𝐃𝐚𝐲𝐬 𝟐 𝐚𝐧𝐝 𝟑 𝐚𝐭 𝐑𝐀𝐌 𝐓𝐏 𝟐𝟎𝟐𝟓 𝐩𝐫𝐨𝐯𝐢𝐝𝐞𝐝 𝐬𝐭𝐮𝐝𝐞𝐧𝐭𝐬 𝐰𝐢𝐭𝐡 𝐚𝐧 𝐢𝐦𝐦𝐞𝐫𝐬𝐢𝐯𝐞 𝐞𝐱𝐩𝐥𝐨𝐫𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝐚𝐝𝐯𝐚𝐧𝐜𝐞𝐝 𝐦𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐚𝐥 𝐜𝐨𝐧𝐜𝐞𝐩𝐭𝐬. 𝐁𝐡𝐚𝐬 𝐁𝐡𝐚𝐦𝐫𝐞 inspired curiosity through visual representations of numbers, innovative approaches to LCM using lasers, and in-depth discussions on Gaussian integers and continued fractions, including the case of √5. 𝐃𝐫. 𝐀𝐬𝐡𝐰𝐢𝐧 𝐆𝐮𝐡𝐚 made sophisticated ideas accessible, introducing linear regression via the "squarest country" challenge and guiding students through curve fitting, Lagrange interpolation, and conic sections. Under the guidance of 𝐃𝐫. 𝐒. 𝐌𝐮𝐫𝐚𝐥𝐢𝐝𝐡𝐚𝐫𝐚𝐧, students engaged rigorously with Number Theory, exploring Modular Arithmetic (including Fermat's and Wilson's theorems), characterizing primes expressible as sums of two squares, and examining proofs such as the non-existence of integer solutions to x⁴ + y⁴ = z². 𝐃𝐫. 𝐒𝐚𝐢 𝐉𝐚𝐠𝐚𝐧𝐦𝐨𝐡𝐚𝐧 provided elegant connections across topics, delving into symmetry-adapted variables, scaling arguments, and the interplay between geometry and algebra. Additional sessions featured explorations of p-adic numbers and the "three-in-one-line" problem with 𝐃𝐫. 𝐀𝐧𝐮𝐩 𝐃𝐢𝐱𝐢𝐭, continued fractions with 𝐃𝐫. 𝐒𝐢𝐝𝐝𝐡𝐢 𝐏𝐚𝐭𝐡𝐚𝐤, and practical cryptographic techniques such as secret sharing. Each day concluded with unique perspectives: 𝐁𝐚𝐫𝐚𝐤 𝐍𝐞𝐡𝐨𝐫𝐚𝐧 (Princeton) elucidated the fundamentals of quantum computing on Day 2, while 𝐕𝐢𝐯𝐢𝐤𝐭𝐡 𝐑𝐚𝐠𝐡𝐚𝐯𝐚𝐧 𝐍𝐚𝐫𝐚𝐲𝐚𝐧𝐚𝐧 offered insights into the mathematics underlying insurance on Day 3. These sessions fostered collaborative problem-solving, rigorous proofs, and a deeper appreciation for the richness of mathematics.