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Welcome to Week 11 Lecture 4 of the course "Mathematics for Data Science I" by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview This lecture introduces weighted graphs, where each edge is assigned a cost or weight, and explores how this changes the problem of pathfinding compared to unweighted graphs. We study two fundamental problems: the single-source shortest path problem (finding the shortest path from one starting vertex to all others) and the all-pairs shortest path problem (finding shortest paths between every pair of vertices). We also discuss the challenges posed by negative edge weights and the phenomenon of negative cycles, which can prevent shortest paths from being well-defined. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #WeightedGraph #GraphTheory #ShortestPath #SingleSourceShortestPath #AllPairsShortestPath #NegativeEdgeWeights #NegativeCycles #Algorithms #DataStructures #AdjacencyMatrix
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