https://www.gravatar.com/avatar/fd1eff01a63e48f3ceb93bed42b10add 2026-11-01T12:43:21.413Z https://txj2006.github.io/ Xujiang Tang txj_262538@163.com Hexo https://txj2006.github.io/2026/11/01/2026-11-01-basic-mathematics-geometry-topology-volume-01/ 2026-11-01T00:00:00.000Z 2026-11-01T12:43:21.413Z

<p>“基础数学系列”的几何与拓扑讲义现已完成第一册的八章正文。本册从仿射与欧氏空间出发，建立度量空间和一般拓扑的基础，再讨论连续映射、分离与可数性、紧性、连通性，以及商空间和几何粘合。</p> <p><a href="/files/basic-mathematics/geome

https://txj2006.github.io/2026/10/31/2026-10-31-basic-mathematics-analysis-volume-01/ 2026-10-31T02:00:00.000Z 2026-11-01T12:43:21.413Z

<p>接下来我会更新基础数学系列，分为几何与拓扑、代数学、分析学三个类别，并且附上我认为值得思考的题目，以及知识点手册，均为本科期间的思考与积累工作。目前更新到第一本。</p> <p>本篇发布《分析学讲义·第一册：实数、极限、微积分与测度》。全册从有序域和 Dedekind 分割

https://txj2006.github.io/2026/10/29/2026-10-29-basic-mathematics-algebra-volume-02/ 2026-10-29T08:00:00.000Z 2026-11-01T12:43:21.413Z

<p>“基础数学系列”继续更新，分为几何与拓扑、代数学、分析学三个类别。系列将整理知识点手册，并附上我认为值得思考的题目，均为本科期间的思考与积累工作。目前代数学讲义更新至第二册。</p> <p><a href="/files/basic-mathematics/algebra-

https://txj2006.github.io/2026/10/27/2026-10-27-basic-mathematics-algebra-problems/ 2026-10-27T14:00:00.000Z 2026-11-01T12:43:21.413Z

<p>《代数学综合高阶习题集》开始更新。它是一部独立的综合题集，采用连续题号，不按讲义分册配题；从集合与映射出发，逐步进入更深入的代数问题。</p> <p>目前收入首批 <strong>8 题，共 17 页</strong>。题目依次涉及不相交平移、双射构造、共同代表集、反链与极

https://txj2006.github.io/2026/10/26/2026-10-26-basic-mathematics-algebra-volume-01/ 2026-10-26T02:00:00.000Z 2026-11-01T12:43:21.413Z

<p>接下来，我会持续更新“基础数学系列”，分为几何与拓扑、代数学、分析学三个类别。系列将整理知识点手册，并附上我认为值得思考的题目。这些内容均为本科期间的思考与积累工作。</p> <p>本篇收录《代数学讲义·第一册》。系列现已更新至<a href="/2026/10/29/20

https://txj2006.github.io/2026/10/25/2026-10-25-gre-sub-book-recommendation/ 2026-10-25T01:05:00.000Z 2026-11-01T12:43:21.413Z

<p>推荐 Ian Coley 的《Math GRE Bootcamp: Lecture Notes》，用于申请博士时准备数学 GRE Subject Test。</p> <p><a href="/files/gre-sub/lecture-notes.pdf">点击阅读《Mat

https://txj2006.github.io/2026/10/25/2026-10-25-introduction-to-graph-theory-books/ 2026-10-25T01:00:00.000Z 2026-11-01T12:43:21.413Z

<p>Mikhail Lavrov 的《Start Doing Graph Theory》从具体问题出发，介绍图、路径、树、匹配与染色等内容，各章配有习题，可作为图论入门读物。</p> <p><a href="/files/graph-theory/start-doing-gra

https://txj2006.github.io/2026/10/23/2026-10-23-reading-hatcher-chapter-1-fundamental-group/ 2026-10-23T02:00:00.000Z 2026-11-01T12:43:21.413Z

A close reading of Hatcher §1.1, pp. 25–27: paths, endpoint-fixed homotopies, homotopy classes, and full proofs of the group axioms

https://txj2006.github.io/2026/10/17/2026-10-17-writing-sample/ 2026-10-17T01:00:00.000Z 2026-11-01T12:43:21.413Z

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Reading notes on quotient spaces, cell attachments, CW complexes, and the first attaching-map calculation

https://txj2006.github.io/2026/10/14/2026-10-14-supplement-weak-derivatives-sobolev/ 2026-10-14T02:10:00.000Z 2026-11-01T12:43:21.413Z

Reading notes on test functions, distributions, weak derivatives, Sobolev spaces, and weak formulations

https://txj2006.github.io/2026/10/14/2026-10-14-supplement-measure-lebesgue-lp/ 2026-10-14T02:00:00.000Z 2026-11-01T12:43:21.413Z

Reading notes on measurable spaces, Lebesgue integration, convergence, and Lp spaces

https://txj2006.github.io/2026/10/13/2026-10-13-reading-hatcher-chapter-0-homotopy/ 2026-10-13T02:00:00.000Z 2026-11-01T12:43:21.413Z

Reading notes on homotopy, retractions, deformation retractions, and homotopy equivalence