https://echo.ishian.me/tags/math/Recent content in math on IshianHugoenMon, 05 May 2025 00:00:00 +0000https://echo.ishian.me/2025/05/05/probability-rdnvar/Mon, 05 May 2025 00:00:00 +0000https://echo.ishian.me/2025/05/05/probability-rdnvar/汇总常见离散与连续随机变量的分布、期望与方差推导及高阶矩结论https://echo.ishian.me/2025/04/22/algo-prime-selection/Tue, 22 Apr 2025 00:00:00 +0000https://echo.ishian.me/2025/04/22/algo-prime-selection/讲解埃氏筛与欧拉筛两种质数筛法的原理、实现及时间复杂度https://echo.ishian.me/2025/04/20/algo-math-ext-euler-theorem/Sun, 20 Apr 2025 00:00:00 +0000https://echo.ishian.me/2025/04/20/algo-math-ext-euler-theorem/陈述并证明扩展欧拉定理，用于快速模幂中不互素情形的降幂https://echo.ishian.me/2024/11/14/matlab-beginner/Thu, 14 Nov 2024 00:00:00 +0000https://echo.ishian.me/2024/11/14/matlab-beginner/介绍 MATLAB 基本语法、常用命令与向量矩阵算术操作https://echo.ishian.me/2024/11/01/concretemath-special-coefficient/Fri, 01 Nov 2024 00:00:00 +0000https://echo.ishian.me/2024/11/01/concretemath-special-coefficient/讲解二项式系数的性质、母函数运算及第二类斯特林数等特殊系数https://echo.ishian.me/2024/10/16/concretemath-rounding/Wed, 16 Oct 2024 00:00:00 +0000https://echo.ishian.me/2024/10/16/concretemath-rounding/讲解上下取整函数的性质、区间整数计数、谱系划分及均分分组等应用https://echo.ishian.me/2024/10/02/concretemath-summation/Wed, 02 Oct 2024 00:00:00 +0000https://echo.ishian.me/2024/10/02/concretemath-summation/讲解和式的表示方法与清单法、求和因子法、扰动法等求和技巧及多重和式https://echo.ishian.me/2024/09/27/discretemath-abstract-algebra/Fri, 27 Sep 2024 00:00:00 +0000https://echo.ishian.me/2024/09/27/discretemath-abstract-algebra/讲解半群、群、子群、循环群及环、域等近世代数结构的定义与性质https://echo.ishian.me/2024/09/21/concretemath-recursion/Sat, 21 Sep 2024 00:00:00 +0000https://echo.ishian.me/2024/09/21/concretemath-recursion/讲解递归函数与数学归纳法，分析汉诺塔、直线划分平面等经典递归问题https://echo.ishian.me/2024/08/07/discretemath-algebra-system/Wed, 07 Aug 2024 00:00:00 +0000https://echo.ishian.me/2024/08/07/discretemath-algebra-system/讲解代数系统的定义、二元运算的性质及幺元、零元、逆元等特殊元素https://echo.ishian.me/2024/05/31/linearalgebra-rank/Fri, 31 May 2024 00:00:00 +0000https://echo.ishian.me/2024/05/31/linearalgebra-rank/介绍矩阵秩的性质及其在向量组与线性方程组中的应用https://echo.ishian.me/2024/05/20/linearalgebra-analytic-geometry/Mon, 20 May 2024 00:00:00 +0000https://echo.ishian.me/2024/05/20/linearalgebra-analytic-geometry/介绍向量的线性表示与运算、平面/空间直线方程及二次曲面https://echo.ishian.me/2024/05/14/linearalgebra-determinant/Tue, 14 May 2024 00:00:00 +0000https://echo.ishian.me/2024/05/14/linearalgebra-determinant/介绍行列式的结论与特殊行列式、消零等运算技巧https://echo.ishian.me/2024/05/11/linearalgebra-matrix/Sat, 11 May 2024 00:00:00 +0000https://echo.ishian.me/2024/05/11/linearalgebra-matrix/介绍矩阵的概念、运算、转置、分块与初等变换https://echo.ishian.me/2024/04/23/calculus-multivar-diff/Tue, 23 Apr 2024 00:00:00 +0000https://echo.ishian.me/2024/04/23/calculus-multivar-diff/讲解多元函数的二重极限、连续性、偏导与全微分及其应用https://echo.ishian.me/2024/04/20/calculus-diff-equation/Sat, 20 Apr 2024 00:00:00 +0000https://echo.ishian.me/2024/04/20/calculus-diff-equation/讲解常微分方程的基本概念与分离变量法等初等解法，并附例题https://echo.ishian.me/2024/04/17/calculus-series-exercise/Wed, 17 Apr 2024 00:00:00 +0000https://echo.ishian.me/2024/04/17/calculus-series-exercise/整理常数项级数敛散性判别与幂级数求和的解题思路和常用结论https://echo.ishian.me/2024/04/14/calculus-series/Sun, 14 Apr 2024 00:00:00 +0000https://echo.ishian.me/2024/04/14/calculus-series/讲解常数项级数的敛散性、常见级数、性质及幂级数的相关概念https://echo.ishian.me/2023/12/11/calculus-exercise-1/Mon, 11 Dec 2023 00:00:00 +0000https://echo.ishian.me/2023/12/11/calculus-exercise-1/微积分极限与积分的计算练习题集，附详细求解过程https://echo.ishian.me/2023/12/03/calculus-improper-int/Sun, 03 Dec 2023 00:00:00 +0000https://echo.ishian.me/2023/12/03/calculus-improper-int/讲解无穷区间与无界函数两类反常积分的计算方法及敛散性判断https://echo.ishian.me/2023/11/28/calculus-definite-int/Tue, 28 Nov 2023 00:00:00 +0000https://echo.ishian.me/2023/11/28/calculus-definite-int/整理定积分的定义、可积条件、性质与积分中值定理https://echo.ishian.me/2023/11/12/calculus-indefinite-int/Sun, 12 Nov 2023 00:00:00 +0000https://echo.ishian.me/2023/11/12/calculus-indefinite-int/整理不定积分的基本公式、拓展公式、凑微分与换元等积分方法https://echo.ishian.me/2023/11/05/calculus-limit-exercise/Sun, 05 Nov 2023 00:00:00 +0000https://echo.ishian.me/2023/11/05/calculus-limit-exercise/极限练习题集，讲解数列极限存在性证明与极限不存在的判定方法https://echo.ishian.me/2023/10/30/calculus-limitation/Mon, 30 Oct 2023 00:00:00 +0000https://echo.ishian.me/2023/10/30/calculus-limitation/整理极限求解的注意事项与常见题型，包括单调有界收敛定理与反函数求法