an interval $[a, b]$ then there is at least one point $c$ in the interval $[a, b]$ such that:
+$$f(c) = \dfrac{1}{b-a}\int_a^bf(x)dx $$
+This formula can also be stated as $\int_a^b f(x)dx = f(c)(b-a)$
+This theorem tells us that a continuous function on the closed interval will obtain its average for at least one point in the interval.
+
+# U-Substitution
+When you see $dx$ or $du$ in a function, it can be thought of as roughly analogous to $\Delta x$, where the change in $x$ is infinitesimally small.
+
+Thinking back to derivatives, when solving for $\dfrac{dy}{dx}$, you're solving for the rate of change of $y$ (across an infinitely small distance) over the rate of change of $x$ (across an infinitely small instance). Given that the *slope* of a line is described as $\dfrac{\text{rise}}{\text{run}}$, we know that $\dfrac{dy}{dx}$ describes the slope of a line at a particular point.
+## Formulas
+- $\int k {du} = ku + C$
+- $\int u^n du = \frac{1}{n+1}u^{n+1} + C$
+- $\int \frac{1}{u} du = \ln(|u|) + C$ 
+- $\int e^u du = e^u + C$
+- $\int \sin(u) du = -\cos(u) + C$
+- $\int \cos(u) du = \sin(u) + C$
+- $\int \dfrac{1}{\sqrt{a^2 - u^2}} du = \arcsin(\frac{u}{a}) +C$ 
+- $\int \dfrac{1}{a^2+u^2}du = \dfrac{1}{a} \arctan(\frac{u}{a}) + C$ 
+- $\int \dfrac{1}{u\sqrt{u^2 - a^2}} du = \dfrac{1}{a}arcsec(\dfrac{|u|}{a}) + C$  
+
+# Length of a Curve
+## Review of the Mean Value Theorem
+If $f$ is a continuous function on the interval $[a, b]$ and differentiable on $(a, b)$, then there exists a number $c$ in the interval $(a, b)$ such that:
+
+$$ f'(c) = \dfrac{f(b) - f(a)}{b - a} $$
+
+This also implies that for some $c$ in the interval $(a, b)$:
+$$ f(b) - f(a) = f'(c)(b-a) $$
+
+## Intuitive Approach
+Given that we divide a curve into $n$ sub-intervals, and we can find the location of the right endpoint of each interval.
+
+With a series of points on a curve we can find the distance between each point.
+
+As we increase $n$, the precision of which the curve is estimated increases.
+
+This means that:
+$$ \text{length of a curve} = \lim_{n \to \infty} \sum_{i=1}^{n}(\text{length of line segment)}$$
+Using the distance formula, we know that the length of the line segment can be found with:
+$$ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
+1. So the entire equation is:
+$$ \text{length of a curve} = \lim_{n \to \infty} \sum_{i=1}^{n}(\sqrt{(x_i - x_{i-1})^2 + (y_i - y_{i-1})^2}) $$
+	This can also be described as:
+$$ \text{length of a curve} = \lim_{n \to \infty} \sum_{i=1}^{n}(\sqrt{(\Delta x)^2 +(\Delta y)^2}) $$
+2. Using the mean value theorem:
+$$ \lim_{n \to \infty} \sum_{i = 1}^n\sqrt{\Delta x^2 + (f(x_i) - f(x_{i-1}))i^2} $$l
+$$ \lim_{n \to \infty} \sum_{i=1}^n \sqrt{\Delta x ^2 + (f'(x_{\hat{i}}))(x_i - x_{i-1})^2}$$
+3. Factoring out $\Delta x$
+$$ \lim_{n \to \infty} \sum_{i=1}^n \sqrt{\Delta x^2(1 + f'(x_{\hat{i}}))}$$
+4. Moving $\Delta x$ out of the root
+
+$$ \lim_{n \to \infty} \sum_{i=1}^n \sqrt{(1 + f'(x_{\hat{i}}))} \Delta x$$
+5. As an integral:
+$$ L =\int_a^b \sqrt{1 + f'(x)^2} dx$$
+## Examples
+> Find the length of the curve $y = -\frac{5}{12}x + \frac{7}{12}$ from the point $(-1, 1)$
+
+1. $L = \int_{-1}^8 \sqrt{1 + (-\frac{5}{12})^2} dx$ 
+2. $= \int_{-1}^8 \sqrt{1 + \frac{25}{144}} dx$ 
+3. = $\int_{-1}^8 \sqrt{\frac{169}{144}}dx$
+4. $= \int_{-1}^8 \frac{13}{12} dx$
+5. $\frac{13}{12} x \Big| _{-1}^8$
+
+> Find the distance from the point ${\frac{1}{2}, \frac{49}{48}}$ to the point $(5, \frac{314}{15})$ along the curve $y = \dfrac{x^4 - 3}{6x}$.
+> *note*: The complete evaluation of this problem is more work than typically required, and is only done for demonstration purposes.
+1. $y' = \dfrac{4x^3(6x) - (x^4 + 3)6}{36x^2}$: Find the derivative of the curve using the quotient rule
+2. $= \dfrac{18x^4 - 18}{36x^2}$: Simplify
+3. $= \dfrac{18(x^4 - 1)}{18(2x^2)}$: Factor out $18$
+4. $= \dfrac{x^4 - 1}{2x^2}$: Factor out $18$ again
+5. $L = \int_{1/2}^5 \sqrt{1 + (\dfrac{4x-1}{2x^2})^2}dx$ : Use the length formula
+6. $= \int_{1/2}^5 \sqrt{1 + \dfrac{x^8 - 2x^4 + 1}{x^4}} dx$: Apply the $^2$ 
+7. $= \int_{1/2}^5 \sqrt{\dfrac{4x^4 + x^8 -2x^4 + 1}{4x^4}}dx$: Set $1 = \dfrac{4x^4}{4x^4}$ and add
+8. $= \int_{1/2}^5 \sqrt{\dfrac{x^8 + 2x^4 + 1}{4x^4}}dx$: Factor the numerator
+9. $= \int_{1/2}^5 \sqrt{\dfrac{(4x+1)^2}{4x^4}}dx$ : Get rid of the square root
+10. = $\int_{1/2}^5 \dfrac{x^4 + 1}{2x^2}dx$: Move the constant $\frac{1}{2}$ outside of the integral
+11. $= \frac{1}{2}\int_{1/2}^5 \dfrac{x^4 + 1}{x^2}$: Rewrite to remove the fraction
+12. $= \frac{1}{2} \int_{1/2}^5 (x^4 + 1)(x^{-2})dx$: distribute
+13. $= \frac 1 2 \int_{1/2}^5 (x^2 - x^{-2})dx$: Find the indefinite integral
+14. $= \dfrac{1}{2} (\frac{1}{3}x^3 - x^-1)\Big|_{1/2}^5$ : Plug and chug
+15. $= (\frac{125}{6} - \frac{1}{10}) - (\frac{1}{48} - 1)$ 
+16. $=(\frac{5000}{240} - \frac{24}{240}) - (\frac{5}{240} - \frac{240}{240})$ 
+
+> Find the length of the curve $y = \sqrt{1 - x^2}$
+1. $y$ has a domain of $[-1, 1]$
+2. $y' = \dfrac{1}{2}(1-x^2)^{-1/2}(-2x)$
+3. $= -\dfrac{x}{\sqrt{1 - x^2}}$
+4. $L = \int_{-1}^1 \sqrt{1 + (-\dfrac{x}{\sqrt{1-x^2}})^2}dx$ 
+5. $L = \int_{-1}^1 \sqrt{1 + \dfrac{x^2}{1-x^2}}dx$ 
+6. $L = \int_{-1}^1 \sqrt{\dfrac{1}{1-x^2}}dx$ 
+7. $L = \int_{-1}^1 \dfrac{1}{\sqrt{1-x^2}}dx$ 
+8. $L = \arcsin(x) \Big|_{-1}^1$ 
+
+> Set up an integral to find the length of the curve $y = \sin(x)$ from the point $(0, 0)$ to the point $(2\pi, 0)$.
+
+1. $L = \int_0^{2\pi} \sqrt{1 + \cos^2{x}}dx$ :  The derivative of $\sin$ is $\cos$
+2. Plug into calculator
+
+# Area Between Curves
+If the area under the curve is found by approximating the space between the curve and the $x$ intercept, then the area *between* two curves can be found by approximating the space between the top curve and the bottom curve.
+
+Visualized as a set of rectangles, each rectangle would have a corner on the top curve, and a corner on the bottom curve, with a width of $\Delta x$.
+
+The height of the rectangle, or the distance between the curves at a given point can be found with the formula $f(x) - g(x)$ where $f(x) \ge g(x)$ 
+
+The Riemann Sum definition of the area between two curves is as follows:
+
+$$ \lim_{n \to \infty} \sum_{i = 1}^n (f(x_i)-g(x_i)\cdot \Delta x)$$
+- $i$ is the sub-interval
+- $x_i$ is the $x$ coordinate at a given sub-interval
+- $\Delta x$ is the width of each sub-interval.
+
+This sum can also be described as:
+$$ = \int_a^b(f(x)-g(x))dx $$
+
+Where the two lines intersect each other, you'll need to split the solution into a sum of integrals to ensure that $f(x) \ge g(x)$, by swapping the two.
+
+# Rotating a Solid Formed from a Rotation of a Plane Region
+Similar to finding the area between two curves, the volume can be found by approximating with rectangles.
+
+The area of each slice can be found by taking the area of the inner circle ($\pi r^2$) and subtracting it from the bigger circle ($\pi R ^2$). The area of a washer (or cylinder) can be found with $\text{base} * \text{height}$, and the height of each subsection is $\Delta x$. 
+
+The Riemann Sum definition is defined as follows:
+$$ \lim_{x \to \infty} \sum_{i = 1}^n ((\pi\cdot(f(x_i))^2-\pi\cdot(g(x_i))^2)\Delta x$$
+- $\Delta x$: The width of each section
+- $\pi * (f(x_i))^2$: The area of larger circle formed by $f(x_i)$
+- $\pi * (f(x_i))^2$: The area of smaller circle formed by $f(x_i)$

