To begin studying physics and mathematics independently, foundational knowledge in mathematics is essential. Recommended topics include introductory algebra, trigonometry, college algebra, calculus (single and multi-variable), and an introduction to linear algebra and differential equations. For physics, starting with classical mechanics is advised, with textbooks like Resnick & Halliday and Kleppner & Kolenkow suggested for deeper understanding. Free online resources such as Khan Academy and MIT OpenCourseWare are valuable for self-study. Engaging with specific problems rather than broad topics can enhance understanding, and seeking help from online forums or study groups is encouraged. It's important to maintain a balanced approach to studying, taking breaks when needed to avoid burnout.