簡介
在我高二時，我和我的組員一起，在國立清華大學數學系完成了科學班的高二專題。我們選擇的主題是處處不可微的連續函數。我們學到了以下兩個定理：
- 存在一個處處不可微的連續函數。
- 處處不可微的函數在連續函數空間 $ C[a,b] $ 中構成一個稠密的 $ G_\delta $ 集。
為了證明這兩個定理，我們需要發展一些來自數學分析的概念，這段經歷激發了我對數學的興趣。如想了解更多詳情，請查看這個連結。
Introduction
In my second year of high school, together with my teammate, we completed a study in the math department at National Tsing Hua University. Our chosen topic was nowhere differentiable continuous functions. We learned the following two theorems:
- There exists a continuous function that is nowhere differentiable.
- Nowhere differentiable functions form a dense $G_\delta$ set in the continuous function space $C[a,b]$.
To prove these two theorems, we had to develop some concepts from Analysis, and this experience sparked my interest in Mathematics. For further details, feel free to check out this link.