适用于数学 / PDE / Reaction–Diffusion / 应用数学方向博士生
可直接复制到 Obsidian / Notion / Markdown
🎯 前言：为什么你需要这本手册
写论文时最痛苦的不是语言，而是：
不知道一个段落怎么起
不知道该用什么动词
逻辑连不起来
内容有了但写不顺
复制以前论文的句型很别扭
这本手册帮你解决这些问题：
你不需要从零开始写——只要打开它，选句型，套用即可。
Chapter 1. 论文的整体逻辑写法
1.1 如何写一个逻辑清晰的段落（PEEL 法）
P – Point（观点句）
一句话说明本段做什么。
E – Evidence（依据：理论/公式/引用/数据）
E – Explanation（解释意义，推论）
L – Link（连接下一段）
模板：
This section examines …
To justify this result, we first …
This implies that …
Therefore, we proceed to …
1.2 文章结构（适用于数学论文）
数学论文常见结构
Introduction
Preliminaries
Main Results
Proofs
Numerical Experiments
Conclusion
每节目标
Introduction：告诉读者“为什么要做 + 你做了什么”
Preliminaries：定义符号
Results：陈述定理
Proofs：证明
Simulations：展示数值
Conclusion：总结贡献、未来方向
1.3 逻辑连接词体系（非常重要）
表示“递进/进一步”
moreover
furthermore
in addition
besides
what is more
表示“转折/对比”
however
nevertheless
on the other hand
in contrast
whereas
表示“因果”
therefore
hence
thus
consequently
as a result
表示“举例/证明支持”
for example
for instance
in particular
notably
表示“总结/结论”
in summary
overall
in conclusion
to sum up
表示“强调”
indeed
in fact
notably
importantly
Chapter 2. 学术动词与表达体系（最实用）
下面是你经常需要的动词对比，我分门别类整理。
2.1 “表明/显示”类动词区别
（你的论文 Introduction、Results 中最常用）
动词 强度 用法 示例
show 中 直接展示事实 The result shows that …
demonstrate 强 通过推理/证明展示 We demonstrate that the solution exists.
reveal 强 揭示隐藏的规律 The analysis reveals the key mechanism.
indicate 弱 间接、倾向性 The behavior indicates that …
suggest 弱–中 提出可能解释 This suggests that the domain expansion affects persistence.
推荐使用：show / demonstrate / reveal
2.2 “提出/假设/争论”类动词
动词 含义 用法
propose 提出一种方法/模型 We propose a reaction–diffusion model.
suggest 提出可能性 We suggest that domain growth plays a role.
argue 提出论点，带推理 We argue that the solution is unique.
claim 声称（强，但略主观） Some authors claim that…（谨慎用）
assume 假设条件 We assume that $g$ is monotone.
2.3 “描述/展现”类动词
动词 含义 用法
describe 给出一般性描述 We describe the model as follows.
present 正式呈现 We present our main theorem.
illustrate 用例子/图来说明 Fig. 1 illustrates the dynamics.
depict 图像“描绘” The figure depicts the solution profile.
capture 抓住特征 The function captures the periodicity.
represent 表示数学对象 The operator represents …
2.4 “分析/模拟/建模”类
analyze
investigate
examine
model
simulate
evaluate
模板句：
We analyze the long-term behavior of the solution.
We investigate how domain expansion affects persistence.
We model the population dynamics by …
We conduct numerical simulations to illustrate …
2.5 “变化”类动词
increase / decrease
grow / decline
stabilize
converge
oscillate
fluctuate
模板：
The solution converges to its steady state.
The boundary oscillates periodically.
The population density decreases as …
Chapter 3. 学术句型（可直接套用）
3.1 定义概念
We define the function ϕ as follows.
Let Ω be a bounded domain in R^n.
We denote by λ_0 the principal eigenvalue.
3.2 提出现象 / 引入问题
A fundamental question in population dynamics is …
Motivated by this observation, we investigate …
This raises the following problem:
3.3 描述已有研究（文献综述）
Previous studies have focused on …
It has been shown that …
Several authors have established …
3.4 陈述结果（定理句型）
Our main result can be stated as follows.
Theorem 1.1 establishes the existence of …
We now present the proof of Theorem 2.3.
3.5 强调贡献
The main contributions of this work are summarized as follows:
(1) …
(2) …
(3) …
3.6 写方法（Models / Methods）
We consider the following reaction–diffusion model:
We assume that the domain evolves according to …
Under these assumptions, the system becomes …
3.7 写数值结果（Numerical Experiments）
Figure 2 illustrates the time evolution of …
The numerical results show that …
We observe that the solution stabilizes when …
3.8 写总结（Conclusion）
In conclusion, we have analyzed …
Our results reveal that …
Future work may focus on …
Chapter 4. 论文各部分的写作框架
4.1 Introduction 的五步法（通用）
背景：为什么有趣？
文献：别人做了什么？
缺口：什么地方还没被解决？
贡献：你做了什么？
结构：文章怎么组织？
可直接套模板：
In recent years, there has been growing interest in …
Many works have investigated …
However, less attention has been paid to …
In this paper, we address this gap by …
The paper is organized as follows:
4.2 Preliminaries
In this section, we recall several basic notions.
Let Ω ⊂ R^n be a bounded domain.
We denote by …
We will frequently use the following lemma.
4.3 Main Results
We now present our main theorem.
Theorem 2.1. Assume that …
Then the solution satisfies …
4.4 Proofs
Proof. We divide the proof into three steps.
Step 1. …
Step 2. …
Step 3. …
This completes the proof.
4.5 Numerical Experiments
We perform numerical simulations to support our theoretical results.
We take Ω_t = (0, ρ(t)π) with ρ(t) = …
For each case, we illustrate the solution profiles.
4.6 Conclusion
This work has investigated …
Our results demonstrate that …
Further extensions include …
Chapter 5. 常见错误与检查清单（必备）
5.1 中式英语常见问题
句子太长 → 应拆分
名词化过多
逻辑跳跃
被动语态滥用
重复表达（时而 show，时而 demonstrate）
5.2 论文提交前的 Checklist
结构检查
Introduction 有完整五步
Contributions 清晰
Each section has a purpose sentence
语言检查
每段首句明确主题
动词使用精确
符号一致
数学检查
所有定理已编号
引用的 lemma 已解释
证明中没有逻辑跳跃
Appendix A. 数学写作常用句型（特为你）
We consider the initial-boundary value problem …
Let u(t,x) denote the population density.
We show that the solution remains uniformly bounded.
We prove the existence of a unique positive periodic solution.
The principal eigenvalue plays a crucial role in …