ISL 197 - Analytical Thinking and Mathematics

This course aims to equip first-year university students with the foundational skills in Analytical Thinking and Mathematical Reasoning. It focuses on developing critical analysis, logical reasoning, and effective problem-solving skills in different areas of mathematics. Students learn to construct and evaluate arguments, communicate complex ideas clearly, and apply systematic approaches to address abstract and practical challenges. This comprehensive foundation prepares students for subsequent academic studies and develops the skills necessary for lifelong learning and success in many disciplines.

This course introduces students to the foundations of mathematical reasoning, drawing attention to the definition of analytical thinking and its relationship with numerical thinking. Following an understanding of propositional logic, mathematical logic, and proof methods, the course will focus on fundamental mathematical expressions such as solving equations, exponential and radical expressions, and mathematical solutions to real-life problems. In addition, functions and graphical solutions—critical for connecting different mathematical concepts—the concept of maximum and minimum in quadratic functions, exponential and logarithmic functions, and basic limit and derivative knowledge will be provided. Students who take this course will apply logical reasoning to solve numerical problems, discover the convenience mathematics provides in real-life situations, and learn to think analytically with the help of mathematics. The curriculum aims to develop problem-solving abilities, sharpen analytical skills, and enhance clarity in mathematical communication, serving as an important bridge to subsequent mathematical studies.