---
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title: 离散数学
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description: 计算机科学与技术等专业《离散数学》教学大纲、章节课件与复习专题讲义。内容涵盖命题逻辑、一阶逻辑、二元关系、等价与偏序、图论及代数结构。
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# 离散数学

《离散数学》是计算机类专业常见的基础课程，内容包括命题逻辑、一阶逻辑、二元关系和图论基础等。本页面提供章节课件与专题习题讲义下载。

<p class="mobile-desktop-hint">建议使用电脑桌面端访问，以获得更佳的课件浏览与下载体验。</p>

---

## 章节大纲与课件下载

### 第 1 章：命题逻辑

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">1.1</td>
      <td class="chap-title">命题符号化与联结词</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-1_Propositional_Symbolization_and_Connectives.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">1.2</td>
      <td class="chap-title">命题公式及其分类</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-2_Propositional_Formulas_and_Classification.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">1.3</td>
      <td class="chap-title">命题等值演算</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-3_Propositional_Equivalence_Calculus.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">1.4</td>
      <td class="chap-title">命题范式</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-4_Propositional_Normal_Forms.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">1.5</td>
      <td class="chap-title">命题逻辑推理理论</td>
      <td class="download-cell"><a :href="CDN_BASE + '/1-5_Inference_Theory.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
  </tbody>
</table>

### 第 2 章：一阶逻辑

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">2.1</td>
      <td class="chap-title">一阶逻辑的基本概念</td>
      <td class="download-cell"><a :href="CDN_BASE + '/2-1_Basic_Concepts_of_First_Order_Logic.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">2.2</td>
      <td class="chap-title">合式公式与解释</td>
      <td class="download-cell"><a :href="CDN_BASE + '/2-2_Well_Formed_Formulas_and_Interpretations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">2.3</td>
      <td class="chap-title">一阶逻辑等值演算与前束范式</td>
      <td class="download-cell"><a :href="CDN_BASE + '/2-3_Equivalence_Calculus_and_Prenex_Normal_Form_in_First_Order_Logic.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">2.4</td>
      <td class="chap-title">一阶逻辑形式推理理论</td>
      <td class="download-cell"><a :href="CDN_BASE + '/2-4_Formal_Inference_Theory_of_First_Order_Logic.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
  </tbody>
</table>

### 第 4 章：二元关系与函数

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">4.1</td>
      <td class="chap-title">笛卡尔积与二元关系</td>
      <td class="download-cell"><a :href="CDN_BASE + '/4-1_Cartesian_Product_Binary_Relations.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">4.2</td>
      <td class="chap-title">关系的运算、性质与闭包</td>
      <td class="download-cell"><a :href="CDN_BASE + '/4-2_Relation_Ops_Props_Closures.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">4.3</td>
      <td class="chap-title">等价关系与偏序关系</td>
      <td class="download-cell"><a :href="CDN_BASE + '/4-3_Equivalence_Partial_Order.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">第四章习题课与实践专题</td>
      <td class="download-cell"><a :href="CDN_BASE + '/4-4_Chapter4_Practice_Session.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">复习 PDF 📂</a></td>
    </tr>
  </tbody>
</table>

### 第 5 章：图论基础

<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">章节</th>
      <th style="width: 73%">知识要点</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td class="chap-num">5.1</td>
      <td class="chap-title">图的基本概念</td>
      <td class="download-cell"><a :href="CDN_BASE + '/5-1_Basic_Concepts_of_Graphs.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">5.2</td>
      <td class="chap-title">通路、连通性与矩阵表示</td>
      <td class="download-cell"><a :href="CDN_BASE + '/5-2_Paths_Connectivity_Representation.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">5.3</td>
      <td class="chap-title">最短路径算法</td>
      <td class="download-cell"><a :href="CDN_BASE + '/5-3_Shortest_Paths_Algorithms.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">5.4</td>
      <td class="chap-title">关键路径法</td>
      <td class="download-cell"><a :href="CDN_BASE + '/5-4_Critical_Path_Method.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
    <tr>
      <td class="chap-num">5.5</td>
      <td class="chap-title">图的着色问题</td>
      <td class="download-cell"><a :href="CDN_BASE + '/5-5_Graph_Coloring.pdf'" target="_blank" rel="noopener" class="btn-dl">PDF 📂</a></td>
    </tr>
  </tbody>
</table>

---

## 期末复习


<table class="academic-table">
  <thead>
    <tr>
      <th style="width: 12%">类型</th>
      <th style="width: 73%">资料名称</th>
      <th style="width: 15%; text-align: center;">授课课件 / 复习讲义</th>
    </tr>
  </thead>
  <tbody>
    <tr class="review-row">
      <td class="chap-num">样卷</td>
      <td class="chap-title font-review">期末复习参考样卷（学生自测版）</td>
      <td class="download-cell"><a :href="CDN_BASE + '/student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">下载 PDF 📂</a></td>
    </tr>
    <tr class="review-row">
      <td class="chap-num">复习</td>
      <td class="chap-title font-review">期末专题复习讲义</td>
      <td class="download-cell">
        <div class="dl-group">
          <a :href="CDN_BASE + '/final_review_handout_student.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">学生版 📂</a>
          <a :href="CDN_BASE + '/final_review_handout_teacher.pdf'" target="_blank" rel="noopener" class="btn-dl btn-review">教师版 📂</a>
        </div>
      </td>
    </tr>
  </tbody>
</table>

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