Foundations of Algorithmic Thinking

This unit introduces core algorithmic concepts and practical problem-solving techniques used in computer science and data-driven applications. Students will learn to implement and compare fundamental algorithms (sorting, graph traversal, search), perform basic linear algebra without libraries, and evaluate strategies for managing and optimizing large or noisy data sets, preparing them for more advanced algorithm design and data systems in subsequent units.

Learning Objectives

• Analyze algorithm behavior by comparing time and space complexity for sorting algorithms (merge sort, quick sort) and graph traversal methods (BFS, DFS), and justify algorithm selection for specific problem constraints
• Apply problem-solving workflows and implement algorithms in Google Colab, including custom vector and matrix operations without NumPy, merge sort, quick sort, and basic graph traversals, producing working notebooks as evidence
• Demonstrate techniques for managing and reducing data—such as basic compression, data transformation, feature scaling using linear functions, and strategies for handling large data sets—by producing examples and measuring effects on storage or performance
• Evaluate algorithmic strategies (greedy methods, dynamic programming, randomized algorithms, local search, and heuristics) by selecting and defending the most appropriate approach for optimization and search problems in given scenarios