Spaces:

slimshadow
/

streamlit-md

Paused

App Files Files Community

streamlit-md / maths.html

slimshadow

Upload 12 files

fd37dba verified about 1 year ago

raw

history blame contribute delete

9.83 kB

	<!DOCTYPE html>
	<html>
	<head>
	<title>maths.md</title>
	<meta http-equiv="Content-type" content="text/html;charset=UTF-8">

	<style>
	/* https://github.com/microsoft/vscode/blob/master/extensions/markdown-language-features/media/markdown.css */
	/*---------------------------------------------------------------------------------------------
	* Copyright (c) Microsoft Corporation. All rights reserved.
	* Licensed under the MIT License. See License.txt in the project root for license information.
	--------------------------------------------------------------------------------------------/

	body {
	font-family: var(--vscode-markdown-font-family, -apple-system, BlinkMacSystemFont, "Segoe WPC", "Segoe UI", "Ubuntu", "Droid Sans", sans-serif);
	font-size: var(--vscode-markdown-font-size, 14px);
	padding: 0 26px;
	line-height: var(--vscode-markdown-line-height, 22px);
	word-wrap: break-word;
	}

	#code-csp-warning {
	position: fixed;
	top: 0;
	right: 0;
	color: white;
	margin: 16px;
	text-align: center;
	font-size: 12px;
	font-family: sans-serif;
	background-color:#444444;
	cursor: pointer;
	padding: 6px;
	box-shadow: 1px 1px 1px rgba(0,0,0,.25);
	}

	#code-csp-warning:hover {
	text-decoration: none;
	background-color:#007acc;
	box-shadow: 2px 2px 2px rgba(0,0,0,.25);
	}

	body.scrollBeyondLastLine {
	margin-bottom: calc(100vh - 22px);
	}

	body.showEditorSelection .code-line {
	position: relative;
	}

	body.showEditorSelection .code-active-line:before,
	body.showEditorSelection .code-line:hover:before {
	content: "";
	display: block;
	position: absolute;
	top: 0;
	left: -12px;
	height: 100%;
	}

	body.showEditorSelection li.code-active-line:before,
	body.showEditorSelection li.code-line:hover:before {
	left: -30px;
	}

	.vscode-light.showEditorSelection .code-active-line:before {
	border-left: 3px solid rgba(0, 0, 0, 0.15);
	}

	.vscode-light.showEditorSelection .code-line:hover:before {
	border-left: 3px solid rgba(0, 0, 0, 0.40);
	}

	.vscode-light.showEditorSelection .code-line .code-line:hover:before {
	border-left: none;
	}

	.vscode-dark.showEditorSelection .code-active-line:before {
	border-left: 3px solid rgba(255, 255, 255, 0.4);
	}

	.vscode-dark.showEditorSelection .code-line:hover:before {
	border-left: 3px solid rgba(255, 255, 255, 0.60);
	}

	.vscode-dark.showEditorSelection .code-line .code-line:hover:before {
	border-left: none;
	}

	.vscode-high-contrast.showEditorSelection .code-active-line:before {
	border-left: 3px solid rgba(255, 160, 0, 0.7);
	}

	.vscode-high-contrast.showEditorSelection .code-line:hover:before {
	border-left: 3px solid rgba(255, 160, 0, 1);
	}

	.vscode-high-contrast.showEditorSelection .code-line .code-line:hover:before {
	border-left: none;
	}

	img {
	max-width: 100%;
	max-height: 100%;
	}

	a {
	text-decoration: none;
	}

	a:hover {
	text-decoration: underline;
	}

	a:focus,
	input:focus,
	select:focus,
	textarea:focus {
	outline: 1px solid -webkit-focus-ring-color;
	outline-offset: -1px;
	}

	hr {
	border: 0;
	height: 2px;
	border-bottom: 2px solid;
	}

	h1 {
	padding-bottom: 0.3em;
	line-height: 1.2;
	border-bottom-width: 1px;
	border-bottom-style: solid;
	}

	h1, h2, h3 {
	font-weight: normal;
	}

	table {
	border-collapse: collapse;
	}

	table > thead > tr > th {
	text-align: left;
	border-bottom: 1px solid;
	}

	table > thead > tr > th,
	table > thead > tr > td,
	table > tbody > tr > th,
	table > tbody > tr > td {
	padding: 5px 10px;
	}

