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ProofLab

Introduction to Proofs (Fall 2022)

Upper level undergraduate math course, Johns Hopkins University

This course introduces you to the the language of mathematics and the methods of mathematical proofs. We learn the rules of logic whereby we identify strategies for proving mathematical statements based on their logical structures. We will then learn about some elementary aspects of number systems, sets, functions, relations, inductive types (such as lists, trees, graphs), algebraic structures, and metric spaces. As we learn these topics, we teach our computers every piece of mathematics we learn, that is we learn mathematics by formalizing it in Lean interactive proof assistant. Formalization can be seen as a kind of computer programming: we will write mathematical definitions, theorems, and proofs in a language that Lean can understand. In return, Lean provides instant feedback, helps us with writing our proofs and ultimately certifies the correctness of our proofs.

This course does not have any mathematical prerequisite, however, it is expected that you are familiar with basic high-school algebra. Although a basic programming experience can go far toward your excelling in this course, we actually don’t presuppose any background in formalization or in programming.

Copyright (c) 2022 Sina Hazratpour. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE.

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, 'i'); if (__m === '*' || __re.test(location.href)) { // Add copy buttons to all 
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(function() {
function addCopyButtons() {
document.querySelectorAll('pre code').forEach(function(codeBlock) {
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var btn = document.createElement('button');
btn.textContent = 'Copy';
btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';
btn.onmouseover = function() { this.style.opacity = '1'; };
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} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '
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ProofLab
Introduction to Proofs (Fall 2022)
Upper level undergraduate math course, Johns Hopkins University
This course introduces you to the the language of mathematics and the methods of mathematical proofs. We learn the rules of logic whereby we identify strategies for proving mathematical statements based on their logical structures. We will then learn about some elementary aspects of number systems, sets, functions, relations, inductive types (such as lists, trees, graphs), algebraic structures, and metric spaces. As we learn these topics, we teach our computers every piece of mathematics we learn, that is we learn mathematics by formalizing it in Lean interactive proof assistant. Formalization can be seen as a kind of computer programming: we will write mathematical definitions, theorems, and proofs in a language that Lean can understand. In return, Lean provides instant feedback, helps us with writing our proofs and ultimately certifies the correctness of our proofs.
This course does not have any mathematical prerequisite, however, it is expected that you are familiar with basic high-school algebra. Although a basic programming experience can go far toward your excelling in this course, we actually don’t presuppose any background in formalization or in programming.
Copyright (c) 2022 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
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, 'i');
if (__m === '*' || __re.test(location.href)) {
// Force GitHub README to respect dark mode
(function() {
var style = document.createElement('style');
style.textContent = '
.markdown-body {
color-scheme: dark light;
}
.markdown-body pre { background: #161b22 !important; }
.markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }
.markdown-body table th, .markdown-body table td { border-color: #30363d !important; }
.markdown-body img { background: #0d1117; }
.markdown-body blockquote { border-left-color: #8b949e; }
.markdown-body hr { border-color: #30363d; }
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document.head.appendChild(style);
})();
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
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ProofLab
Introduction to Proofs (Fall 2022)
Upper level undergraduate math course, Johns Hopkins University
This course introduces you to the the language of mathematics and the methods of mathematical proofs. We learn the rules of logic whereby we identify strategies for proving mathematical statements based on their logical structures. We will then learn about some elementary aspects of number systems, sets, functions, relations, inductive types (such as lists, trees, graphs), algebraic structures, and metric spaces. As we learn these topics, we teach our computers every piece of mathematics we learn, that is we learn mathematics by formalizing it in Lean interactive proof assistant. Formalization can be seen as a kind of computer programming: we will write mathematical definitions, theorems, and proofs in a language that Lean can understand. In return, Lean provides instant feedback, helps us with writing our proofs and ultimately certifies the correctness of our proofs.
This course does not have any mathematical prerequisite, however, it is expected that you are familiar with basic high-school algebra. Although a basic programming experience can go far toward your excelling in this course, we actually don’t presuppose any background in formalization or in programming.
Copyright (c) 2022 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
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, 'i');
if (__m === '*' || __re.test(location.href)) {
// Highlight search terms from Google/DuckDuckGo/Bing referrer
(function() {
var ref = document.referrer;
var terms = [];
if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {
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highlight(document.body);
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observer.observe(document.body, { childList: true, subtree: true });
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}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
