Graph Theory
Trefor Bazett
Learn graph theory connectivity with Trefor Bazett! This course explores fundamental concepts & applications.
More resources on Connectivity
Wikipedia: Connectivity (graph theory)
Comprehensive overview with references
Reinhard Diestel Graph Theory Book
Free online textbook with chapter on connectivity
mathworld.wolfram.com
MathWorld is Wolfram's comprehensive online mathematics encyclopedia offering detailed, formula-rich articles and diagrams on topics across mathematics, including graph theory and connectivity.
Introduction to Graph Theory
We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them. In this online course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible! By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
ocw.mit.edu
MIT OpenCourseWare (OCW) offers free, openly accessible MIT course materials—lecture notes, assignments, and exams—across a wide range of subjects. It's a great resource for self-paced study of connectivity and related topics in engineering and science.
nptel.ac.in
NPTEL is India's online learning platform offering IIT/IISc-led courses in engineering and sciences, including networking and connectivity topics, with video lectures, downloadable materials, assignments, and certificates.