education/math/MATH1210 (calc 1)/Limits.md

@@ -77,5 +77,36 @@ Let $f$ be a continuous function on the interval $[a, b]$ and let $N$ be any num
 | Well behaved function | A function that is continuous, has a single value, and is defined everywhere. |
 
 
+# L'Hospital's Rule
+If you have a limit of the indeterminate form $\dfrac{0}{0}$, the limit can be found by taking the derivative of the numerator, divided by the derivative of the denominator.
+$$ \lim_{x \to 2} \dfrac{x-2}{x^2-4} = \lim_{x \to 2} \dfrac{1}{2x}$$
 
+L'Hospital's Rule can also be used when both the numerator and denominator approach some form of infinity.
+$$ \lim_{x \to \infty} \dfrac{x^2-2}{3x^2-4} = \lim_{x \to \infty} \dfrac{2x}{6x}$$
+The above problem can be solved more easily *without* L'Hospital's rule, the leading coefficients are 1/3, so the limit as $x$ approaches $\infty$ is 1/3.
+
+L'Hospital's rule **cannot** be used in any other circumstance. 
+
+## Examples
+1. $\lim_{x \to 0} \dfrac{7^x - 5^x}{2x}$
+2. $= \lim_{x \ to 0}\dfrac{7^x \ln(7) -5^x(\ln(5)}{2}$
+3. $= \dfrac{\ln(7) - \ln(5)}{2}$ 
+# Indeterminate form $(0 * \infty)$
+If the $\lim_{x \to a}f(x) = 0$  and $\lim_{x\to a} g(x) = \infty$ then $\lim_{x \to a}(f(x) * g(x)$ may or may not exist.
+
+To evaluate an indeterminate product ($0 * \infty$), use algebra to convert the product to an equivalent quotient and then use L'Hopsital's Rule.
+
+$$ \lim_{x \to 0^+} x\ln(x) = \lim_{x \to 0^+}\dfrac{\ln x}{\dfrac{1}{x}} = \lim_{x \to 0^+} \dfrac{1/x}{-1/(x^2)} = \lim_{x \to 0^+} -x = 0 $$
+# Indeterminate form $(\infty - \infty)$:
+If the $\lim_{x \to a}f(x) = \infty$  and $\lim_{x \to a} (g(x)) = \infty$ , then $\lim_{x \to a}(f(x) - g(x))$ may or may not exist.
+
+# Indeterminate Powers
+When considering the $\lim_{x \to a} f(x)^{g(x)}$, the following are indeterminate:
+- $0^0$
+- $\infty^0$
+- $1^\infty$ 
+
+1. $\lim_{x \to 0^+} x^x$ 
+2. $= \lim_{x \to 0} e^{\ln(x^x)}$ - wrap $e^{\ln{x}}$ around the function
+3. $= e^{\lim_{x \to 0} x \ln(x)}$ -use L'Hospital's rule
 