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try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
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ProofLab
Introduction to Proofs (Fall 2022)
Upper level undergraduate math course, Johns Hopkins University
This course introduces you to the the language of mathematics and the methods of mathematical proofs. We learn the rules of logic whereby we identify strategies for proving mathematical statements based on their logical structures. We will then learn about some elementary aspects of number systems, sets, functions, relations, inductive types (such as lists, trees, graphs), algebraic structures, and metric spaces. As we learn these topics, we teach our computers every piece of mathematics we learn, that is we learn mathematics by formalizing it in Lean interactive proof assistant. Formalization can be seen as a kind of computer programming: we will write mathematical definitions, theorems, and proofs in a language that Lean can understand. In return, Lean provides instant feedback, helps us with writing our proofs and ultimately certifies the correctness of our proofs.
This course does not have any mathematical prerequisite, however, it is expected that you are familiar with basic high-school algebra. Although a basic programming experience can go far toward your excelling in this course, we actually don’t presuppose any background in formalization or in programming.
Copyright (c) 2022 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
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, 'i');
if (__m === '*' || __re.test(location.href)) {
// Strip utm_, fbclid, gclid, etc. from all links on page
(function() {
var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',
'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',
'ref', 'ref_src', 'source', 'medium', 'campaign'];
function cleanUrl(url) {
try {
var u = new URL(url, window.location.origin);
var changed = false;
trackingParams.forEach(function(p) {
if (u.searchParams.has(p)) {
u.searchParams.delete(p);
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});
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function cleanLinks() {
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});
});
observer.observe(document.body, { childList: true, subtree: true });
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}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '
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ProofLab
Introduction to Proofs (Fall 2022)
Upper level undergraduate math course, Johns Hopkins University
This course introduces you to the the language of mathematics and the methods of mathematical proofs. We learn the rules of logic whereby we identify strategies for proving mathematical statements based on their logical structures. We will then learn about some elementary aspects of number systems, sets, functions, relations, inductive types (such as lists, trees, graphs), algebraic structures, and metric spaces. As we learn these topics, we teach our computers every piece of mathematics we learn, that is we learn mathematics by formalizing it in Lean interactive proof assistant. Formalization can be seen as a kind of computer programming: we will write mathematical definitions, theorems, and proofs in a language that Lean can understand. In return, Lean provides instant feedback, helps us with writing our proofs and ultimately certifies the correctness of our proofs.
This course does not have any mathematical prerequisite, however, it is expected that you are familiar with basic high-school algebra. Although a basic programming experience can go far toward your excelling in this course, we actually don’t presuppose any background in formalization or in programming.
Copyright (c) 2022 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
About
sinhp.github.io/teaching/2022-introduction-to-proofs
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, 'i');
if (__m === '*' || __re.test(location.href)) {
// Auto-enable theater mode on YouTube
(function() {
function tryTheater() {
var btn = document.querySelector('button[aria-label="Theater mode"], ytd-player #player button[title="Theater mode"]');
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btn.click();
}
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// Try immediately
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if (location.href !== lastUrl) {
lastUrl = location.href;
setTimeout(tryTheater, 500);
}
}, 1000);
// Also try on player load
var observer = new MutationObserver(tryTheater);
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
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try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
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ProofLab
Introduction to Proofs (Fall 2022)
Upper level undergraduate math course, Johns Hopkins University
This course introduces you to the the language of mathematics and the methods of mathematical proofs. We learn the rules of logic whereby we identify strategies for proving mathematical statements based on their logical structures. We will then learn about some elementary aspects of number systems, sets, functions, relations, inductive types (such as lists, trees, graphs), algebraic structures, and metric spaces. As we learn these topics, we teach our computers every piece of mathematics we learn, that is we learn mathematics by formalizing it in Lean interactive proof assistant. Formalization can be seen as a kind of computer programming: we will write mathematical definitions, theorems, and proofs in a language that Lean can understand. In return, Lean provides instant feedback, helps us with writing our proofs and ultimately certifies the correctness of our proofs.
This course does not have any mathematical prerequisite, however, it is expected that you are familiar with basic high-school algebra. Although a basic programming experience can go far toward your excelling in this course, we actually don’t presuppose any background in formalization or in programming.
Copyright (c) 2022 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
About
sinhp.github.io/teaching/2022-introduction-to-proofs
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, 'i');
if (__m === '*' || __re.test(location.href)) {
