Explore essential problem-solving techniques in this comprehensive lecture, focusing on geometry, trigonometry, and probability. Learn nine key principles to enhance your mathematical reasoning skills, illustrated through practical examples and interactive questions. Dive into topics such as the inscribed angle theorem, floor functions, alternating series sums, and probability graphs using Desmos. Engage with Python programming for probability problems and discover the artistic potential of mathematical expressions in Desmos. Benefit from expert tips, audience interactions, and a structured approach to tackling complex mathematical challenges.