Group 1 - Many investors start their investment journey with index funds and seek ways to achieve good returns from them [2] - A limited-time free course is available that introduces investment techniques for index funds [2] - The course includes notes and mind maps to help learners quickly understand the course structure and learn more efficiently [2] Group 2 - The unpredictability of short-term stock price fluctuations has been a topic of interest since the inception of the stock market [7] - The theory that market movements are unpredictable was first proposed by French mathematician Bachelier over a century ago [7] - Bachelier's research established that the pricing of financial securities is determined by investors at any given moment, and the transaction price reflects a consensus between buyers and sellers [9] Group 3 - Bachelier also demonstrated that price fluctuations in financial markets resemble random movements, akin to Brownian motion observed in nature [11] - This analogy explains why short-term stock price movements are difficult to predict, as they lack discernible patterns [11]