---
layout: doc
title: 离散数学 (2026秋季)
breadcrumb: 离散数学 (2026秋季)
description: 计算机科学与技术等专业《离散数学》（2026秋季学期）教学大纲、章节课件与授课讲义。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。
head:
  - - meta
    - name: keywords
      content: 离散数学, 命题逻辑, 命题符号化, 命题公式, 等值演算, 主范式, 推理理论, 一阶逻辑, 二元关系, 笛卡尔积, 关系的性质, 等价关系, 偏序关系, 图论, 通路, 最短路径, 关键路径, 图的着色, 离散数学课件, 课件下载
prev: false
next: false
---

<script setup>
const CDN_BASE = '/pdf/discrete/2026-2027-1'
</script>

# 离散数学 <span class="subtitle">2026 秋季学期</span>

《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 2026 秋季学期授课课件下载，随教学进度逐步开放更新。

<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</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_Logic_Symbols_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_Truth_Tables.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_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_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</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"><span class="btn-lock">待更新 🔒</span></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"><span class="btn-lock">待更新 🔒</span></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"><span class="btn-lock">待更新 🔒</span></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"><span class="btn-lock">待更新 🔒</span></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</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"><span class="btn-lock">待更新 🔒</span></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"><span class="btn-lock">待更新 🔒</span></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"><span class="btn-lock">待更新 🔒</span></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</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"><span class="btn-lock">待更新 🔒</span></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"><span class="btn-lock">待更新 🔒</span></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"><span class="btn-lock">待更新 🔒</span></td>
    </tr>
    <tr>
      <td class="chap-num">5.4</td>
      <td class="chap-title">关键路径法</td>
      <td class="download-cell"><span class="btn-lock">待更新 🔒</span></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"><span class="btn-lock">待更新 🔒</span></td>
    </tr>
  </tbody>
</table>

<style scoped>
.subtitle {
  display: block;
  font-size: 0.95rem;
  font-weight: 500;
  color: var(--mn-text-muted);
  text-transform: uppercase;
  letter-spacing: 1px;
  margin-top: -10px;
  margin-bottom: 24px;
}

.sec-eng {
  font-size: 0.85rem;
  font-weight: 500;
  color: var(--mn-text-muted);
  text-transform: uppercase;
  letter-spacing: 1px;
  margin-left: 8px;
}

/* 高颜值学术表格样式 */
.academic-table {
  width: 100%;
  border-collapse: separate;
  border-spacing: 0;
  margin: 16px 0 32px;
  background: var(--vp-c-bg-soft);
  border: 1px solid rgba(0, 0, 0, 0.05);
  border-radius: 12px;
  overflow: hidden;
  box-shadow: var(--shadow-sm);
  transition: border-color 0.3s;
}

.dark .academic-table {
  background: rgba(22, 27, 34, 0.2);
  border-color: rgba(255, 255, 255, 0.04);
}

.academic-table th {
  background: rgba(56, 189, 248, 0.05) !important;
  color: var(--mn-text) !important;
  font-size: 0.88rem !important;
  font-weight: 700 !important;
  text-transform: uppercase;
  letter-spacing: 0.5px;
  padding: 14px 18px !important;
  border-bottom: 1.5px solid rgba(56, 189, 248, 0.15) !important;
}

.dark .academic-table th {
  background: rgba(56, 189, 248, 0.02) !important;
  border-bottom-color: rgba(56, 189, 248, 0.1) !important;
}

.academic-table td {
  padding: 14px 18px !important;
  border-bottom: 1px solid rgba(0, 0, 0, 0.03) !important;
  color: var(--mn-text-soft);
  font-size: 0.95rem !important;
  vertical-align: middle;
  transition: all 0.2s ease;
}

.dark .academic-table td {
  border-bottom-color: rgba(255, 255, 255, 0.02) !important;
}

.academic-table tr:last-child td {
  border-bottom: none !important;
}

.academic-table tr:hover td {
  background: rgba(56, 189, 248, 0.03);
  color: var(--mn-text);
}

.dark .academic-table tr:hover td {
  background: rgba(255, 255, 255, 0.01);
}

/* 章节号强调 */
.chap-num {
  font-family: var(--vp-font-family-mono);
  font-weight: 700;
  color: var(--mn-primary) !important;
}

.chap-title {
  font-weight: 500;
}

/* 高颜值下载徽章 */
.download-cell {
  text-align: center !important;
  padding: 8px 18px !important;
}

.btn-dl {
  display: inline-flex;
  align-items: center;
  justify-content: center;
  padding: 4px 12px;
  font-size: 0.85rem;
  font-weight: 600;
  border-radius: 20px;
  background: var(--mn-primary-soft);
  color: var(--mn-primary) !important;
  border: 1px solid var(--mn-primary-ring);
  text-decoration: none !important;
  transition: all 0.25s cubic-bezier(0.4, 0, 0.2, 1);
  box-shadow: 0 1px 2px rgba(56, 189, 248, 0.05);
}

.btn-dl:hover {
  background: var(--mn-primary);
  color: #ffffff !important;
  transform: translateY(-1px);
  box-shadow: 0 4px 12px var(--mn-primary-ring);
}

/* 暂未开放状态样式 */
.btn-lock {
  display: inline-flex;
  padding: 4px 12px;
  font-size: 0.82rem;
  font-weight: 500;
  color: var(--mn-text-muted);
  border: 1px dashed rgba(0, 0, 0, 0.12);
  border-radius: 20px;
  background: transparent;
}

.dark .btn-lock {
  border-color: rgba(255, 255, 255, 0.08);
}
</style>