https://yahel1216.github.io/tags/math/Recent content in Math on Yahel UffenheimerHugoen-USSat, 10 Jan 2026 00:00:00 +0000https://yahel1216.github.io/posts/matroid-theory/Sat, 10 Jan 2026 00:00:00 +0000https://yahel1216.github.io/posts/matroid-theory/<h1 id="basic-matroid-theory-and-infinite-extensions">Basic Matroid Theory and Infinite Extensions</h1> <p><strong>Prerequisites:</strong></p> <ul> <li><strong>Linear Algebra:</strong> Vector spaces, basis, dimension, and linear independence.</li> <li><strong>Graph Theory:</strong> Graphs, connected components, cycles, and spanning trees.</li> <li><strong>Set Theory:</strong> Basic cardinality and Zorn&rsquo;s Lemma (for the infinite section).</li> </ul> <hr> <p>In this post, we will discuss the basics of <strong>Matroid Theory</strong>. While often taught merely as a theoretical framework for Greedy Algorithms, matroids are a rich combinatorial structure in their own right. We will start with the finite foundations and then explore how these definitions behave (and break) when extended to the infinite case.</p>