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<!DOCTYPE html>
<html>
<head>
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script type="text/javascript" id="MathJax-script" async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js">
</script>
<!-- Other imports... -->
<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/gh/aaaakshat/cm-web-fonts@latest/fonts.css">
<style>
body {
font-family: "Palatino Linotype", Arial, sans-serif;
color: #333333;
}
div {
min-width: 500px;
width:auto;
min-height:0px;
height:auto;
background-color: #f1fdf7;
border: 1px solid blue;
box-sizing: border-box;
padding-left: 20px;
}
</style>
</head>
<body>
<h1>Grass</h1>
<h2>About me</h2>
<p>Hello there. I'm a highschool student who is interested in mathematics. To that end, I have self-studied a little on my own, and am still learning the fundamentals. Currently, set theory has enthralled me the most, because of fascinating results such as the independence of <font face = "Computer Modern Serif, serif">AC</font> from <font face = "Computer Modern Serif, serif">ZFC</font>. These results are <em>far</em> above my knowledge now, but hopefully I'll get there in a couple years!</p>
<hr>
<h2>Nice quote</h2>
<p>"Mathematics in general, and analysis in particular, is not a spectator sport. It is learned by doing... Of course the need for very critical (and slow) reading of mathematics is nicely summed up in the old quote that “To read without a pencil is daydreaming.” The reader should ask him/herself after every sentence “What does this mean? Why is this justified?"...</p>
<p>To get the most out of this text, the reader is encouraged to <em>not</em> look for hints and solutions in other background materials. In fact, even for proofs that are adaptations of proofs in this text, it is advantageous to try to create the proof without looking up the roof that is to be adapted There is evidence that the struggle to solve a problem which can take days for a single proof, is exactly what ultimately contributes to the development of strong skills. "Shortcuts," while pleasant, can actually diminish this development. Readers interested in quantitative evidence that shows how the struggle to acquire a skill actually can lead to deeper learning may find the article <a href="#footnote-4">[4]</a> quite enlightening. A better survival mechanism that shortcuts is the development of connections between newly learned content and existing knowledge. The reader will need to find these connections to his/her existing knowledge, but the structure of the text is intended to help by motivating all abstractions. Readers interested in how knowledge is activated more easily when it was learned in a known context may be interested in the article <a href="#footnote-5">[5]</a>" ― Bernd Schröder</p>
<p id="footnote-4">[4] R. Bjork (1994), Memory and Metamemory Considerations in the Training of Human Beings, in J. Metcalfe and A. Shimamura (eds.), Metacognition: Knowing about knowing, MIT Press, Cambridge, MA, 185-205.</p>
<p id="footnote-5">[5] J.Bransford, R. Sherwood, N. Vye, and J. Rieser (1986), Teaching Thinking and Problem Solving, American Psychologist, October issue.</p>
<hr>
<h2>Self-Studying </h2>
<ul>
<li>Last updated on: 16/3/24 (DD/MM/YY).</li>
<li>Unless otherwise stated, exercises/questions/etc in the latex PDFs below are ones that I thought of myself.</li>
<li>If hints were not copied from the authors' exercises, I did not use them. (unless I forgot to copy them ><)</li>
<li>Nowadays I try to do my ideation and experimentation (e.g. on phrasing my proofs differently) in latex too. Most of these are in my VSCode comments and not generated in the PDFs below, in which you find my final proofs.</li>
<li>A nonstrict chronological order is used below.</li>
</ul>
<ol>
<li>Calculus by Michael Spivak</li>
<a href="https://grassglass.github.io/Self-Study-PDFs/Spivak's-Calculus.pdf">Chapters 1-2 (latex)</a><br>
<li>Elements of Set Theory by Herbert Enderton</li>
<a href="https://grassglass.github.io/Self-Study-PDFs/Enderton'sElementsofSetTheory.pdf">Chapters 1-6.2 (latex)</a><br>
<a href="https://grassglass.github.io/Self-Study-PDFs/Enderton-Handwritten.pdf">Chapters 6.3-9 (handwritten)</a>
<li>Linear Algebra by Friedberg, Insel, Spence</li>
<a href="https://grassglass.github.io/Self-Study-PDFs/Linear-Algebra-By-FIS.pdf">Chapters 1-1.6 (latex)</a><br>
<a href="link to be added">Chapters 1.6-4 (handwritten)</a> (pdf tba)<br>
<a href="https://grassglass.github.io/Self-Study-PDFs/FIS-16.3.24.pdf">Chapters 5- (latex)</a> (ongoing)
<li>Mathematical Analysis: A Concise Introduction by Bernd Schröder</li>
<a href="link to be added">Chapters 1-5.2 (handwritten)</a> (pdf tba)<br>
<a href="https://grassglass.github.io/Self-Study-PDFs/Schroder-16.3.24.pdf">Chapters 5.3-8.1 (latex)</a> (ongoing)
<li>Principles of Mathematical Analysis by Walter Rudin (Reading it with a Discord study group)</li>
<a href="https://grassglass.github.io/Self-Study-PDFs/Rudin-16.3.24.pdf">Chapters 1-3 (latex)</a> (ongoing)
</ol>
<hr>
<h2>Notes</h2>
O/A-Levels <a href="https://github.com/GrassGlass/A-Levels">(latex source code)</a> [Copyright License: GPL-3.0]
</body>
</html>