Introduction to Graph Theory: From Königsberg Bridges to Genome Assembly

How does an 18th-century puzzle about walking across bridges connect to the modern technology used to decode the human genome? Graph theory provides the elegant mathematical framework that bridges these two seemingly unrelated worlds. This text-based course guides you through the foundational concepts of graph theory, taking you from historical mathematical riddles to cutting-edge computational biology. You will develop a strong conceptual understanding of how networks, paths, and cycles organize complex data, and how these structures are applied to solve real-world sequencing challenges today. What you will learn: - Understand the fundamental components of graphs, including vertices, edges, degrees, and directed networks. - Explore the historic Seven Bridges of Königsberg problem and how it birthed the field of graph theory. - Identify and construct Eulerian paths and cycles using classical mathematical algorithms. - Map biological sequence data into de Bruijn graphs to model DNA assembly. - Analyze how modern genome assemblers handle errors, repeats, and massive datasets using graph-based algorithms. - Practice tracing paths and solving network puzzles through structured written exercises. You will start with essential terminology and the historical origins of network mathematics. From there, you will transition into algorithmic thinking, culminating in a conceptual walkthrough of how modern bioinformatics software reconstructs genomes. This course is designed for curious beginners, aspiring computer scientists, and biology students looking for a solid conceptual entry point into graph algorithms, with no advanced mathematical or programming background required. Start reading today to unlock the mathematical principles that power modern genetic sequencing.