├── .editorconfig ├── .gitattributes ├── .github ├── ISSUE_TEMPLATE │ └── 发现笔误.md └── workflows │ └── latex.yml ├── .gitignore ├── .vscode ├── keybindings.json └── settings.json ├── README.md ├── chinese-emph.sty ├── chinese-footnote.sty ├── contact_me_via_wechat.svg ├── copy.sh ├── makefile ├── math-arc.sty ├── math-graph.sty ├── math-operator.sty ├── math-set.sty ├── math-tuple.sty ├── math.bib ├── math.tex ├── miskatonic-university.jpg ├── my-math-note.sty ├── natural-set.sty ├── parts ├── 几何学.tex ├── 初等数学.tex ├── 前言.tex ├── 单变量微积分.tex ├── 复分析.tex ├── 多变量微积分.tex ├── 封面.tex ├── 抽象代数.tex ├── 拓扑学.tex ├── 数值分析.tex ├── 概率论与数理统计.tex ├── 测度论.tex ├── 线性代数.tex ├── 线性代数1.tex ├── 线性代数2.tex ├── 组合学.tex ├── 附录.tex └── 集合论.tex ├── print_used_latex_packages.py ├── push.sh ├── release.sh ├── setup-remote.sh ├── stat.sh ├── tex-input-check.py ├── tex-linter.py ├── 几何学 ├── 平面几何.tex ├── 欧氏几何.tex ├── 欧氏几何 │ └── 欧氏公理 │ │ ├── 关联公理.tex │ │ ├── 关联公理和顺序公理的推论.tex │ │ ├── 几何元素和五组公理.tex │ │ ├── 合同公理.tex │ │ ├── 合同公理的推论.tex │ │ ├── 平行公理.tex │ │ ├── 连续公理.tex │ │ └── 顺序公理.tex ├── 解析几何.tex └── 解析几何 │ ├── 二次曲线方程 │ ├── 二次曲线方程的不变量.tex │ ├── 二次曲线方程的切线.tex │ ├── 二次曲线方程的化简及其类型.tex │ ├── 二次曲线方程的对称中心.tex │ ├── 二次曲线方程的直径和对称轴.tex │ └── 引言.tex │ ├── 几何空间的线性结构和度量结构 │ ├── 几何空间的线性结构.tex │ ├── 向量及其线性运算.tex │ ├── 向量的内积.tex │ ├── 向量的外积.tex │ ├── 向量的混合积.tex │ └── 本章总结.tex │ ├── 坐标变换 │ ├── 代数曲面.tex │ ├── 平面的仿射坐标变换.tex │ ├── 平面的直角坐标变换.tex │ ├── 空间的仿射坐标变换.tex │ └── 空间的直角坐标变换.tex │ ├── 射影平面和射影变换 │ ├── 射影坐标及其变换.tex │ ├── 射影平面.tex │ ├── 射影平面上的交比.tex │ ├── 射影平面上的对偶原理.tex │ ├── 射影映射.tex │ ├── 引言.tex │ └── 配极.tex │ ├── 常见曲面 │ ├── 二次曲面.tex │ ├── 曲面的交线.tex │ ├── 柱面和锥面.tex │ ├── 球面和旋转面.tex │ └── 直纹面.tex │ ├── 平面二次曲线及其方程 │ ├── 双曲线.tex │ ├── 圆.tex │ ├── 抛物线.tex │ └── 椭圆.tex │ ├── 平面和直线 │ ├── 仿射坐标系中平面的方程.tex │ ├── 几何元素之间的度量关系.tex │ ├── 直线的方程.tex │ └── 直角坐标系中平面的方程.tex │ └── 正交变换和仿射变换 │ ├── 二次曲线的正交分类和仿射分类.tex │ ├── 几何空间的正交变换和仿射变换.tex │ ├── 图形的度量性质和仿射性质.tex │ ├── 平面的仿射变换.tex │ └── 平面的正交变换.tex ├── 初等数学 ├── 不等式 │ ├── 不等式的概念与性质.tex │ ├── 不等式的证明.tex │ └── 常见不等式.tex ├── 函数 │ ├── 三角函数.tex │ ├── 其他常见函数.tex │ ├── 函数的性质.tex │ ├── 函数的概念.tex │ ├── 初等函数.tex │ ├── 双曲函数.tex │ ├── 反三角函数.tex │ ├── 反函数与复合函数.tex │ ├── 取整函数.tex │ ├── 幂函数.tex │ ├── 幂指函数.tex │ ├── 抽象函数.tex │ ├── 符号函数.tex │ ├── 绝对值函数.tex │ └── 隐函数.tex ├── 初等代数.tex ├── 初等数论.tex ├── 复数.tex ├── 数列.tex └── 算术基础.tex ├── 复分析 ├── 复变函数.tex ├── 复数.tex ├── 留数定理 │ ├── 利用留数定理计算实积分.tex │ ├── 留数定理.tex │ └── 辐角原理及其应用.tex ├── 解析函数.tex ├── 解析函数的积分表示.tex ├── 解析函数的积分表示 │ ├── 复变函数的积分.tex │ ├── 柯西积分公式.tex │ ├── 柯西积分定理.tex │ └── 解析函数与调和函数的关系.tex └── 解析函数的级数表示 │ ├── 函数项级数.tex │ ├── 常数项级数.tex │ ├── 幂级数.tex │ ├── 解析函数在孤立奇点附近的性态.tex │ ├── 解析函数的泰勒展开式.tex │ └── 解析函数的罗朗展开式.tex ├── 实分析基础.tex ├── 微积分 ├── 不定积分 │ ├── 不定积分的概念与性质.tex │ ├── 分部积分法.tex │ ├── 换元积分法.tex │ ├── 有理函数的积分.tex │ └── 本章总结.tex ├── 偏微分方程.tex ├── 函数图形的绘制 │ ├── 单调性和凹凸性.tex │ ├── 曲率.tex │ ├── 本章总结.tex │ ├── 极值和最值.tex │ └── 渐近线.tex ├── 函数极限 │ ├── 函数极限的性质.tex │ ├── 函数极限的概念.tex │ ├── 函数极限的运算.tex │ ├── 分类 │ │ ├── 基上的极限.tex │ │ ├── 自变量趋于无穷大时函数的极限.tex │ │ └── 自变量趋于有限值时函数的极限.tex │ ├── 夹逼准则.tex │ ├── 收敛准则.tex │ ├── 无穷小与无穷大.tex │ ├── 本章总结.tex │ └── 海涅定理.tex ├── 函数项级数 │ ├── 一致收敛级数的判别和性质.tex │ ├── 一般周期函数的傅里叶级数.tex │ ├── 傅里叶级数.tex │ ├── 函数展开成幂级数.tex │ ├── 函数的幂级数展开式的应用.tex │ ├── 函数项级数.tex │ ├── 幂级数.tex │ ├── 本章总结.tex │ └── 蔡塔函数.tex ├── 卷积分.tex ├── 反常积分 │ ├── 伽马函数.tex │ ├── 反常积分的审敛法.tex │ ├── 无界函数的反常积分.tex │ ├── 无穷限的反常积分.tex │ ├── 本章总结.tex │ ├── 柯西主值积分.tex │ └── 贝塔函数.tex ├── 多元函数微分法 │ ├── 一元向量值函数及其微积分.tex │ ├── 二元函数的泰勒公式.tex │ ├── 偏导数.tex │ ├── 全微分.tex │ ├── 多元函数微分学的几何应用 │ │ ├── 曲面的切平面与法线.tex │ │ ├── 空间曲线的切线与法平面.tex │ │ └── 空间曲线的曲率.tex │ ├── 多元函数的极值.tex │ ├── 多元函数的极限.tex │ ├── 多元函数的连续性.tex │ ├── 多元复合函数的求导法则.tex │ ├── 方向导数和梯度.tex │ ├── 最小二乘法.tex │ ├── 隐函数的求导公式.tex │ ├── 雅克比矩阵.tex │ └── 黑森矩阵.tex ├── 定积分 │ ├── 分部积分法.tex │ ├── 定积分的应用.tex │ ├── 定积分的概念与性质.tex │ ├── 微积分基本公式.tex │ ├── 换元积分法.tex │ ├── 本章总结.tex │ ├── 积分不等式.tex │ └── 面积原理.tex ├── 导数与微分 │ ├── 函数的求导法则.tex │ ├── 导数的基本概念.tex │ ├── 微分.tex │ ├── 本章总结.tex │ ├── 