希望同學能藉由此課程學會如何用數學的語言與符號來論證，訓練邏輯推理與分析的能力，與如何敘述一個完整證明的技巧，以及集合、函數、等價關係與集合基數的概念，學會這些對於同學日後學習其他數學專業科目將有很大的幫助。

I hope that through this course, students will learn how to use mathematical language and symbols to demonstrate, train their ability to reconstruct and analyze logical reasoning and analysis, and how to describe a complete certification technique, as well as the concepts of sets, functions, etc. and set basis. Learning these will be of great help to learn other professional mathematical subjects after the course of study.

主要內容為集合函數，以及證明的技巧。
集合部份為介紹什麼是集合、聯集與交集的意思及相關的性質。
函數的內容為介紹什麼是函數、一對一、映成函數的意思及相關的性質，也介紹基數(cardinality)的觀念。
證明的技巧主要是講述如何證明一個問題，也會提及相關的邏輯觀念。

The main content is collection functions and certification techniques.
The collection part introduces what is the meaning of sets, connections and intersections and their related properties.
The content of a function introduces what is a function, one to one, and the meaning and related properties of a function, and also introduces the concept of cardinality.
The skills of certification are mainly about how to prove a problem, and also mention related logical concepts.

書名： A Transition to Advanced Mathematics, 8th Edition
作者： Douglas Smith, Maurice Eggen & Richard St. Andre
出版商（出版年）：CENGAGE Learning (2014)
（滄海書局代理）

Book name: A Transition to Advanced Mathematics, 8th Edition
Author: Douglas Smith, Maurice Eggen & Richard St. Andre
Publisher (Publication Year): CENGAGE Learning (2014)
(Agent from the Hsiaohai Books Bureau)