education/math/MATH1210 (calc 1)/Max and Min.md

@@ -0,0 +1,45 @@
+z# Maximum/Minimum
+A function $f$ has an *absolute maximum* at $c$ if $f(c) >= f(x)$. We call $f(c)$ the maximum value of $f$.
+The absolute **maximum** is the largest possible output value for a function.
+
+A function $f$ has an absolute minimum at $c$ if $f(c) <= f(x)$. $f(c)$ is the absolute minimum value of $f$.
+The absolute **minimum** is the smallest possible output value for a function.
+
+- Where the derivative of a function is zero, there is either a peak or a trough.
+
+# Critical Numbers
+A number is considered critical if the output of a function exists and $\dfrac{d}{dx}$ is zero or undefined.
+
+# Local Max/Min
+A local max/min is a peak or trough at any point along the graph.
+
+# Extreme Value Theorem
+If $f$ is a continuous function in a closed interval $[a, b]$, then $f$ achieves both an absolute maximum and an absolute minimum in $[a, b]$. Furthermore, the absolute extrema occur at $a$ or at $b$ or at a critical number between $a$ and $b$.
+
+## Examples
+> Find the absolute maximum and absolute minimum of the function $f(x) = x^2 -3x + 2$ on the closed interval $[0, 2]$:
+
+1. $x=0$ and $x=2$ are both critical numbers because they are endpoints. Endpoints are *always* critical numbers because $\dfrac{d}{dx}$ is undefined.
+2. $\dfrac{d}{dx} x^2 -3x + 2 = 2x -3$
+3. Setting the derivative to zero, $0 = 2x - 3$
+4. Solving for x, we get $x = \dfrac{3}{2}$. Three halves is a critical number because $f'(\dfrac{3}{2})$ is $0$. 
+5. Now check the outputs for all critical numbers ($f(x)$ at $x = \{0, 2, \dfrac{3}{2}\}$)
+6. $f(0) = 0^2 -3(0) + 2 = 2$
+7. $f(2) = 2^2 - 3(2) + 2) = 0$
+8. $f(\dfrac{3}{2}) = (\dfrac{3}{2})^2 - 3(\dfrac{3}{2}) + 2 = -\dfrac{1}{4}$
+9. The minimum is the lowest of the three, so it's $-\dfrac{1}{4}$ and it occurs at $x = \dfrac{3}{2}$ 
+10. The maximum is the highest of the three, so it's $2$ at $x = 0$.
+
+
+> Find the absolute maximum and absolute minimum of the function $h(x) = x + 2cos(x)$ on the closed interval $[0, \pi]$.
+
+ 1. $x = 0$ and $x = \pi$ are both critical numbers because they are endpoints. Endpoints are critical because $\dfrac{d}{dx}$ is undefined.
+ 2. $\dfrac{d}{dx} x + 2\cos(x) = 1 - 2sin(x)$ 
+ 3. Setting that to zero, we get $0 = 1 - 2\sin(x)$
+ 4. $\sin(x) = \dfrac{1}{2}$ 
+ 5. In the interval $[0, \pi]$, $\sin(x)$ has a value of $\dfrac{1}{2}$ in two places: $x = \dfrac{\pi}{6}$ and $x = \dfrac{5\pi}{6}$. These are both critical numbers because they are points where $\dfrac{d}{dx}$ is zero.
+ 6. Now we plug these values into the original function:
+ 7. $h(0) = 0 + 2\cos 0 = 2$
+ 8. $h(\pi) = \pi + 2\cos(\pi) = \pi - 2 \approx 1.14159$
+ 9. $h(\dfrac{\pi}{6}) = \dfrac{\pi}{6} + 2\cos(\dfrac{\pi}{6}) = \dfrac{\pi}{6} + 2(\dfrac{\sqrt{3}}{2} = \dfrac{\pi}{6} + \sqrt{3} \approx 2.2556$ 
+ 10. $h(\dfrac{5\pi}{6}) = \dfrac{5\pi}{6} + 2\cos(\dfrac{5\pi}{6}) = \dfrac{5\pi}{6} - \sqrt{3} \approx 0.88594$

education/music/Liszt's 6 etudes de Paganini.md

@@ -1,55 +0,0 @@
-# Work
-## Historical, Superficial
-Franz Liszt was a huge fan of Paganini because of his incredible skill, and the technicality of his music. This led him to set out and compose a set of etudes[^1] inspired from Paganini's works. He originally released them in 1838 as the "Études d'exécution transcendante d'après Paganini", then revised them in 1851, dedicating the later revision to Clara Schumann[^2]. He made this revision because the first versions were so absurdly difficult that they were considered impossible to play by many. Even after the revision, many consider these some of the most technically demanding works in piano literature. 
-
-[^1]: Literally translating to "study", an etude is a short song usually meant to help practice a particular technique
-[^2]: Wife of Robert Schumann, Clara Schumann was an accomplished pianist and composer. 
-## Analysis
-
-### Questions
-> What did the composer have in mind?
-
-> What is the general mood?
-The music is generally pretty dramatic and intense, although there are some slower, gentler sections.
-
-> What might it mean?
-
-> What parts do you most like?
-I really like 
-> What parts do you least like?
-
-> What style is it?
-
-> How do you know?
-
-> What medium is it
-
-> What texture
-
-# Composer
-## History
-Liszt fell very ill, to the extent that an obituary notice was printed in a Paris newspaper, and he underwent a long period of religious doubts and pessimism.
-- guitar face for pianos
-## Last Name
-https://german.stackexchange.com/questions/67786/is-liszt-really-pronounced-like-the-english-word-list
-TODO
-
-## Freakishly Large Hands
-His hands weren't as large as Rachmaninoff, but they had effectively no connective tissues at the base of each finger
-
-# Notes during production
-- was going to include a pic of a cast of his hands, but it's pretty manky
-- can you imagine the crushing disappointment 
-
-# Links
-https://en.wikipedia.org/wiki/Franz_Liszt
-
-https://en.wikipedia.org/wiki/Grandes_%C3%A9tudes_de_Paganini
-
-https://imslp.org/wiki/Grandes_%C3%A9tudes_de_Paganini,_S.141_(Liszt,_Franz)
-
-https://researchrepository.wvu.edu/cgi/viewcontent.cgi?article=6402&context=etd
-
-https://lisztmuseum.hu/permanent_exhibition/dining-room-120755
-
-https://www.pianostreet.com/smf/index.php?topic=65517.0

education/political science/Donald Trump Campaign.md

@@ -1,25 +0,0 @@
-# Campaign Points
-https://www.donaldjtrump.com/issues
-## Economic
-### Data
-Trump's published economic policy points include reducing taxes for the middle class, increasing the child tax credit, and attempting to increase job opportunities by "slashing job-killing regulations". His campaign website argues that he increased "real wages" and household income, while poverty went down during his time in office. He promises to lower taxes, increase paychecks, and increase job opportunities. 
-### Analysis
-## Budgetary
-## Social
-
-## Foreign Policy
-Trump's campaign website argues that we cannot have free and open trade when some other countries are exploitative of it. He primarily focuses on changes he made during his time in office, including stopping the Trans-Pacific Partnership, replacing NAFTA with USMCA, and talks about fixing "unfair" foreign trade policies, and implementing tariffs. For his 2024 campaign, he promises to reduce reliance on China, specifically in the medical, security, and infrastructure industries. 
-
-Trump's campaign website also argues that he will secure the \[southern] border. 
-
-## Gun Control
-
-## Energy/Environmental
-Trump's campaign website argues that during his time in office, the United States became the number one producer of oil and natural gas by approving the Keystone and Dakota Access pipelines, opening federal lands and offshore areas for production, and ending the Paris Climate Accord. For his future policies, he argues that he can bring energy independence, lower the prices of various energy sources, and eliminate the Green New Deal. 
-
-# Personal
-
-# Arguments against Biden
-- Campaign website argues that Biden decreases job opportunities and increases inflation with government spending. 
-- Campaign website argues that Biden ended the "Trump Energy Revolution" and is helping foreign adversaries. 
-- Campaign website argues that Biden "turned our country into a giant sanctuary for dangerous alien criminals"

