https://haifei-home.pages.dev/en/tags/abstract-algebra/Recent content in Abstract Algebra on Haifei's HomeHugoenhfwang132@gmail.com (hfwang132)hfwang132@gmail.com (hfwang132)This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.Thu, 16 Mar 2023 21:54:23 +0800https://haifei-home.pages.dev/en/post_20230316_%E7%94%A8%E4%B8%80%E9%81%93%E5%B0%8F%E5%AD%A6%E6%95%B0%E5%AD%A6%E9%A2%98-%E5%A4%8D%E4%B9%A0%E7%BE%A4-%E7%8E%AF-%E5%9F%9F-%E6%A8%A1%E5%92%8C%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4/Thu, 16 Mar 2023 21:54:23 +0800hfwang132@gmail.com (hfwang132)https://haifei-home.pages.dev/en/post_20230316_%E7%94%A8%E4%B8%80%E9%81%93%E5%B0%8F%E5%AD%A6%E6%95%B0%E5%AD%A6%E9%A2%98-%E5%A4%8D%E4%B9%A0%E7%BE%A4-%E7%8E%AF-%E5%9F%9F-%E6%A8%A1%E5%92%8C%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4/<h2 id="0-introduction-to-the-problem">0. Introduction to the Problem</h2> <p>With this single college entrance examination mock question, we can review concepts from abstract algebra such as groups, rings, fields, modules, and vector spaces. The problem is shown below:</p> <figure class="post-figure" style="--post-figure-width: 80%;"><img src="https://haifei-home.pages.dev/post_20230316_%E7%94%A8%E4%B8%80%E9%81%93%E5%B0%8F%E5%AD%A6%E6%95%B0%E5%AD%A6%E9%A2%98-%E5%A4%8D%E4%B9%A0%E7%BE%A4-%E7%8E%AF-%E5%9F%9F-%E6%A8%A1%E5%92%8C%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4/images/v2-70861b2eb74a8876bd392f4da8da0aef_r.jpg" loading="lazy"/></figure> <p>A college entrance examination mock question from somewhere; in fact, you can figure it out with a little trial and error—it is not difficult.</p> <p>Simply put, it is a matter of “pulling one hair and moving the surrounding area.” Changing one cell also rotates the surrounding cells. I believe many people have played this puzzle game. Even elementary school students can understand this game.</p>