查看“︁学科导航”︁的源代码

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本站按 12 个主要学习方向组织数学知识。每个入口至少有三篇展开讲解的核心词条，包含定义条件、证明与算例；多个入口可以通向同一个概念。

<div class="math-subject-grid">
<div class="math-subject"><div class="math-subject-number">01</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">∀</span><div><h3 class="math-subject-title">[[:分类:基础与逻辑|基础与逻辑]]</h3><p class="math-subject-description">从集合、映射与推理，学会准确表达数学。</p></div></div><div class="math-subject-links">[[集合]] / [[函数]] / [[逻辑]] / [[皮亚诺公理]]</div></div>
<div class="math-subject"><div class="math-subject-number">02</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">A</span><div><h3 class="math-subject-title">[[:分类:代数|代数]]</h3><p class="math-subject-description">理解线性结构、运算规律与对称。</p></div></div><div class="math-subject-links">[[矩阵]] / [[向量空间]] / [[线性代数]] / [[群]] / [[柯西不等式]]</div></div>
<div class="math-subject"><div class="math-subject-number">03</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">ℤ</span><div><h3 class="math-subject-title">[[:分类:数论|数论]]</h3><p class="math-subject-description">在整数、素数与余数中寻找规律。</p></div></div><div class="math-subject-links">[[整数整除]] / [[素数]] / [[同余]]</div></div>
<div class="math-subject"><div class="math-subject-number">04</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">△</span><div><h3 class="math-subject-title">[[:分类:几何|几何]]</h3><p class="math-subject-description">把形状的直观转化为可证明的关系。</p></div></div><div class="math-subject-links">[[欧氏几何]] / [[勾股定理]] / [[圆锥曲线]] / [[余弦定理]] / [[海伦公式]]</div></div>
<div class="math-subject"><div class="math-subject-number">05</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">○</span><div><h3 class="math-subject-title">[[:分类:拓扑|拓扑]]</h3><p class="math-subject-description">研究连续变化下保留的空间结构。</p></div></div><div class="math-subject-links">[[拓扑空间]] / [[连续映射]] / [[环面]]</div></div>
<div class="math-subject"><div class="math-subject-number">06</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">∫</span><div><h3 class="math-subject-title">[[:分类:分析|分析]]</h3><p class="math-subject-description">用极限理解局部变化与累积。</p></div></div><div class="math-subject-links">[[极限]] / [[导数]] / [[积分]] / [[微积分]] / [[欧拉公式]]</div></div>
<div class="math-subject"><div class="math-subject-number">07</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">∂</span><div><h3 class="math-subject-title">[[:分类:微分方程与动力系统|微分方程与动力系统]]</h3><p class="math-subject-description">从变化规律重建随时间演化的状态。</p></div></div><div class="math-subject-links">[[微分方程]] / [[一阶线性微分方程]] / [[洛吉斯蒂模型]] / [[差分方程模型]] / [[捕食者-猎物模型]]</div></div>
<div class="math-subject"><div class="math-subject-number">08</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">P</span><div><h3 class="math-subject-title">[[:分类:概率与统计|概率与统计]]</h3><p class="math-subject-description">描述随机现象，并解释数据支持什么结论。</p></div></div><div class="math-subject-links">[[统计图]] / [[概率分布]] / [[概率]] / [[期望]] / [[贝叶斯定理]] / [[统计推断]]</div></div>
<div class="math-subject"><div class="math-subject-number">09</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">G</span><div><h3 class="math-subject-title">[[:分类:离散数学|离散数学]]</h3><p class="math-subject-description">在计数、网络和有限结构中训练证明。</p></div></div><div class="math-subject-links">[[逻辑]] / [[组合数学]] / [[图论]] / [[抽屉原理]]</div></div>
<div class="math-subject"><div class="math-subject-number">10</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">≈</span><div><h3 class="math-subject-title">[[:分类:数值分析|数值分析]]</h3><p class="math-subject-description">控制近似计算的误差与稳定性。</p></div></div><div class="math-subject-links">[[二分法]] / [[牛顿法]] / [[数值积分]]</div></div>
<div class="math-subject"><div class="math-subject-number">11</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">min</span><div><h3 class="math-subject-title">[[:分类:优化与运筹|优化与运筹]]</h3><p class="math-subject-description">在约束下选择方案，并给出最优性证据。</p></div></div><div class="math-subject-links">[[优化]] / [[线性规划]] / [[最短路径]]</div></div>
<div class="math-subject"><div class="math-subject-number">12</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">↔</span><div><h3 class="math-subject-title">[[:分类:应用与建模|应用与建模]]</h3><p class="math-subject-description">让假设、数据、方程与验证形成闭环。</p></div></div><div class="math-subject-links">[[数学建模]] / [[最小二乘法]] / [[量纲分析]] / [[线性模型]]</div></div>
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== 这套分类怎样使用 ==
这是一套面向学习的导航，不是互斥分类，也不宣称覆盖全部数学研究分支。数论、几何、代数和分析之间有大量交叉；数值分析、优化与建模也会同时使用不同理论工具。研究文献中的更细分类可参见 [https://msc2020.org/ Mathematics Subject Classification 2020（MSC2020）]；本站不把尚未建立词条的细类包装成已有内容。

初读可以沿[[学习路径]]前进，也可以从一个具体问题反向查找先修概念。词条把具体算例、逐步推导与图解接在一起；阅读时可以先重算例子，再对照一般结论。

== 阅读与编写工具 ==
* [[希腊字母发音表]]：24 个字母的大小写、英美音标、词典试听与数学用法。
* [[帮助:词条写作标准]]：本站关于深度、证明、算例、历史、来源与图解审校的统一要求。
* [[格致开物:关于|AI 生成与内容核验说明]]：了解内容来源与核验范围。