education/political science/Hazelwood v Kuhlmeier.md

@@ -1,8 +0,0 @@
-https://www.uscourts.gov/educational-resources/educational-activities/facts-and-case-summary-hazelwood-v-kuhlmeier
-https://www.oyez.org/cases/1987/86-836
-- The case was over the constitutional right to freedom of the press, and whether or not the school had a right to censor a school paper.
-- Students at hazelwood east high school wrote articles in the school newspaper about teen pregnancy, and the impact of divorce. 
-- When the articles were published in a school sponsored newspaper, the principal deleted the pages that contained the stories prior to publication without telling the students. 
-- The students took their case to a District Court in St. Louis, and the trial court ruled that the school had the authority to remove those articles.
-- The students then appealed the Court of Appeals for the Eighth Circuit, and it reversed the lower court, and found that the paper was a "public forum", and that school officials could only censor content under extreme circumstances.
-- In a 5-3 ruling, the Supreme Court held that the principal's actions did not volate the students' free speech. The Court noted that the paper was sponsored by the school, and that it had legitimate interest in preventing the publication of articles it deemed inappropriate. They ruled that the school paper was not a public forum, it was a limited forum that served as a learning exercise for journalism students.

education/political science/Think Again.md

@@ -1,34 +0,0 @@
-Notes on Think Again, by Adam Grant. 
-## Chapter 3
-### Main idea
-- People build more developed belief systems and improve if they are willing to challenge their beliefs.
-- It's unhealthy to hold beliefs and defend them so aggressively
-- Being wrong and recognizing that is healthy
-- Recognize when a reaction is emotional, and a defense of the ego, rather than intellectual, and a defense of the idea.
-- Do not base a personality around ideas, base it around broad, positive values. The material changes, but values can be applied to the material in infinite ways.
-### Personal reflection
-> Think about yourself personally, which group would you be more likely to identify with: the group who hated being challenged, or the group who thought that the abusive challenges were fun? Explain your POV.
-
-I believe I do not fit into either group, and would react differently in many different ways, depending on the context at hand. For a long time, I would defend my beliefs aggressively, and was confident that my perspective was more correct. I made no attempt at attempting to understand the motivations behind the opposing viewpoint, and spent most of my time taking an axe to nuance, working to prove the opposing viewpoint wrong, rather than trying to understand it, and look for the flaws in my own viewpoint. I believe I am getting better at understanding opposing viewpoints, but would still find the experience unpleasant, and react poorly. 
-
-### Relation to poli sci
-The political system in the United States is composed primarily of a two party system. If a candidate wishes to have any chance of being elected, they must appeal to one of the two parties. If a candidate doesn't align closely enough to the beliefs of the party, then they have a significantly worse chance of winning. Anyone who attempts to question ideas, may be considered a 'fake' republican | democrat. Each party conforms to a stringent beliefs system, and many of the viewpoints are held, simply because they're the opposite of the other party. This whole system discourages reflection and improvement, holding on to ideas that stagnate and grow convoluted, holding bitterly onto one 'correct' viewpoint. 
-
-### Quotes
-"Values are your core principles in life - they might be excellence and generosity, freedom and fairness, or security and integrity. Basing your identity on these kinds of principles enables you to remain open minded about the best ways to advance them" (Grant 64).
-
-"When they define themselves by values rather than opinions, they buy themselves the flexibility to update their practices in light of new evidence" (Grant 64).
-
-"When I asked him about how he stays in that mode, he said he refuses to let his ideas become part of his identity" (Grant 62).
-
-"Attachment. That's what keeps us from recognizing when our opinions are off the mark and rethinking them. To unlock the joy of being wrong, we need to detach" (Grant 62).
-
-"When a core belief is questioned, though, we tend to shut down rather than open up" (Grant 59).
-
-"If you want to be a better forecaster today, it helps to let go of your commitment to the opinions you held yesterday" (Grant 69).
-
-### Reaction
-I belief Grant phrased a key issue really elegantly, and believe that more people should try to apply his advice in their life
-
-### Was this info new?
-The idea isn't new to me.

education/unmanned aerial system/Radio Communications Procedures (ch 6).md

@@ -1,2 +0,0 @@
-pay attention when flying around an airport
-

education/unmanned aerial system/final.md

@@ -1,43 +0,0 @@
-There is currently no way to get a waiver for beyond line of sight \[for package delivery].
-
-To determine if an MOA is active, you can refer to the phone number listed under the legend for special use airspace. This information is not listed under the military operations directory
-
-An sUAS accident must be reported to the FAA within 10 days.
-
-Lightning is considered the most hazardous condition when flying in the vicinity of thunderstorms.
-
-The presence of ice pellets at the surface is evidence of a temperature inversion, with freezing rain at a higher altitude.
-
-Angle of attack is the angle between the wing chord line and the relative wind.
-
-An autonomous operation requires a Remote PIC, and nothing else.
-
-An increase in load factor will cause an unmanned aircraft to stall at a higher airspeed. 
-
-Acute fatigue is short term fatigue gained from a specific event
-
-METARs report wind in true north.
-
-The angle of attack at which an airfoil stalls is not influenced by gross weight.
-
-Military training routes below 1,500 feet have a 4 digit number, routes above have 3 digits. 
-
-Someone with a marijuana conviction can apply for a remote pilot certificate one year after the conviction. 
-
-Use a spectral analyzer to avoid interference with the radio
-
-After landing at a tower controlled airport, a pilot should contact ground control when advised by the tower.
-
-Lines of longitude cross the equator at right angles.
-
-The pilot's handbook of aeronautical knowledge should be consulted for the impact of drugs and alcohol on flight.
-
-When flight efficiency is a priority, the drone should be operated
-
-Advection fog develops when an air mass moves inland from the coast in winter.
-
-Binoculars do not count as line of sight
-
-Consult the  Pilot's Operating Handbook or UAS Flight Manual for center of gravity limits.
-
-The amount of excess load that can be imposed upon the wing of an airplane depends on the speed of the airplane

