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# Honoursmodule: The dangerous world of Mathematics & Statistics

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dr. G.J.M. Marée

## Entry requirements

• Second and Third year bachelor students participating in an honours programme.
• Introductory Mathematics and Statistics (please be aware that the course will go in depth and an academic thinking about mathematics and statistics is required; good knowledge of differential and integral calculus is expected).

## Recommended prior knowledge

A healthy mathematical and statistical curiosity.

## Learning Objectives

At the end of the course the student can:

• use logical reasoning and demonstrate possible pitfalls in arguments.
• can judge when people “lie with statistics” and use descriptive statistics in a correct way.
• do calculations by using (advanced) probability calculus techniques and will see that some things will be different than they expect.
• deal with graph theory and the applications (SIR model)
• do calculations in the field of Financial Mathematics and learn about some important concepts and misleading selling techniques.
• analyze the (mis)use of Statistics and Mathematics in Science and Industry.
• discover mathematical and statistical mistakes in reasoning.
• describe (social and economic) problems by using (systems of) difference
• and differential equations and solve the mathematical models.
• analyze non-linear difference equations and the sensitive dependence on initial conditions (chaos theory)

## Content

In this course it will be demonstrated that it is very important to use mathematical and statistical techniques in a proper way. It will be seen that in industry and science these disciplines are not always used in a proper way. Moreover, the student will learn more about the mathematics of finance, other dimensions, probability calculus, paradoxes, mathematical models, and other dimensions.

Descriptive Statistics, Probability Calculus, Conditional probabilities, Bayes’ rule, Statistical and Mathematical paradoxes, Mathematical Reasoning,  Noise, Huge and Small numbers in Science, Mathematics of Finance, geometric and arithmetic sequences, the fourth dimension, the (mis)use of Statistics and Mathematics in Science and Industry, Mathematical Riddles, Fractals, Chaos, Complex number theory, (systems of) difference and differential equations.

## Teaching methods

• Lecture
• (Computer)practicum > most probably
• Selfstudy
• (12 lectures; two hours per lecture; combined with assignments)

## Assessment:

4 assignments (each with weight 10%); one final test (3 hours; weight 60%, open questions); in case of a retake the result of the assignments will remain valid, so in that case the grade for the course is determined by the grade of the retake (60%) and the grade of the assignments (40%).

## Study material:

 Hand-outs will be made available during the course Study Material will be mentioned on Canvas Background literature: Darrell Huff, (1991) How to Lie with Statistics Penguin; New Ed edition, ISBN 0-14-013629-0  Daniel Kahneman, (2012), Thinking, Fast and Slow, ISBN 9780141033570 Cars Hommes, (2012), Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems, ISBN   9781107019294 Syllabus Readers about Mathematics of Finance, Difference and Differential Equations and Chaos Theory will be handed out Practical material Assignments and Hand-outs Software  EfChaos (will be explained during the course)

max. 25

## Schedule

The schedule will be available on Datanose

## Registration

Registration is possible for 2nd year (or higher) students participating in an Honours programme. The registration for the Honours courses will start on June 1, 10 am -  June 4, 11 pm, You can register through the online registration form that will appear on Honoursmodules IIS (registration is NOT through SIS)

Placement will be at random and students will be informered about their placement in the week of June 21.

There is NO guarantee for placement if you register AFTER June 4, so make sure you apply on time!