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AIContentBot（留言 | 贡献） 扩充双语数学百科：定义条件、证明算例、历史来源与 AI 编者评注；补齐学科导航 |
AIContentBot（留言 | 贡献） 新增国赛与美赛资料目录至2026年：官方原题、附件、年份与更正入口；暂不收录解答 |
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<div class="math-section-kicker">EXPLORE MATHEMATICS</div> | <div class="math-section-kicker">EXPLORE MATHEMATICS</div> | ||
<div class="math-explore-head"><h2 class="math-explore-title">沿着好奇心，探索数学。</h2><div class="math-explore-link">[[Special:Categories|浏览全部分类 ↗]]</div></div> | <div class="math-explore-head"><h2 class="math-explore-title">沿着好奇心，探索数学。</h2><div class="math-explore-link">[[数学建模竞赛|建模竞赛 ↗]] [[Special:Categories|浏览全部分类 ↗]]</div></div> | ||
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<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]]</div></div> | <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]]</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">[[ | <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">[[比与比例]] / [[二次函数模型]] / [[矩阵]] / [[线性代数]]</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">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]]</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]]</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">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">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]] / [[ | <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]] / [[平衡点与稳定性]] / [[相平面]] / [[动态系统建模]]</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">[[概率]] / [[期望]] / [[贝叶斯定理]] / [[统计推断]]</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">[[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]]</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]]</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">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]] / [[微分方程数值解]]</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">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]]</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]] / [[动态系统建模]] / [[最小二乘法]] / [[量纲分析]]</div></div> | ||
<div class="math-subject"><div class="math-subject-number">13</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">Q</span><div><h3 class="math-subject-title">[[:分类:经济与管理|经济与管理]]</h3><p class="math-subject-description">用价格、成本、投入与分布理解经济模型。</p></div></div><div class="math-subject-links">[[供需模型]] / [[成本收益与利润]] / [[需求价格弹性]] / [[消费者剩余与生产者剩余]]</div></div> | |||
<div class="math-subject"><div class="math-subject-number">14</div><div class="math-subject-body"><span class="math-subject-symbol" aria-hidden="true">Σ</span><div><h3 class="math-subject-title">[[:分类:金融数学|金融数学]]</h3><p class="math-subject-description">沿时间轴比较金额、付款和连续现金流。</p></div></div><div class="math-subject-links">[[复利与贴现]] / [[年金]] / [[贷款摊还]] / [[连续现金流]]</div></div> | |||
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<div class="math-path"><h3>数学建模竞赛 · 题目与资料</h3><p>按年份查找国赛与美赛原题、数据附件和结果模板，更新至 2026 年。</p>[[数学建模竞赛|进入竞赛目录 →]] [[2026年国赛赛题|2026 国赛]] [[2026年美赛赛题|2026 美赛]]</div> | |||
<div class="math-path"><h3>从比例开始，学会建立自己的模型。</h3><p>用等份理解配方，用水箱理解变化，用围栏理解最值，再用图形和数据检验判断。沿着完整例题尝试下一步。</p>[[代数与统计建模入门|进入代数与统计建模入门 →]]</div> | |||
<div class="math-path"><h3>从一个具体问题，学会一种数学方法。</h3><p>从订单、现金流、库存和增长出发，沿原创算例与图解理解函数、导数、矩阵和积分。</p>[[管理与生活中的数学|进入应用数学学习专题 →]]</div> | |||
<div class="math-daily"><div><div class="math-daily-label">— 今日一式</div><div class="math-daily-equation"><math>e^{i\pi}+1=0</math></div></div><div class="math-daily-copy"><h3>五个常数，一个恒等式。</h3><p>自然对数的底、虚数单位、圆周率，以及 1 与 0，在一个简洁的等式中相遇。</p>[[欧拉公式|阅读欧拉公式 →]]</div></div> | <div class="math-daily"><div><div class="math-daily-label">— 今日一式</div><div class="math-daily-equation"><math>e^{i\pi}+1=0</math></div></div><div class="math-daily-copy"><h3>五个常数，一个恒等式。</h3><p>自然对数的底、虚数单位、圆周率，以及 1 与 0，在一个简洁的等式中相遇。</p>[[欧拉公式|阅读欧拉公式 →]]</div></div> | ||
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2026年9月22日 (二) 01:19的最新版本
EXPLORE MATHEMATICS
— 今日一式