notes/3D printing/Filament.md

@@ -0,0 +1,279 @@
+https://www.youtube.com/watch?v=weeG9yOp3i4
+
+# PLA (Polylactic acid)
+| Pros                                                                                                                                 | Cons                                                                                                                                                  |
+| ------------------------------------------------------------------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------------------------------------------------------------- |
+| - Easy to print<br>- Very cheap<br>- Widely available<br>- Prints quickly<br>- Prints well<br>- Stiffest non-composite thermoplastic | - Can permanently deform with consistent load application<br>- Not UV resistant<br>- Warps under heat<br>- Shatters<br>- Difficult to sand/glue/paint |
+## Variants
+### Silk PLA
+Silk PLA has an additive to make prints shinier. This weakens the print, but it makes supports easier to remove. When silk PLA heats up, it puffs up and this can damage the extruder. 
+
+Silk PLA trades performance for aesthetics and can damage both a Bambu AMS and a Prusa MMU.
+
+### PLA-CF (Carbon Fiber PLA)
+Carbon fiber PLA is made by adding chopped or ground PLA to the filament. It does not typically improve the strength of prints, but it stabilizes the filament as it cools (preventing warping and shrinkage), and it can improve detail. 
+
+The addition of carbon fiber makes the end product stiffer, but more brittle. PLA-CF is one of the best filaments for detail oriented printing. It's overall a better filament than PLA, with the only drawbacks being a hardened steel nozzle requirement, and lack of color options. 
+
+### Metal-filled PLA
+Metal filled PLA is made by adding metal shavings to the filament during production. This makes the print heavier and infuses the print with some of the properties of the metal added. Copper infused filament can gain a patina, stainless steel infused filament can be polished, iron is magnetic, et cetera et cetera.
+
+The addition of metal particulate reduces the strength of the print and makes it more brittle. Metal-filled PLA is extremely expensive, difficult to print with, and anything that can be achieved with metal-filled PLA can also be achieved using paint, inserts, or some form of electroplating.
+
+### Wood-filled PLA
+Wood-filled PLA is  comprised of sawdust, and PLA. Cheap wood-filled PLA looks brown and has no particular wood-like qualities, but higher quality WF-PLA has visible chips of wood. This impacts the print by giving it a wood-like texture and allowing you to use varnish on the print.
+
+WF-PLA is difficult to print with, it easily absorbs humidity and sputters from the nozzle. The resulting product is also weaker.
+
+### PLA Alloys
+This category of PLA is created by combining PLA with another plastic additive to change the properties of the resulting filament in some way.
+
+There are 3 primary categories of PLA alloys:
+1. "Tough" PLA
+Tough PLA is created by combining PLA with polybutylene terephthalate, or PBT. PBT is commonly used in keycaps for keyboards.
+
+Tough PLA prints and acts similarly to PLA, but it has higher temp and impact resistance, and it's less brittle. This is largely an upgrade to PLA with no real drawbacks.
+
+2. "Matte" PLA
+Matte PLA is created by combining PLA with a plant based additive.
+
+Matte PLA has a higher impact and shatter resistance than regular PLA, but it absorbs humidity more easily and is more likely to jam in an extruder during printing. This is largely a side-grade to regular PLA, it makes a slightly different set of tradeoffs.
+3. "High speed" PLA
+High speed PLA has a lower melting temperature and a reduced viscosity, greatly increasing the speed at which it can be printed at.
+
+# PCL (Polycaprolactone)
+PCL has an extremely low melting point, printing at just 100 Celsius. The melting point is so low that you can shape it in a warm bath, or with a hair dryer.
+
+It has a warm waxy consistency that no adhesive will stick to.
+
+# PETG/PET-G (Polyethylene terephthalate-glycol)
+
+| Pros                                                                                                                       | Cons                                                                                                                                        |
+| -------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------- |
+| - Tougher<br>- Better temperature resistance<br>- Highly transparent<br>- Very low coefficient of friction.<br>- Food safe | - Slightly more difficult to print than PLA<br>- Struggles with overhangs<br>- Struggles with support removal<br>- High humidity absorption |
+## Variants
+### PETG-CF (Carbon Fiber PETG)
+Carbon fiber stabilizes molten filament, and given that PETG struggles with overhangs, PETG-CF has massively improved print support quality, along with improved stiffness. 
+
+The combination of matte carbon fiber with shiny polyester tends to create a very unique, aesthetically pleasing finish.
+
+# PCTG (Polycyclohexylenedimethylene Pthalate-Glycol)
+PCTG is a newer, better, alternative to PETG, compared to PETG:
+
+| Pros                                                                                                                 | Cons                                                                        |
+| -------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------- |
+| - Higher toughness<br>- Lower water retension<br>- Very little warping or sagging<br>- Almost perfect layer adhesion | - Supports are difficult to remove<br>- Expensive<br>- Not widely available |
+# PET (Polyethylene Terephthalate)
+PET is the foundation of PET-G, but without the addition of glycol as a plasticizer. Compared to PETG:
+
+| Pros                                                                                                                                                 | Cons                                                                                            |
+| ---------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------- |
+| - Stiffer<br>- Tougher<br>- Shinier<br>- Very high temp resistance<br>- Easier to print than other engineering filaments like nylon or polycarbonate | - Extremely high print temp (275C minimum)<br>- Struggles with humidity, overhangs, and warping |
+## Variants
+### PET-CF (Carbon Fiber PET)
+- Almost as easy to print as PETG
+- Extremely stiff
+- Hard to find, expensive
+
+# PVB (Polyvinyl Butyrate)
+- Printing qualities similar to PLA
+- Behaves similar to PETG, weaker but more flexible
+- When exposed to isopropanol alcohol, the layers melt and fuse together, resulting in a very glossy, seamless finish.
+
+# ABS (Acrylonitrile Butadiene Styrene)
+- Very common in consumer injection-molded parts.
+
+| Pros                                                                                                                                                                                                             | Cons                                                                         |
+| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------- |
+| - Melts in acetone, acetone vapor smoothing can be used to improve surface finish<br>- Prints fairly quickly<br>- Very high toughness relative to PLA or PETG<br>- High temperature resistance<br>- UV resistant | - Very high warpage<br>- Smells horrid and outputs toxic fumes when printing |
+# ASA (Acrylonitrile Styrene Acrylate)
+Chemically similar to ABS, just better.
+
+| Pros                                                                                                                                                                   | Cons                                                               |
+| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------ |
+| - Very high temp resistance (past 100C)<br>- Very high UV resistance<br>- Matte surface finish<br>- Prints *very quickly*<br>- Greatly reduced warping compared to ABS | - Equally bad fumes as ABS<br>- Still somewhat difficult to print. |
+# HIPS (High Impact Polystyrene)
+Similar to ABS, but softer, waxier, and more flexible. 
+
+Has a very low density, works well for wearables and props. HIPS is commonly used as a support material for ASA or ABS because limonene will dissolve HIPS but does not impact other plastics in the styrene family (ABS, ASA).
+
+# Nylon
+Nylon filaments are engineering filaments. They're difficult to print but have excellent mechanical properties.
+
+## Variants
