Exploring Functions in Advanced Mathematics
Exploring Functions
Functions sit at the heart of advanced mathematics
This series walks through core ideas, properties, elementary families, and classic constants.
Course Highlights
- Build intuition for what a function really is, not just how to manipulate formulas.
- See how properties like monotonicity, parity, periodicity, and convexity shape graphs and reasoning.
- Connect abstract definitions with constants you know: , , and the golden ratio .
- Practice-focused: each module includes short exercises with guided answers.
Repetition is a feature, not a bug—reviewing the same idea in different contexts makes it stick.
Author’s Note
When you see a year in history, don’t just memorize the digits. Ask what dynasty China was in and what happened elsewhere in the world. Let your brain stay curious instead of scrolling passively.
总结
本文出现的符号
| 符号 | 类型 | 读音/说明 | 在本文中的含义 |
|---|---|---|---|
| 希腊字母 | e | 自然常数，后续章节的主角之一 | |
| 希腊字母 | Pi（派） | 圆周率，后续章节的主角之一 | |
| 希腊字母 | Phi（费） | 黄金比例，后续章节的主角之一 |
中英对照
| 中文术语 | 英文术语 | 音标 | 说明 |
|---|---|---|---|
| 函数 | function | /ˈfʌŋkʃən/ | 描述变量依赖关系的数学对象 |
| 单调性 | monotonicity | /ˌmɒnəʊtəˈnɪsɪti/ | 函数随自变量变化的增减趋势 |
| 奇偶性 | parity | /ˈpærəti/ | 函数图像的对称特征 |
| 周期性 | periodicity | /ˌpɪərɪəˈdɪsəti/ | 函数值按固定间隔重复的性质 |
| 凸性 | convexity | /kɒnˈvɛksəti/ | 函数曲线向上或向下弯曲的性质 |
Chapters
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Exploring Functions in Advanced Mathematics
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