Understand the limitations of traditional multiplication - Explore why the conventional "grade school" method becomes inefficient for large numbers and recognize the O(n²) complexity bottleneck.

Master Karatsuba's recursive divide-and-conquer approach - Learn how clever mathematical insights can reduce multiplication complexity from O(n²) to O(n^1.585) through strategic problem decomposition.

Experience hands-on algorithm implementation - Practice implementing the Karatsuba algorithm step-by-step, understanding base cases, recursive calls, and result combination techniques.

Analyze real-world performance improvements - Compare execution times and operation counts between traditional and Karatsuba methods, discovering the practical impact of algorithmic optimization in cryptography and large-number arithmetic.