+### PA-6
+| Pros                                                                                                                                     | Cons                                                                                                                                               |
+| ---------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------- |
+| - Extremely strong<br>- Excellent layer bonds<br>- High flexibility<br>- Very high temp resistance<br>- Very low coefficient of friction | - Horrible to print<br>- Very high moisture retention<br>- Can't be too dry<br>- Very high warpage<br>- Requires a closed (ideally heated) chamber |
+### PA-12
+- Higher warpage than PA-6
+- Higher toughness
+- Higher temp resistance
+- Durable but brittle
+### PA-CF (Carbon Fiber Nylon)
+- Very stiff
+- Less warping
+- High friction
+- High end printer required
+
+### PA-GF (Glass Filled Nylon)
+- Used in the real world (handguns, chainsaws)
+- More affordable than PA-CF
+- Much stiffer, tougher, and more resistant to heat and abrasion than vanilla nylon.
+- Greatly reduced warping
+- Fairly easy to print
+- Still requires a high-end printer (tungsten carbide or gemstone nozzle, abrasion resistant drive gears)
+- Durable enough to act as a viable alternative to machined aluminum
+
+### PA-PETG (Nylon PET alloy)
+Often called tough PETG or low temp nylon, PA-PETG is meant to serve as both a step up from PETG and a more accessible nylon alternative.
+- Bad warping, poor bed adhesion
+- Often just better to use nylon *or* PETG
+
+# Polycarbonate (PC)
+- In the real world, polycarbonate is used to make bulletproof glass. While FDM polycarbonate is not bulletproof, many of the properties of polycarbonate still apply. 
+
+| Pros                                                                                                                        | Cons                                                                               |
+| --------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------- |
+| - One of the toughest, stiffest filaments<br>- Extremely high temp resistance<br>- Does not shatter<br>- Highly transparent | - Extremely high moisture retention<br>- Prints above 300C<br>- Difficult to print |
+## Variants
+### PC-CF (Carbon Fiber Polycarbonate)
+- Record setting stiffness, prints can withstand hundreds of kilos
+- Will destroy most drive motors
+- Surprisingly cheap (~60USD/kilo at the time of writing)
+  
+### PC-PBT (PBT Infused Polycarbonate)
+PBT flaccifies the polycarbonate but preserves PC's strength and shatter resistance in the cold, making it one of the few cold-resistant filaments. 
+- Lower print temp
+- Improved print quality
+- Very low warping
+- One of the easiest filaments to print in
+  
+### PMMA (Polymethylmethacrylate)
+Also known as acrylic plexiglass, the high transparency of PMMA is the only advantage it has over other polycarbonates for printing.
+
+| Pros                                                                                                                                         | Cons                                                                                                                                                                                                          |
+| -------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| - Highest transparency thermoplastic<br>- Can be buffed to a frosted/polished surface<br>- High UV resistance<br>- Relatively affordable<br> | - Horrible bed adhesion<br>- Bad layer adhesion<br>- High coefficient of thermal expansion leads to constant print failures during or after the printing process<br>- Very brittle<br>- High water absorption |
+# TPU (Thermoplastic Polyurethane)
+TPU is the most common flexible filament
+
+| Pros                                                                                                                      | Cons                                                                                                                    |
+| ------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------- |
+| - Flexibility<br>- Cheap<br>- Wide range of colors and hardnesses<br>- Perfect layer adhesion<br>- Basically shatterproof | - Permanently bonds to most build plates (use gluestick)<br>- Very high water absorption, needs to be dry to print well |
+## Variants
+### TPU (~99D)
+- Harder than a skateboard wheel
+- Basically rigid
+- Useful because it's "shatterproof"
+- Often used for combat gear or robotic applications
+- Easiest TPU variant to print
+
+### TPU (~80D)
+- About as hard as the sole of a running shoe
+- Good for things like bumpers or hinges
+- Still fairly easy to print
+### TPU (~80A)
+- Very soft
+- Prints at very low speed, can wrap itself around the drive gears
+
+# TPE (Thermoplastic Elastomer)
+
+| Pros                     | Cons                               |
+| ------------------------ | ---------------------------------- |
+| - Flexible<br>- Stretchy | - **Very** difficult to print with |
+# SEBS (Styrene Ethylene Butterine Styrene)
+TPE enhanced with the same chemicals used to make ABS.
+
+| Pros                                                       | Cons                                                                                                                                    |
+| ---------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------- |
+| - Prints much better than TPE<br>- Very flexible and tough | - Very hygroscopic<br>- Styrene fumes released during printing<br>- Softens at a very low temp<br>- Still requires some level of tuning |
+# PP (Polypropylene)
+- Very bendable
+- Very rugged
+- Perfect layer adhesion
+- Very low density
+- Horrible bed adhesion
+- High warping
+- Supports are impossible to remove
+## Variants
+### PP-GF (Glass-filled PP)
+- Standard for industrial machinery
+- More difficult to print than regular PP
+- One of the toughest, most durable filaments
+- Very lightweight
+# OBC (Olefin Block Copolymer)
+- Fairly new for 3D printing
+- Attempts to combine the good qualities of PP and PET-G
+- Very low bed adhesion
+- Very expensive
+- Typically requires printing on a purpose made printer
+
+# HDPE (High Density Polyethylene)
+- Most bottles and jugs use this filament
+- Horrible to print in every way
+- Useful for purging the nozzle when switching between high and low temp filaments
+
+# POM (Polyoxylmethylene)
+POM is most commonly used when CNCing plastic.
+- It's cheap and very easy to print, with a low coefficient of friction.
+- Zero bed adhesion
+- Very poor layer adhesion
+- When it overheats, it turns into formaldehyde
+
+# PVDF (Polyvinylidene Flouride)
+- A chemical cousin of teflon
+- As easy to print as PET-G
+- Extremely tough
+- High heat/friction resistance
+- Hydrophobic
+- Most important because of its chemical resistance.
+- Fairly expensive
+- When mildly overheated, turns into horribly toxic chemicals (carbon monoxide, hydrogen cyanide, hydrofluoric acid, even more)
+
+# PEEK (Poly-ether Ether Ketone)
+- Mechanical properties massively beyond other plastics
+- Close to steel
+- Twice as tough as the toughest polycarbonate
+- Used in missiles and is fireproof
+- $700 a kilo (at the time of writing)
+- Prints at 400C
+- Requires a 140C heated chamber
+- Extremely high water retention
+- Special bed adhesive required
+- Difficult to print
+
+# PEKK (Polyether Ketone Ketone)
+Same building blocks as PEEK, in different levels
+- Worse than PEEK mechanically, still far beyond other filaments
+- Much easier to print compared to PEEK
+
+# PPS (Polyphenylene Sulphide)
+- Most chemically resilient filament
+- $200/kilo
+
+# PSU (Polysulphone)
+- Weakest superpolymer 
+- Mechanical properties similar to PA6 nylon
+- Very high glass transition temperature (187C)
+
+# Additive Superpolymers
+As a general rule, these (CF-PEEK, et cetera), are all extremely difficult to print and put a ton of strain on the printer. They *do* warp less than the vanilla counterparts.
+
+# PEI (Polyetherimide)
+- Used to coat print beds
+- Sold in two grades, 1010 and 9085 (9085 is horrible and shouldn't be used)
+- $400/kilo
+- Second strongest filament after PEEK
+- Glass transition temp at 217C
+- Electrically/chemically/radiation resistant
+- Prints at 425C nozzle/160C bed
+- Needs a special bed
+- Relatively friendly to print once equipment requirements are met
+
+# TPI (Thermoplastic Polyamide)
+- Kapton tape, in a filament
+- Glass transition temp above 250C
+- Most heat-proof filament
+- Mechanical properties about 25% worse than PEEK
+- Printing is basically impossible

