Why Algorithms Work - Algorithm Analysis Deep Dive Course

Explore university-level algorithm and data structure analysis in this comprehensive 6-hour course that goes beyond coding to teach why algorithms work, not just how they function. Master core mathematical tools and various complexity analysis techniques essential for understanding algorithmic efficiency. Begin with fundamental concepts including time complexity introduction and detailed analysis of insertion sort, then progress through asymptotic analysis to understand how algorithms scale. Dive deep into divide and conquer strategies using both recurrence tree methods and master theorem approaches. Examine probabilistic analysis through quicksort implementation and learn to calculate average case scenarios and expected values. Study essential data structures including heaps and heapsort algorithms, explore hashtable implementations and collision resolution strategies, and analyze binary search tree operations and properties. Conclude with amortized analysis techniques to understand the average performance of data structures over sequences of operations. Gain mathematical rigor in algorithm analysis that remains crucial even in the AI era, with practical applications to sorting algorithms and fundamental data structures that form the backbone of computer science.