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• Preparatory Course: Mathematics and Computer Science for Modeling

## 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 Lecturer
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