Partial differential equations (PDEs) are mathematical equations that describe relationships between functions of multiple variables and their partial derivatives. In theoretical biology, PDEs are used to model dynamic processes that occur in space and time, such as population growth, disease spread, and tissue development.

What are the key features of PDEs?

• Multiple variables: PDEs involve functions of two or more variables, such as space and time.
• Partial derivatives: PDEs contain partial derivatives of the functions, which describe the change of the function with respect to one of the variables.
• Dynamic processes: PDEs are used to model dynamic processes, such as the change of a population over time or the spread of a substance through a tissue.

What is the importance of PDEs?

PDEs are important in theoretical biology for the following reasons:

• Realistic modeling: PDEs can realistically model complex processes in nature, including the effects of spatial and temporal variation.

Cellular automata are discrete dynamical systems that consist of a regular grid of cells. Each cell has a finite number of states, and the state of a cell changes over time according to a set of rules that depend on the states of the cell and its neighbors.

What are key features of cellular automata?

• Discrete dynamical systems: Cellular automata evolve over time according to a set of rules.
• Regular grid: The cells are arranged in a regular structure, such as a lattice.
• Finite states: Each cell can be in one of a finite number of states.
• Transition rules: The state of a cell changes over time according to a set of rules that depend on the states of the cell and its neighbors.

What is the importance of cellular automata?

• Powerful tool for modeling complex systems in nature, mathematics, and computer science.
• Simulate a wide range of phenomena, such as:

Multiple choice questions

Question 1

A study looks at the relationship between gender, age and social resilience. Which of these variable(s) can only play a role in psychological research as an independent variable?

1. Sex.
2. Age.
3. Sex and age.
4. All three variables can act as both dependent and independent variables.

Question 2

Given are the 110-meter times of a sprinter from the last four races: 10.9, 11.2, 11.0 and 11.3. What is the standard deviation of these results?

1. 0.10.
2. 0.158.
3. 0.183.
4. 0.316.

Question 3

A business psychologist has checked for 200 managers what their blood pressure (X) is and how much

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