隐函数的导数.tex │ └── 高阶导数.tex ├── 常数项级数 │ ├── 交错级数及其审敛法.tex │ ├── 常数项级数的概念和性质.tex │ ├── 无穷乘积.tex │ ├── 本章总结.tex │ ├── 正项级数及其审敛法.tex │ ├── 绝对收敛与条件收敛.tex │ └── 阿贝尔-狄利克雷审敛法.tex ├── 微分中值定理 │ ├── 微分中值定理.tex │ ├── 本章总结.tex │ ├── 泰勒中值定理.tex │ ├── 洛必达法则.tex │ └── 线性插值.tex ├── 微分方程 │ ├── 一阶微分方程.tex │ ├── 二阶常系数非齐次线性微分方程.tex │ ├── 二阶常系数齐次线性微分方程.tex │ ├── 可降阶的高阶微分方程.tex │ ├── 常系数线性微分方程组的解法.tex │ ├── 微分方程的基本概念.tex │ ├── 微分方程的解的存在性和唯一性.tex │ ├── 本章总结.tex │ ├── 欧拉方程.tex │ └── 高阶线性微分方程的解的结构.tex ├── 数列极限 │ ├── 夹逼准则.tex │ ├── 实数公理.tex │ ├── 收敛准则.tex │ ├── 数列极限的四则运算.tex │ ├── 数列极限的性质.tex │ ├── 数列极限的概念.tex │ ├── 施托尔茨定理.tex │ └── 无穷小与无穷大.tex ├── 极限 │ ├── 函数的连续性与间断点.tex │ └── 极限存在准则.tex ├── 积分变换.tex ├── 线积分与面积分 │ ├── 两类曲线积分之间的联系.tex │ ├── 两类曲面积分之间的联系.tex │ ├── 对坐标的曲线积分.tex │ ├── 对坐标的曲面积分.tex │ ├── 对弧长的曲线积分.tex │ ├── 对面积的曲面积分.tex │ ├── 斯托克斯公式.tex │ ├── 本章总结.tex │ ├── 格林公式.tex │ └── 高斯公式.tex ├── 连续函数 │ ├── 函数的一致连续性.tex │ ├── 连续函数.tex │ ├── 连续函数的运算.tex │ ├── 迭代数列的敛散性.tex │ └── 闭区间上的连续函数.tex └── 重积分 │ ├── 三重积分.tex │ ├── 二重积分.tex │ ├── 含参变量的积分.tex │ ├── 多重积分的一般性理论.tex │ ├── 本章总结.tex │ ├── 积分不等式.tex │ └── 重积分的应用.tex ├── 抽象代数 ├── 域 │ └── 域.tex ├── 格 │ ├── 偏序格.tex │ ├── 分配格.tex │ └── 有补格.tex ├── 环 │ ├── 体.tex │ ├── 同构同态.tex │ ├── 环.tex │ └── 连加与连乘.tex └── 群 │ ├── 同态.tex │ ├── 同构.tex │ ├── 子群.tex │ ├── 正规子群.tex │ └── 群.tex ├── 拓扑学 └── 点集拓扑学 │ ├── 分离性 │ ├── 分离性公理.tex │ ├── 可度量化空间.tex │ ├── 完全正则空间.tex │ ├── 扩张定理.tex │ ├── 正则空间.tex │ └── 豪斯多夫空间.tex │ ├── 压缩映射原理 │ └── 压缩映射原理.tex │ ├── 可数性 │ ├── 可分空间.tex │ ├── 可数性公理.tex │ └── 林德洛夫空间.tex │ ├── 子空间-积空间-商空间 │ ├── 一般情形下的积空间.tex │ ├── 商空间.tex │ ├── 子空间.tex │ └── 有限情形下的积空间.tex │ ├── 完备度量空间 │ ├── 度量空间的完备化.tex │ └── 度量空间的完备性与紧致性.tex │ ├── 拓扑空间与连续映射 │ ├── 基.tex │ ├── 序列.tex │ ├── 度量空间.tex │ ├── 拓扑空间.tex │ └── 点的分类.tex │ ├── 映射空间 │ ├── 一致收敛拓扑.tex │ ├── 点式收敛拓扑.tex │ └── 紧致开拓扑.tex │ ├── 紧致性 │ ├── 几种紧致性.tex │ ├── 局部紧致空间.tex │ ├── 度量空间中的紧致性.tex │ ├── 拓扑空间在方体中的嵌入.tex │ ├── 提赫诺夫乘积定理.tex │ ├── 欧氏空间中的紧致子集.tex │ ├── 紧致性与分离性.tex │ └── 紧致空间.tex │ └── 连通性 │ ├── 局部连通空间.tex │ ├── 连通分支.tex │ ├── 连通性的某些简单应用.tex │ ├── 连通空间.tex │ └── 道路连通空间.tex ├── 数值分析 ├── README.md ├── 函数逼近 │ ├── 函数逼近.tex │ ├── 曲线拟合的最小二乘法.tex │ ├── 最佳平方逼近.tex │ └── 正交多项式.tex ├── 引论 │ ├── 数值分析的对象、作用与特点.tex │ ├── 数值计算中算法设计的技术.tex │ ├── 数值计算的误差.tex │ └── 误差定性分析与避免误差危害.tex ├── 插值法 │ ├── 三次样条插值.tex │ ├── 分段低次插值.tex │ ├── 厄米插值 │ │ └── 厄米插值.tex │ ├── 引论.tex │ ├── 拉格朗日插值.tex │ └── 牛顿插值.tex ├── 数值微分 │ └── 数值微分.tex ├── 数值积分 │ ├── 机械求积公式 │ │ ├── romberg_integral.py │ │ ├── 复合求积公式.tex │ │ ├── 数值积分.tex │ │ ├── 柯特斯公式.tex │ │ └── 龙贝格求积公式.tex │ └── 高斯求积公式 │ │ └── 高斯求积公式.tex ├── 用直接法求线性方程组的数值解 │ ├── 误差分析.tex │ └── 高斯消元法.tex └── 用间接法求线性方程组的数值解 │ ├── 一般理论.tex │ ├── 超松弛迭代法.tex │ ├── 雅克比迭代法.tex │ └── 高斯--塞德尔迭代法.tex ├── 未分类 └── 上图像.tex ├── 概率论与数理统计 ├── 假设检验.tex ├── 参数估计 │ ├── 区间估计.tex │ ├── 含有隐变量的参数估计问题.tex │ ├── 引言.tex │ ├── 本章总结.tex │ ├── 极大似然估计法.tex │ ├── 点估计量的评选标准.tex │ └── 矩估计法.tex ├── 多维随机变量及其分布 │ ├── 二维分布.tex │ ├── 二维随机变量函数的分布.tex │ ├── 分布的可加性.tex │ ├── 多维分布.tex │ ├── 最值分布.tex │ ├── 本章总结.tex │ ├── 条件分布.tex │ └── 边缘分布.tex ├── 极限定理.tex ├── 概率论基础 │ ├── 事件发生的概率.tex │ ├── 事件的独立性及伯努利概型.tex │ ├── 条件概率.tex │ ├── 样本空间与随机事件.tex │ └── 等可能概型.tex ├── 概率论的公理化.tex ├── 线性回归分析和方差分析.tex ├── 统计量及其分布 │ ├── 充分统计量.tex │ ├── 常见统计分布.tex │ ├── 总体与样本.tex │ ├── 本章总结.tex │ ├── 次序统计量及其分布.tex │ └── 统计量与抽样分布.tex ├── 自然指数分布族.tex ├── 随机变量及其分布 │ ├── 离散型随机变量及其分布.tex │ ├── 连续型随机变量及其分布.tex │ ├── 随机变量及其分布函数.tex │ └── 随机变量的函数的分布.tex ├── 随机变量的数字特征 │ ├── 偏度.tex │ ├── 协方差.tex │ ├── 变异系数.tex │ ├── 峰度.tex │ ├── 数学期望.tex │ ├── 方差.tex │ ├── 本章总结.tex │ ├── 条件期望.tex │ ├── 相关系数.tex │ └── 矩.tex └── 随机过程 │ ├── CK方程.tex │ ├── 随机过程.tex │ └── 马尔可夫链.tex ├── 测度论 └── 测度.tex ├── 线性代数 ├── lambda矩阵 │ ├── LambdaMatrix.py │ └── lambda矩阵.tex ├── 二次型 │ ├── 二次型.tex │ ├── 二次型化为标准型.tex │ ├── 二次型的应用.tex │ ├── 实二次型的分类.tex │ ├── 本章总结.tex │ └── 矩阵合同的概念.tex ├── 仿射几何与射影几何 │ ├── 仿射几何.tex │ ├── 仿射空间.tex │ └── 射影几何.tex ├── 内积空间 │ ├── 双线性函数.tex │ ├── 对称变换.tex │ ├── 欧几里得空间.tex │ ├── 正交变换.tex │ ├── 正交补.tex │ ├── 辛空间.tex │ └── 酉空间.tex ├── 向量与矩阵.tex ├── 向量与矩阵 │ ├── 分块矩阵的运算.tex │ ├── 向量的内积.tex │ ├── 特殊矩阵.tex │ └── 矩阵的乘法.tex ├── 向量空间 │ ├── 向量空间.tex │ ├── 向量空间及其子空间的基与维数.tex │ ├── 向量组的秩.tex │ ├── 向量组的线性相关性.tex │ ├── 本章总结.tex │ ├── 矩阵乘积的秩.tex │ ├── 矩阵的秩.tex │ ├── 线性方程组与向量空间的联系.tex │ ├── 线性方程组有解的充分必要条件.tex │ ├── 西尔维斯特不等式.tex │ ├── 非齐次线性方程组的解集的结构.tex │ └── 齐次线性方程组的解集的结构.tex ├── 多项式 │ ├── 不可约多项式.tex │ ├── 剩余类环.tex │ ├── 多元多项式环.tex │ ├── 多项式.tex │ ├── 多项式的根.tex │ ├── 实数域上的不可约多项式.tex │ ├── 对称多项式.tex │ ├── 整除性.tex │ ├── 最大公因式.tex │ ├── 最小公倍式.tex │ ├── 有理数域上的不可约多项式.tex │ └── 重因式.tex ├── 特征值与特征向量 │ ├── 实反对称矩阵的相似对角化.tex │ ├── 实对称矩阵的相似对角化.tex │ ├── 幺正矩阵.tex │ ├── 正交矩阵.tex │ ├── 正交规范化方法.tex │ ├── 正规矩阵.tex │ ├── 特征值与特征向量.tex │ ├── 矩阵的分解.tex │ ├── 矩阵的相似.tex │ ├── 矩阵的相似对角化.tex │ └── 矩阵的迹.tex ├── 矩阵的逆 │ ├── 初等矩阵.tex │ ├── 可逆矩阵.tex │ ├── 广义初等变换.tex │ ├── 广义逆.tex │ ├── 应用初等变换求解逆矩阵.tex │ ├── 本章总结.tex │ └── 舒尔定理.tex ├── 矩阵论 │ └── 张量积.tex ├── 线性方程组 │ ├── 克拉默法则.tex │ ├── 消元法.tex │ └── 线性方程组.tex ├── 线性映射 │ ├── 哈密顿凯莱定理.tex │ ├── 幂零变换的结构.tex │ ├── 线性函数与对偶空间.tex │ ├── 线性变换的不变子空间.tex │ ├── 线性变换的最小多项式.tex │ ├── 线性变换的特征值与特征向量.tex │ ├── 线性变换的若尔当标准型.tex │ ├── 线性映射.tex │ ├── 线性映射的核与像.tex │ └── 线性映射的矩阵表示.tex ├── 线性空间 │ ├── 商空间.tex │ ├── 子空间.tex │ ├── 线性空间的同构.tex │ └── 线性空间的结构.tex ├── 行列式 │ ├── 排列与逆序数.tex │ ├── 本章总结.tex │ ├── 柯西比内公式.tex │ ├── 矩阵乘积的行列式.tex │ ├── 行列式.tex │ └── 行列式的展开.tex └── 赋范线性空间 │ └── 范数.tex ├── 组合学 ├── 图论 │ ├── 哈密顿图.tex │ ├── 图.tex │ ├── 图的矩阵表示.tex │ ├── 图的连通性.tex │ ├── 子图.tex │ ├── 平面图.tex │ ├── 无向树.tex │ ├── 有向树.tex │ ├── 欧拉图.tex │ ├── 赋权图.tex │ ├── 路.tex │ └── 顶点度数.tex └── 排列与组合.tex ├── 附录 ├── 参考文献.tex ├── 常见平面曲线.tex ├── 积分表.tex ├── 素数表.tex └── 译名对照表.tex └── 集合论 ├── 基数 ├── 可数集.tex ├── 基数排序.tex ├── 基数算术.tex ├── 无限基数算术.tex ├── 有限集.tex ├── 等势.tex ├── 连续统假设.tex └── 选择公理.tex ├── 数理逻辑.tex ├── 数系构造.tex ├── 数系构造 ├── 实数.tex ├── 整数.tex ├── 有理数.tex └── 自然数.tex ├── 集合论.tex └── 集合论 ├── 关系.tex ├── 排序关系.tex ├── 无穷直积.tex ├── 映射.tex ├── 等价关系.tex ├── 类.tex ├── 集合代数.tex └── 集合公理.tex /.editorconfig: 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