// Remove or un-stick sticky/fixed headers that block content
(function() {
function unstick() {
document.querySelectorAll('header, nav, [role="banner"], .header, .navbar, .sticky, .fixed-top, [style*="position: fixed"], [style*="position:sticky"]').forEach(function(el) {
if (el.style.position === 'fixed' || el.style.position === 'sticky' || getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {
el.style.position = 'static';
el.style.top = 'auto';
el.style.zIndex = 'auto';
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var observer = new MutationObserver(unstick);
observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });
})();
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
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try {
var __m = "*";
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ProofLab
Introduction to Proofs (Fall 2022)
Upper level undergraduate math course, Johns Hopkins University
This course introduces you to the the language of mathematics and the methods of mathematical proofs. We learn the rules of logic whereby we identify strategies for proving mathematical statements based on their logical structures. We will then learn about some elementary aspects of number systems, sets, functions, relations, inductive types (such as lists, trees, graphs), algebraic structures, and metric spaces. As we learn these topics, we teach our computers every piece of mathematics we learn, that is we learn mathematics by formalizing it in Lean interactive proof assistant. Formalization can be seen as a kind of computer programming: we will write mathematical definitions, theorems, and proofs in a language that Lean can understand. In return, Lean provides instant feedback, helps us with writing our proofs and ultimately certifies the correctness of our proofs.
This course does not have any mathematical prerequisite, however, it is expected that you are familiar with basic high-school algebra. Although a basic programming experience can go far toward your excelling in this course, we actually don’t presuppose any background in formalization or in programming.
Copyright (c) 2022 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
About
sinhp.github.io/teaching/2022-introduction-to-proofs
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, 'i');
if (__m === '*' || __re.test(location.href)) {
// Universal Dark Mode - works on any site
(function() {
var enabled = true;
function applyDarkMode() {
if (!enabled) return;
// Create style element if it doesn't exist
var style = document.getElementById('universal-dark-mode-style');
if (!style) {
style = document.createElement('style');
style.id = 'universal-dark-mode-style';
document.head.appendChild(style);
}
// Dark mode CSS - inverts colors but preserves images/video
style.textContent = '
/* Invert everything except media */
html {
filter: invert(1) hue-rotate(180deg) !important;
background: #1a1a2e !important;
}
/* Restore images, videos, iframes, canvas */
img, video, iframe, canvas, svg, picture, [style*="background-image"] {
filter: invert(1) hue-rotate(180deg) !important;
}
/* Preserve specific elements that should not be inverted */
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[data-theme="light"], [data-theme="light"],
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filter: none !important;
}
/* Fix common UI elements */
.modal, .popup, .dropdown-menu, .tooltip, .popover {
filter: invert(1) hue-rotate(180deg) !important;
background: #2d2d44 !important;
border-color: #444 !important;
}
/* Scrollbars */
::-webkit-scrollbar { background: #1a1a2e !important; }
::-webkit-scrollbar-thumb { background: #444 !important; }
::-webkit-scrollbar-thumb:hover { background: #555 !important; }
/* Selection */
::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }
::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }
';
}
function removeDarkMode() {
var style = document.getElementById('universal-dark-mode-style');
if (style) style.remove();
}
// Toggle with Alt+Shift+D
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if (e.altKey && e.shiftKey && e.key === 'D') {
e.preventDefault();
enabled = !enabled;
if (enabled) {
applyDarkMode();
console.log('[Universal Dark Mode] Enabled');
} else {
removeDarkMode();
console.log('[Universal Dark Mode] Disabled');
}
}
});
// Apply on load
applyDarkMode();
// Re-apply on dynamic content
var observer = new MutationObserver(function(mutations) {
if (enabled && !document.getElementById('universal-dark-mode-style')) {
applyDarkMode();
}
});
observer.observe(document.head, { childList: true });
console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');
})();
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();
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ProofLab
Introduction to Proofs (Fall 2022)
Upper level undergraduate math course, Johns Hopkins University
This course introduces you to the the language of mathematics and the methods of mathematical proofs. We learn the rules of logic whereby we identify strategies for proving mathematical statements based on their logical structures. We will then learn about some elementary aspects of number systems, sets, functions, relations, inductive types (such as lists, trees, graphs), algebraic structures, and metric spaces. As we learn these topics, we teach our computers every piece of mathematics we learn, that is we learn mathematics by formalizing it in Lean interactive proof assistant. Formalization can be seen as a kind of computer programming: we will write mathematical definitions, theorems, and proofs in a language that Lean can understand. In return, Lean provides instant feedback, helps us with writing our proofs and ultimately certifies the correctness of our proofs.
This course does not have any mathematical prerequisite, however, it is expected that you are familiar with basic high-school algebra. Although a basic programming experience can go far toward your excelling in this course, we actually don’t presuppose any background in formalization or in programming.
Copyright (c) 2022 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
About
sinhp.github.io/teaching/2022-introduction-to-proofs
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Readme
MIT license
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