	table > tbody > tr + tr > td {
	border-top: 1px solid;
	}

	blockquote {
	margin: 0 7px 0 5px;
	padding: 0 16px 0 10px;
	border-left-width: 5px;
	border-left-style: solid;
	}

	code {
	font-family: Menlo, Monaco, Consolas, "Droid Sans Mono", "Courier New", monospace, "Droid Sans Fallback";
	font-size: 1em;
	line-height: 1.357em;
	}

	body.wordWrap pre {
	white-space: pre-wrap;
	}

	pre:not(.hljs),
	pre.hljs code > div {
	padding: 16px;
	border-radius: 3px;
	overflow: auto;
	}

	pre code {
	color: var(--vscode-editor-foreground);
	tab-size: 4;
	}

	/** Theming */

	.vscode-light pre {
	background-color: rgba(220, 220, 220, 0.4);
	}

	.vscode-dark pre {
	background-color: rgba(10, 10, 10, 0.4);
	}

	.vscode-high-contrast pre {
	background-color: rgb(0, 0, 0);
	}

	.vscode-high-contrast h1 {
	border-color: rgb(0, 0, 0);
	}

	.vscode-light table > thead > tr > th {
	border-color: rgba(0, 0, 0, 0.69);
	}

	.vscode-dark table > thead > tr > th {
	border-color: rgba(255, 255, 255, 0.69);
	}

	.vscode-light h1,
	.vscode-light hr,
	.vscode-light table > tbody > tr + tr > td {
	border-color: rgba(0, 0, 0, 0.18);
	}

	.vscode-dark h1,
	.vscode-dark hr,
	.vscode-dark table > tbody > tr + tr > td {
	border-color: rgba(255, 255, 255, 0.18);
	}

	</style>

	<style>
	/* Tomorrow Theme */
	/* http://jmblog.github.com/color-themes-for-google-code-highlightjs */
	/* Original theme - https://github.com/chriskempson/tomorrow-theme */

	/* Tomorrow Comment */
	.hljs-comment,
	.hljs-quote {
	color: #8e908c;
	}

	/* Tomorrow Red */
	.hljs-variable,
	.hljs-template-variable,
	.hljs-tag,
	.hljs-name,
	.hljs-selector-id,
	.hljs-selector-class,
	.hljs-regexp,
	.hljs-deletion {
	color: #c82829;
	}

	/* Tomorrow Orange */
	.hljs-number,
	.hljs-built_in,
	.hljs-builtin-name,
	.hljs-literal,
	.hljs-type,
	.hljs-params,
	.hljs-meta,
	.hljs-link {
	color: #f5871f;
	}

	/* Tomorrow Yellow */
	.hljs-attribute {
	color: #eab700;
	}

	/* Tomorrow Green */
	.hljs-string,
	.hljs-symbol,
	.hljs-bullet,
	.hljs-addition {
	color: #718c00;
	}

	/* Tomorrow Blue */
	.hljs-title,
	.hljs-section {
	color: #4271ae;
	}

	/* Tomorrow Purple */
	.hljs-keyword,
	.hljs-selector-tag {
	color: #8959a8;
	}

	.hljs {
	display: block;
	overflow-x: auto;
	color: #4d4d4c;
	padding: 0.5em;
	}

	.hljs-emphasis {
	font-style: italic;
	}

	.hljs-strong {
	font-weight: bold;
	}
	</style>

	<style>
	/*
	* Markdown PDF CSS
	*/

	body {
	font-family: -apple-system, BlinkMacSystemFont, "Segoe WPC", "Segoe UI", "Ubuntu", "Droid Sans", sans-serif, "Meiryo";
	padding: 0 12px;
	}

	pre {
	background-color: #f8f8f8;
	border: 1px solid #cccccc;
	border-radius: 3px;
	overflow-x: auto;
	white-space: pre-wrap;
	overflow-wrap: break-word;
	}

	pre:not(.hljs) {
	padding: 23px;
	line-height: 19px;
	}

	blockquote {
	background: rgba(127, 127, 127, 0.1);
	border-color: rgba(0, 122, 204, 0.5);
	}

