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In this video tutorial, Charlie, also known as Senior Mars, demonstrates how he writes his math notes and completes his math homework as a math major in college using Vim and LaTeX. He highlights the importance of having legible notes, especially in math, to refer back to when solving problems. Textbooks may not always provide detailed solutions, so clear notes are essential for understanding concepts and proving solutions. Charlie aims to showcase his method of efficiently organizing math notes for effective problem-solving.