Functional Equations Masterclass 2 | Discrete Domains, Induction & 25 Solved Problems

Most students approach Functional Equations on ℕ and ℤ exactly the same way they approach equations on the real numbers. That is usually a mistake. Once the domain becomes discrete, continuity disappears. Differentiation is no longer available. Instead, an entirely different toolkit takes over. In this lecture you'll learn the four fundamental techniques behind almost every discrete-domain Functional Equation: Strong Induction Recurrence Relations Multiplicative Conditions Binary Expansion & Recursive Bisection Together, these techniques form a systematic framework for solving problems from JEE Advanced, ISI UGA/UGB, CMI, and Mathematical Olympiads. Rather than memorising isolated tricks, you'll learn when each tool applies, why it works, and how to combine them on difficult problems. This lecture includes 25 fully worked examples from JEE Advanced, ISI, CMI, Olympiads and standard references. Timestamps 00:00:00 — 4 Fundamentals of Functional Equations on Discrete Domains 00:03:15 — Strong Induction 00:06:02 — Recurrence Relations 00:13:32 — Multiplicative Conditions 00:21:16 — Binary Expansion 25 Fully Solved Problems Throughout Perfect for JEE Advanced ISI UGA / UGB CMI Entrance Olympiad Mathematics Students who want to master Functional Equations from first principles Subscribe to Mathsmerizing for complete university and olympiad-level mathematics taught from first principles.