### CS-E5745 - Mathematical Methods for Network Science D, 14.01.2021-18.02.2021

Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

#### LEARNING OUTCOMES

This course will provide students an overview on mathematical topics and tools in network science. The students will develop skills in doing pen-and-paper calculations and an understanding of analytical methods that are common in network science.

Credits: 5

Schedule: 14.01.2021 - 18.02.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Mikko Kivelä

Teacher in charge (applies in this implementation): Mikko Kivelä

Contact information for the course (valid 23.12.2020-21.12.2112):

You can contact the instructor or the TA by sending an email to:

Instructor: Mikko Kivelä, mikko.kivela@aalto.fi

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English

##### Content
• Valid 01.08.2020-31.07.2022:

Mathematical methods and their use in networks science. Topics are mostly related to large random graphs and include  common approximations and assumptions  in network science, network models,  component size distributions, percolation,  branching processes, excess degree distributions, probability generating functions, master  equations, rate equations, growing network models, processes on networks, exponential  random graphs, and stochastic block  models. The project can be on a recent research topic.

##### Assessment Methods and Criteria
• Valid 01.08.2020-31.07.2022:

Grades (1-5) are given on the basis of weekly mandatory exercises and project work, there is no exam.

• Applies in this implementation:

A grade between 0-5 is given to the students based on the returned homework problems and the project. In order for the homework problems to
be graded the students must participate in the homework sessions and
mark each problem they want to return as done. If the problem is marked
as done the student is expected to be able to present it on the
whiteboard.

• Applies in this implementation:

The course does not have an exam, but passing and grading is based on returning 5 sets of homework assignments and the "final project" and participating in 5 homework sessions (TBA).
There is also 6 lectures and a voluntary contact class every week where students can ask for advice on solving the problems. To get grade 1 the
students are expected to successfully complete at least half of the
exercises.

#### DETAILS

##### Study Material
• Applies in this implementation:

Participants can find these sources useful for this course:

##### Prerequisites
• Valid 01.08.2020-31.07.2022:

Basic mathematics courses, basics of network science (CS-E5740 Complex Networks), basics on stochastic processes (MS-C2111 Stochastic Processes).