notes/ANS Theory.md

@@ -1,8 +1,8 @@
 <https://arxiv.org/abs/1311.2540>
 
-In standard numeral systems, different digits are treated as containing the same amount of information. A 7 stores the same amount of info as a 9, which stores the same amount of info as a 1. 
+In standard numeral systems, different digits are treated as containing the same amount of information. A 7 is stored using the same amount of info as a 9, which is stored using the same amount of info as a 1, that is, 1 digit. 
 
-This makes the amount of information a single digit stores *uniform* across all digits. However, that's far from the most efficient way to represent most datasets. 
+This makes the amount of information a single digit stores *uniform* across all digits. However, that's far from the most efficient way to represent most datasets, because real world data rarely follows a uniform distribution.
 
 ANS theory is based around the idea that digits that occur more often can be stored in a way that requires less information, and digits that occur less often can be stored using more information.
 
@@ -12,4 +12,38 @@ Taking a look at the standard binary numeral system, there are two digits in the
 
 Given that $x$ represents a natural number, and $s$ is the digit we're adding. In a standard binary system, adding $s$ to the least significant position means that in the new number $x$ (before the addition) now represents the Nth appearance of an even (when $s = 0$ ), or odd (when $s = 1$). With ANS, the goal is is to make that asymmetrical, so that you can represent more common values with a denser representation.
 
+# Arithmetic Coding
+Arithmetic coding works by taking a stream of data, and converting it into an infinitely precise number between $0.00$, and $1.00$. This is based off of the idea that the sum of the probability of all events happening will always amount to $100\%$. 
 
+For example, the probability of a coin flip resulting in tails is 50%, and the probability of a coin flip resulting in heads is 50%. The probability of a coin flip resulting in heads *or* tails is %100.
+
+If we wanted to keep track of the result of a series of coin flips, this could be done by subdividing a range. If the coin flip is between $0$ and $0.5$, then we know that the first flip must have been tails.
+
+If the coin flip is between $0.5$ and $1$, then we know that the first flip must have been heads.
+
+This subdivision process can be repeated infinitely to store an infinite number of coin flips by dividing each range again.
+
+To store two coin flips, you might have the first subdivision represent the outcome of the first coin flip, and the second subdivision represent the outcome of the second coin flip:
+
+| Range         | Result       |
+| ------------- | ------------ |
+| $0.00 - 0.25$ | Tails, Tails |
+| $0.25 - 0.5$  | Tails, Heads |
+| $0.50 - 0.75$ | Heads, Tails |
+| $0.75 - 1.00$ | Heads, Heads |
+Imagine a situation where we want to store all possible outcomes of three consecutive coin flips using a decimal number,  *Heads, Heads, Tails*. 
+Encoding this would happen as follows:
+1. First we subdivide the range by the probability of each event happening. The probability of each is 50%, so that's simple. Referring above, we know that heads is represented by the top half of the range, and tails is represented by the bottom half of the range.
+> Because the *first* coin flip resulted in *Heads*, the output value must be between $0.50$ and $1.00$. 
+2. Subdividing the range $0.50$ and $1.00$ again to store the results of the second flip, we end up with values between $0.50$ and $0.75$ representing the sequence *Heads, Tails*, and values between $0.75$ and $1.00$ representing the sequence *Heads, Heads*. 
+> Because the *second* coin flip resulted in *Heads*, we know that the output value must be between $0.75$ and $1.00$
+3. Subdividing the range $0.75$ and $1.00$ yet again, $0.750$ - $0.875$ means the third coin flip resulted in *Tails*, and a value in the range $0.875$ - $1.000$ means the third coin flip resulted in *Heads*
+> Because the *third coin flip resulted in *Heads*, any value between $0.875$ and $1.000$ encodes the fact that the first three coin flips went *Heads, Heads, Tails*.
+
+The decoding process performs the same series of steps, but by asking a question instead of outputting a value.
+1. Is the value between $0.00$ and $0.50$? If so, the first coin flip resulted in *Tails*. Otherwise if the value is between $0.50$ and $1.00$, the first coin flip resulted in *Heads*. 
+The above process can be repeated just like the encoding process until we've determined the result of the first three coin flips.
+
+These subdivisions can be encoded using $0$ and $1$, where $0$ represents the bottom half of the range, and $1$ represents the top half of the range. 
+
+When the alphabet is large enough that you can't select a particular outcome using one bit, multiple bits can be used instead to divide up and down the range.

notes/SIMD Huffman Decoding.md

@@ -0,0 +1,5 @@
+<https://dougallj.wordpress.com/2022/07/30/parallelising-huffman-decoding-and-x86-disassembly-by-synchronising-non-self-synchronising-prefix-codes/>
+
+# Scratchpad
+- Start decoding at arbitrary points throughout the data
+- \

personal/tech/Deploying my Macbook.md

@@ -1,30 +0,0 @@
-Installed discord
-
-Changed scrolling direction and speed 
-
-Installed spotify
-
-Turned off spring loading
-
-Unpinned stuff from taskbar
-
-Minimize using scale
-
-Autohide dock
-
-Installed brew
-
-Installed chrome
-
-Installed obsidian
-
-See https://www.youtube.com/watch?v=psPgSN1bPLY for below
-set dock to go with maximum speed and power
-
-enabled type to siri
-
-disabled autocorrect
-
-switched back to natural scrolling
-
-installed rectangle

personal/tech/Enabling fingerprint authentication on Zephyrus G15.md

@@ -1,7 +0,0 @@
-****#linux 
-#laptop 
-[Documentation](https://github.com/knauth/goodix-521d-explanation)
-
-From the usbreset directory run `gcc usbreset.c -o usbreset.out` to compile the reset bin, then `sudo ./usbreset.out /dev/bus/usb/<bus>/<device>` to reset it, for this device it's ``sudo ./usbreset.out /dev/bus/usb/003/002``
-
-from goodix-fp-dump run `sudo python run_521d.py` to reflash the firmware

personal/tech/Fixing supergfxctl black screen on dedicated mode.md

@@ -1 +0,0 @@
-https://asus-linux.org/faq/#why-did-nvidia-mode-give-me-black-screen-with-xorg

personal/tech/Themes I like.md

@@ -1,26 +0,0 @@
-
-# We'll call this shell purple
-Primary background: \#1E2030
-alternate background: \##191b29
-Text color: \#C0CAF5
-Cyan Highlights: \#0DB9D7
-
-# Pipe's Nord
-https://github.com/PipeItToDevNull/PLN
-Primary background: \#3b4252
-
-red: \#bf616a;
-orange: \#d08770;
-yellow-light: \#ebcb8b;
-yellow-dark: \#e4b860;
-green: \#a3be8c;
-purple: \#b48ead;
-sea-green: \#8fbcbb;
-cyan: \#88c0d0;
-frost: \#81a1c1;
-blue: \#5e81ac;
-salmon: \#FC6E68;
-
-# 47c Deep Purple
-Dark background: \#180c34
-Lighter background: \#281c44

