## Preparatory Course: Mathematics and Computer Science for Modeling

The "Computer Science and Mathematics" preparatory course will combine a hands-on introduction to programming in python with a revision of elementary mathematical concepts. The topics include data types, data structures, control structures and data visualisation on the programming side and they will be applied to vector/matrix calculation, integration/differentiation of functions and differential equations.

The course is meant for students who are about to start the Cognitive Science Master Program at the Ruhr-University .

## Lecturers

## Daniel Sabinasz, M.Sc.Lecturer |
(+49) 234-32-27973 daniel.sabinasz@ini.rub.de NB 02/74 |

## Details

- Course type
- Lab courses
- Term
- Winter Term 2022/2023

## Teaching Units

##### Unit 1: Introduction to Programming in Python

Document | Jupyter notebook |

Link | Python documentation |

Reference solution | Jupyter notebook with all exercise solutions |

Link | Bonus exercises with varying difficulties |

Lecture slides | Slides |

##### Programming Session I

Lecture slides | Slides |

Document | How to fix Spyder bug |

Reference solution | Solution Task 1 |

Reference solution | Solution Task 2 |

Reference solution | Solution Task 3 |

##### Unit 2: Functions in Math

Link | Interactive simulator for function transformations |

Reference solution | Exercise 1 Solution |

Link | Article on function translation / shift |

Link | Article on function compression, stretching and reflection |

Document | Jupyter notebook |

Reference solution | Exercise 2 Solution |

Reference solution | Exercise 3 Solution |

Lecture slides | Lecture slides |

Document |
Function transformation example
This example shows how function transformations (translation, compression along the x axis and stretching along the y axis) can be used to match a Gaussian distribution to data points. |

##### Unit 3: Linear Algebra

Link | Article on radians |

Link | Article on sine, cosine and tangent |

Lecture slides | Lecture slides |

Reference solution | Exercise 1 Solution |

Reference solution | Exercise 2 Solution |

Reference solution | Exercise 3 Solution |

Link | Article on vector length |

Link | Article on the scalar product |

Link | Article on how to find the angle between two vectors |

Link | Article on matrix-vector multiplication and matrix-matrix multiplication |

##### Unit 4: Calculus

Lecture slides | Lecture slides |

Reference solution | Exercise solutions |

Link | Overview of derivative rules and examples for derivative calculation |

Link | Interactive derivative plotter |

##### Unit 5: Integration

Lecture slides | Lecture slides |

##### Unit 6: Differential Equations

Lecture slides | Lecture slides |

## Documents

Document | Exam topics |

Document | The Final Exam Exercises |

The Institut für Neuroinformatik (INI) is a central research unit of the Ruhr-Universität Bochum. We aim to understand the fundamental principles through which organisms generate behavior and cognition while linked to their environments through sensory systems and while acting in those environments through effector systems. Inspired by our insights into such natural cognitive systems, we seek new solutions to problems of information processing in artificial cognitive systems. We draw from a variety of disciplines that include experimental approaches from psychology and neurophysiology as well as theoretical approaches from physics, mathematics, electrical engineering and applied computer science, in particular machine learning, artificial intelligence, and computer vision.

Universitätsstr. 150, Building NB, Room 3/32

D-44801 Bochum, Germany

Tel: (+49) 234 32-28967

Fax: (+49) 234 32-14210