本課程之目標為使低年級同學瞭解數學分析的基本理論，並培養數學證明的論述能力（包含書寫及上台講解），為將來修習相關進階課程預作準備。本學期的課程內容包含數列與函數之極限的嚴格定義、實數的完備性與重要定理（例如：The Heine–Borel Theorem、The Bolzano–Weierstrass Theorem、The Bounded Monotone Sequence Theorem）及其應用。
The goal of this course is to enable students of lower grades to understand the basic theories of mathematical analysis, and to cultivate mathematical proof of pronunciation (including writing and explanations on the stage), and to prepare for the preparation of relevant advanced courses. The course content of this study includes the strict definition of the limits of the number and functions, the completion of the number and important theorems (for example: The Heine–Borel Theorem, The Bolzano–Weierstrass Theorem, The Bounded Monotone Sequence Theorem) and its applications.
1. A Transition to Advanced Mathematics, 8th Edition （第4章之4.6，4.7及第7章）
2. 課程講義。
1. A Transition to Advanced Mathematics, 8th Edition (Chapter 4: 4.6, 4.7 and 7)
2. Course explanation.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 期中考期中考 Midterm exam |
30 | |
| 期末考期末考 Final exam |
30 | |
| 課堂報告課堂報告 Class Report |
40 | 包含上台講解及書面報告，報告規定於課堂說明。 |