personal/tech/Understanding how to handle paths for Ash.md

@@ -1,13 +0,0 @@
-#notes #programming #rust
-
-
-Absolute paths function as intended
-`cd .` takes you to the bianary location
-#### Relative Paths
-- Paths that are relative can be appended to the current dir
-- `..` should strip the directory before it from the path
-- `.` can be entirely removed from the absolute path and the endpoint will not be changed
-
-
-### The Solution:
-As it turns out, both Windows and Unix have prebuilt functions that handle cleaning up paths, that are implemented under `std::fs::canonicalize` https://doc.rust-lang.org/std/fs/fn.canonicalize.html

personal/tech/WiFi not working after pacman -Syu.md

@@ -1,48 +0,0 @@
-#laptop
-#documentation
-#issue
-#closed
-#linux 
-02/02/2022
-
- Because wifi was broken by a pacman update, I’m reverting to an older point in the repos(01/01/2022).
-
-When updating via pacman -Syyuu, `error: failed to prepare transaction (could not satisfy dependencies)
-
-:: installing expat (2.4.2-1) breaks dependency 'expat=2.4.4' required by lib32-expat
-
-:: installing libcap (2.62-1) breaks dependency 'libcap=2.63' required by lib32-libcap` is returned. 
-
-`lib32-expat ` is an xml parser library [Arch WIki](https://archlinux.org/packages/multilib/x86_64/lib32-expat/), and lib32-libcap is some posix document `[arch wiki](https://archlinux.org/packages/multilib/x86_64/lib32-libcap/)`. 
-
-  
-
-New solution: downgrade lib32-libcap(2.63-1 to 2.62-1) and lib32-expat(2.4.4-1 to 2.4.2-1)
-
-Was going to use expat 2.4.3 but caused dependency issues with the 64 bit version. V2 successfully worked
-
-  
-
-sudo pacman -U /var/cache/pacman/pkg/[PACKAGE].pkg.tar.zst
-
-  
-
-After the above downgrade, `sudo pacman -Syyuu` with “y” on skip the lib32-expat and lib32-libcap worked, but returned 
-
-error: failed to commit transaction (conflicting files)
-
-hwids: /usr/share/hwdata/pci.ids exists in filesystem (owned by hwdata)
-
-hwids: /usr/share/hwdata/pnp.ids exists in filesystem (owned by hwdata)
-
-hwids: /usr/share/hwdata/usb.ids exists in filesystem (owned by hwdata)
-
-[referenced documentation for below as on garuda forums](https://forum.garudalinux.org/t/help-cant-upgrade/16237/2)
-
-Couldn’t figure out how to fix above issue, attempting a different date(15).
-
-  
-
- ISSUE CLOSED.
-
-Solution, using the rollback repos to rollback to 2022/01/15

personal/tech/Writing a completely functional shell in Rust.md

@@ -1,28 +0,0 @@
-I set out on project Ash for a a variety of small reasons: 
-- I wanted to better learn how a shell interacts with an operating system, how it calls different commands 
-- I wanted to get better at writing scaleable code
-
-## The Beginnings
-I happened upon [this](https://brennan.io/2015/01/16/write-a-shell-in-c/) article about writing a shell in C, and was fascinated by the way it was written. It was fascinated by the extremely approchable way the article was written, with function calls defined first, and the actual contents of the function filled out later. Then it could be explained what each function does and why it's there, without relying too heavily on language specific semantics. This made it a great stepping stone, even though it's intended for the C programming language. 
-
-I started by writing a very basic framework to obtain user input as a string. As of right now, it's not an entire I/O lock, and so features like tab autocomplete or capturing Ctrl + C to stop the program from being exited are not currently functional. It functions as a loop that:
-- Captures user input
-- Seperates the user input into a list by spaces(this should probably changed later to account for features like `|, >, ;, &&`, which don't necessarily need a space)
-- It then checks the first argument to see if it's a builtin shell command(`cd`,  `help`,  `exit`)
-
- I found it interesting that `cd` is not an operating system utility, it's a shell utility, and when `cd` is run, it tells the next commands run what directory they were run from. In Rust this is implemented as [current_dir()](https://doc.rust-lang.org/std/process/struct.Command.html) for the Command struct. Initially I actually had a lot of trouble with relative and absolute paths. You can create a functional path by simply appending the relative path to the current absolute path, seperated by `/` (or `\` for Windows). While this is technically functional, it's really not elegant at all. I was ending up with valid file paths like `//./home/../home/./../etc/.`, and felt there must be a better solution. I didn't bother checking to see if Rust had a valid method for it, because I didn't know how to put "cleaning up a file pathpath" into a clean, google-able statement, and I felt I could better understand the process behind parsing it if I implemented it myself. I sat down, absolutely stumped, Obsidian open, writing out various logical rules to clean paths up. I ended up with a few simple precepts that *seemed* mostly functional, but ended up missing edge cases, or having flat out unexplained behavior. The nonfunctional rules are below:
- - Paths that are relative can be appended to the current dir, then
-- `..` should strip the non-`..` directory before it from the path 
-- `.` can be entirely removed from the absolute path and the endpoint will not be changed
-
-This logic was flawed enough that exasperated and tired, I googled it, hoping that someone had made a crate that cleaned it up, or maybe there was some regex I could use. As it turns out, both Windows and Unix have prebuilt functions that handle cleaning up paths, that are implemented under `std::fs::canonicalize` ([docs](https://doc.rust-lang.org/std/fs/fn.canonicalize.html)). 
-
-- If no builtin commands are found, it passes it over to system exec handler. In C, processes must be started by forking the current process to a new thread, creating an exact copy with the `fork()` system call. You then instruct the new thread to replace itself with another process with the `exec()` call. Rust however, has a method that spawns new programs with `std::process::Command`. The first argument in the string is passed as the process to start, and each of the new arguments is passed to the process as an array of arguments with `.args()`, eg: `ls /bin` would start a new `ls` process, and pass `/bin` as an argument. 
-
-### The Future
-I would like to improve on this project and make it good enough that it's daily driveable. Plans for new features include:
-- Switching to a complete IO lock, this allows new features like:
-	- Tab autocomplete
-	- Capturing interrrupts
-- A fully featured configuration file that allows changing prompts and behaviors
-- Implementing the rest of the functionality that I use regularly, including redirects, pipes, and `;` or `&&`

personal/tech/unable to connect to wpa-enterprise via iwd.md

@@ -1,4 +0,0 @@
-#laptop 
-#issue 
-#open
-#linux

personal/tech/wlan0 disabled after restart or wake from hibernate.md

@@ -1,6 +0,0 @@
-#laptop 
-#issue 
-#linux 
-#open 
-### Disabling the watchdog timer
-currently disabled via grub config, trying to disable module loading, don't know module name. Used `lsmod` to list modules, was unable to spot it after a cursory glance. `cat /proc/sys/kernel/watchdog` will show if it's active, and it does return 0, but I want it fully disabled. [see for disabling watchdog timer](https://wiki.archlinux.org/title/improving_performance#Watchdogs), [see for blacklisting modules](https://wiki.archlinux.org/title/Kernel_module#Blacklisting)