UCSCIMAT227.5 ECTSEnglishBachelor
Probability and Networks
Faculteit—
NiveauBachelor
Studiejaar2026-2027
Beschrijving
Course goals
After completing this course, students are able to:
- Use fundamental concepts of probability theory (such as random variables, sample spaces, conditional probability, discrete and continuous probability distributions and densities) to describe scenarios involving randomness and identify appropriate mathematical techniques for analyzing them.
- Determine probabilities of events using combinatorial techniques, Bayes' Theorem, uniform, binomial, geometric, Poisson, exponential, and normal probability distributions and density functions, and the Central Limit Theorem.
- Determine and interpret the expected value and variance of both discrete and continuous random variables.
- Apply the above techniques in a range of scenarios from social and applied sciences.
- Understand and describe the importance of network theory, both in general and in a particular field of their interest.
- Use mathematical concepts to characterize and analyze network structures in a variety of real-world settings such as infrastructure networks, social networks, and networks of data.
- Apply concepts and techniques of linear algebra and graph theory to build and analyze concrete mathematical models, e.g. of financial crises or the spread of diseases..
- Conduct a small research project based on current academic literature in the area of the course, and present findings orally and in writing.
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Content
NOTE: re-titled in 2021-2022 from Mathematical Modeling: Networks. Course cannot be taken again, as content is mostly the same. Now also incorporates content from previous UCSCIMATL4 Introduction to Probability and Statistics.
Content
Probability theory is fundamental in all mathematical and data-driven sciences. This course introduces the core concepts of the field that are useful for students across the natural and social sciences. The course balances interesting applications and examples with a depth of conceptual and theoretical understanding that goes beyond merely pragmatic methods and skills. Topics include discrete and continuous probability distributions, combinatorics, conditional probability, computations with random variables, expectation and variance, the law of large numbers, and the central limit theorem.
The interdisciplinary study of networks is recently receiving much attention. It is revealing unexpected connections between otherwise disparate fields such as sociology, ecology, economics, cognitive neuroscience, and computer science. Network thinking provides new ways to understand our strongly connected world. This approach has generated new tools for the analysis and understanding of complex systems in both the social and natural world. The course will discuss how to describe and quantify networks, provide means to analyze network data (using among others graph theory) and explain how to build and analyze concrete mathematical models, e.g. of the spread of diseases or of financial crises.
Content
Probability theory is fundamental in all mathematical and data-driven sciences. This course introduces the core concepts of the field that are useful for students across the natural and social sciences. The course balances interesting applications and examples with a depth of conceptual and theoretical understanding that goes beyond merely pragmatic methods and skills. Topics include discrete and continuous probability distributions, combinatorics, conditional probability, computations with random variables, expectation and variance, the law of large numbers, and the central limit theorem.
The interdisciplinary study of networks is recently receiving much attention. It is revealing unexpected connections between otherwise disparate fields such as sociology, ecology, economics, cognitive neuroscience, and computer science. Network thinking provides new ways to understand our strongly connected world. This approach has generated new tools for the analysis and understanding of complex systems in both the social and natural world. The course will discuss how to describe and quantify networks, provide means to analyze network data (using among others graph theory) and explain how to build and analyze concrete mathematical models, e.g. of the spread of diseases or of financial crises.
Format
Lectures, exercise classes, project work, presentations
Lectures, exercise classes, project work, presentations
Math track
For students wanting to complete a track in applied mathematics there are interesting level-3 Bachelor courses in social science (economic geography, sociology) and humanities (artificial intelligence, logic, linguistics) and also in science (e.g. in theoretical biology).
For students wanting to complete a track in applied mathematics there are interesting level-3 Bachelor courses in social science (economic geography, sociology) and humanities (artificial intelligence, logic, linguistics) and also in science (e.g. in theoretical biology).
Here is a list of existing UU-courses which should be accessible upon completion of UCSCIMAT22:
- GEO3-3805, ECON-Organisational Networks
- 200300014 Social Networks
- 200300014, MK: Social networks
- B-B3COMB10, Computational Biology
- KI3V12013, Logical Complexity
Master courses (no easy access but to indicate importance of networks):
- WBMV13005, Logic and Computation
- BMB508117, Bioinformatics in neuroscience
- WISM484 Introduction to complex systems
- GEO3-3805, ECON-Organisational Networks
- 200300014 Social Networks
- 200300014, MK: Social networks
- B-B3COMB10, Computational Biology
- KI3V12013, Logical Complexity
Master courses (no easy access but to indicate importance of networks):
- WBMV13005, Logic and Computation
- BMB508117, Bioinformatics in neuroscience
- WISM484 Introduction to complex systems
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