1. 熟悉數學常用的邏輯符號與邏輯推論
2. 熟悉集合的符號、運算；學習利用集合描述數學命題。
2. 熟悉函數的定義，符號與運算；學習利用函數描述數學命題。
4. 學習自然數集、整數集、有理數集乃至實數集的建構過程。

1. Be familiar with common logical symbols and logical inferences in mathematics
2. Be familiar with the symbols and operations of sets; learn to use sets to describe mathematical propositions.
2. Be familiar with the definition, symbols and operations of functions; learn to use functions to describe mathematical propositions.
4. Learn the construction process of the set of natural numbers, the set of integers, the set of rational numbers and even the set of real numbers.

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 set functions and proof techniques.
The set part introduces what sets are, the meanings of unions and intersections, and their related properties.
The content of function is to introduce what a function is, one-to-one, the meaning of mapping into a function and related properties. It also introduces the concept of cardinality.
The techniques of proof mainly describe how to prove a problem, and also mention related logical concepts.

Steven R. Lay, Analysis with an Introduction to Proof, 5th Ed., Pearson.

Steven R. Lay, Analysis with an Introduction to Proof, 5th Ed., Pearson.