	.emoji {
	height: 1.4em;
	}

	code {
	font-size: 14px;
	line-height: 19px;
	}

	/* for inline code */
	:not(pre):not(.hljs) > code {
	color: #C9AE75; /* Change the old color so it seems less like an error */
	font-size: inherit;
	}

	/* Page Break : use <div class="page"/> to insert page break
	-------------------------------------------------------- */
	.page {
	page-break-after: always;
	}

	</style>

	<script src="https://unpkg.com/mermaid/dist/mermaid.min.js"></script>
	</head>
	<body>
	<script>
	mermaid.initialize({
	startOnLoad: true,
	theme: document.body.classList.contains('vscode-dark') \|\| document.body.classList.contains('vscode-high-contrast')
	? 'dark'
	: 'default'
	});
	</script>
	<h1 id="unit-i-mathematical-logic-sets-relations-and-functions">UNIT I: Mathematical Logic, Sets, Relations, and Functions</h1>
	<h2 id="mathematical-logic">Mathematical Logic:</h2>
	<ul>
	<li>Notations, Algebra of Propositions & Propositional functions</li>
	<li>Logical connectives, Truth values & Truth tables</li>
	<li>Tautologies & Contradictions, Normal Forms</li>
	<li>Predicate Calculus, Quantifiers</li>
	</ul>
	<h2 id="set-theory">Set Theory:</h2>
	<ul>
	<li>Sets, Subsets, Power sets, Complement, Union and Intersection</li>
	<li>De Morgan's Law, Cardinality</li>
	</ul>
	<h2 id="relations">Relations:</h2>
	<ul>
	<li>Cartesian Products, relational Matrices, properties of relations, equivalence relations</li>
	</ul>
	<h2 id="functions">Functions:</h2>
	<ul>
	<li>Injection, Surjection, Bijection, Composition of Functions, Permutations, Cardinality</li>
	<li>Characteristic functions, Recursive definitions, Finite induction</li>
	</ul>
	<h1 id="unit-ii-lattices--boolean-algebra">UNIT II: Lattices & Boolean Algebra</h1>
	<h2 id="lattices">Lattices:</h2>
	<ul>
	<li>Lattices as Algebraic Systems, Sublattices</li>
	<li>Some special lattices: Complement, Distributive, Modular</li>
	</ul>
	<h2 id="boolean-algebra">Boolean Algebra:</h2>
	<ul>
	<li>Axiomatic definitions of Boolean algebra as algebraic structures with two operations</li>
	<li>Switching Circuits</li>
	</ul>
	<h1 id="unit-iii-groups-fields--rings">UNIT III: Groups, Fields, & Rings</h1>
	<h2 id="groups">Groups:</h2>
	<ul>
	<li>Definition of groups, axioms, permutation groups</li>
	<li>Subgroups, co-sets, normal subgroups, free subgroups</li>
	<li>Grammars, language</li>
	</ul>
	<h2 id="fields--rings">Fields & Rings:</h2>
	<ul>
	<li>Definition and structure of fields and rings</li>
	<li>Minimal Polynomials, Irreducible Polynomials</li>
	<li>Polynomial roots & its Applications</li>
	</ul>
	<h1 id="unit-iv-graphs">UNIT IV: Graphs</h1>
	<h2 id="graphs">Graphs:</h2>
	<ul>
	<li>Simple Graph, Multigraph & Pseudograph</li>
	<li>Degree of a Vertex, Types of Graphs, Subgraphs, Isomorphic Graphs</li>
	<li>Operations on Graphs, Paths, Cycles, and Connectivity</li>
	<li>Euler and Hamilton Graphs, Shortest Path Problems (BFS, Dijkstra's Algorithm)</li>
	<li>Representation of Graphs, Planar Graphs, Applications of Graph Theory</li>
	</ul>
	<h1 id="unit-v-trees">UNIT V: Trees</h1>
	<h2 id="trees">Trees:</h2>
	<ul>
	<li>Definition and properties of trees, pendant vertices in a tree, center of a tree</li>
	<li>Spanning tree, Binary tree, Tree traversal</li>
	<li>Applications of trees in computer science</li>
	</ul>

	</body>
	</html>