Explore the third lecture in a series on polynomial methods for point counting, focusing on the slice rank method developed by Croot, Lev, Pach, Ellenberg, and Gijswijt. Delve into how this technique demonstrates that sets with no 3-term arithmetic progressions in finite-field settings are small. Learn about the mathematical principles behind this method and its applications in combinatorial geometry. Gain insights into advanced mathematical concepts and problem-solving techniques used in modern research. Enhance your understanding of polynomial methods and their role in solving complex mathematical problems.