Introduction to Analysis

This lecture introduces the fundamental concepts of analysis, focusing on the importance of understanding the behavior of functions in physics, engineering, and biology. It covers the mathematical viewpoint on working with infinity, the significance of proofs in establishing logical conclusions, and the irrationality of square root of 3. The lecture also delves into sets, subsets, operations on sets, and important sets like rational and real numbers. The instructor presents alternative proofs, including the analytical approach to proving the irrationality of numbers. The lecture concludes with a discussion on defining the real numbers and the concept of infimum in analysis.