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What do transportation systems, social networks, the Web, powergrids, financial markets and many biological systems have in common? They are examples in which we seek to understand not only the entities which interact, but also the patterns of interaction between the entities. Graph theory and network science are rooted in Mathematics and Computer science. Topics covered in this course include: graphs as models, paths, cycles, directed graphs, trees, spanning trees, matchings (including stable matchings, the stable marriage problem and the medical school residency matching program), network flows, and graph coloring (including scheduling applications). Following this introduction to graph theory, students will explore theoretical network models, such as random graphs, small world models and scale-free networks, as well as networked datasets from social, infrastructure and information networks. In this context, we will explore topics such as the role of strong and weak ties, triadic closure, and centrality measures, as well as the fragility of networked systems and contagious process on networks of various topologies.
The primary audience for this course is students who wish to concentrate in Computer Science, Information Technology, Mathematics or Applied Mathematics. Students interested in various fields which have a connection to this branch of mathematics (such as cognitive science, data science, economics, computational sociology, mathematical biology) may also be interested in this course.
Prerequisites: Prior to enrolling in this course, students should be fluent in the foundations of mathematics and mathematical proof: logic, methods of proof (both inductive and deductive), sets, relations and functions. This knowledge may be obtained from a course such as Discrete Mathematics, for example.
This online course is offered through Online Learning. You can take this as an individual course or as part of an online degree program, with term starts in March, May, September, November and January. View current term offerings and all online courses. Click here to register for online courses.
Other Areas: The Arts | Business, Management & Economics | Community & Human Services | Communications, Humanities & Cultural Studies | Educational Studies | Historical Studies | Human Development | Labor Studies | Nursing | Science, Math & Technology | Social Science
Term(s) Offered (Subject to Change) : Summer.
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