Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Computer Science
- Code
- wwwhal1u0um17em
- Title
- Mathematics of networks and the WWW (l)
- Usual semester
- Spring
- Published semester
- 2025/26/2
- ECTS
- 3
- Language
- hu
- Learning outcomes
- Knowledge: getting familiar with the main notions of the mathematics of networks Ability: to understand and use the mathematical models of networks Attitude: the need to deepen the applied mathematical knowledge, to gain new applied mathematical skills, to develop competencies. Aspiration to apply the mathematical knowledge for a wide range of problems Autonomy and Responsibility: based on the gained knowledge in the mathematics of networks, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Markov chains and random walks on graphs. Arrival and return probabilities, strongly connected components, ergodic Markov chains. Eigenvalues, eigenvectors and the stationary distribution. • Page Rank and its applications: personalized ranking, similarity search. Reformulation for endpoint distribution of walks and efficient algorithms. • Singular value decomposition: proving the existence of the decomposition. Matrix norms, low-rank approximations. Spectral graph clustering, the relationship between eigenvalue gap and expansion. Expanders. Graph models: Barabási and related models. Small world models. Theorems related to degree distribution and diameter. Temporary storage of websites. Updating the database of search engines.
- Assessment method
- exam