本課程旨在引導學生培養嚴謹的數學思維與論證能力。內容涵蓋集合論、邏輯與推理、函數與關係、等價關係、公理體系、數論初步與群論概念等，作為銜接進階數學課程（如離散數學、線性代數、抽象代數、分析學等）的基礎。本課程著重證明方法的訓練與數學語言的掌握，透過理論與習題並重的方式，幫助學生建立紮實的數學基礎。

This course aims to guide students to develop rigorous mathematical thinking and argumentation skills. The content covers set theory, logic and reasoning, functions and relations, equivalence relations, axiom systems, preliminary number theory and group theory concepts, etc., serving as the basis for connecting to advanced mathematics courses (such as discrete mathematics, linear algebra, abstract algebra, analysis, etc.). This course focuses on the training of proof methods and the mastery of mathematical language. It helps students establish a solid mathematical foundation through equal emphasis on theory and exercises.

學習邏輯、證明技巧、集合、函數的觀念，培養抽象思考與邏輯推論的能力。邏輯的內容主要為介紹基本邏輯敘述。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。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。

Learn the concepts of logic, proof skills, sets, and functions, and cultivate the ability of abstract thinking and logical deduction. The content of logic mainly introduces basic logical narratives. 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. The techniques of proof mainly describe how to prove a problem, and also mention related logical concepts.

The Elements of Advanced Mathematics
Author： Steven G. Krantz
Publisher: CRC Press
Published: 2022

The Elements of Advanced Mathematics
Author: Steven G. Krantz
Publisher: CRC Press
Published: 2022