After this course the student

• masters basic algebraic skills including for example solving (in)equalities, (partial) differentiation and calculation of integrals with help of the techniques of substitution and integration by parts.
• masters elementary proof techniques, e.g. the principle of induction, proof by contradiction, a proof using logic reasoning.
• can perform calculations in plane and space geometry, involving e.g. distance, parametric representations, perpendicularity.
• knows the mathematical model of probability and can calculate (conditional) probabilities.
• can use combinatorics and set theory and apply these in probability theory.
• can work with discrete and continuous random variables and knows the specifics of the most commonly used classes of univariate distributions.
• can calculate expectation, variance, moments and moment generating functions of random variables.

Specifics

Relation to other courses

The methods and techniques learned in this course provide the necessary background for the courses Analysis 1 (first seven weeks of the course) and Probability and Statistics (last seven weeks of the course).

Highschool mathematics mainly focuses on acquiring mathematical techniques. However, graduates in Econometrics & OR are confronted with mathematical problems which are too diverse and complex to solve with these basic techniques only. Therefore, students Econometrics & OR should not only master these basic techniques, but they should also understand the mathematical theory underlying these techniques. Only then they will be able to understand and develop more advanced techniques.

In mathematical terms this means that the proof of a mathematical theorem is as important as the mathematical theorem itself. In this course we deal with a number of basic mathematical techniques and pay explicit attention to mathematical proofs. The concept of logical argumentation plays an important role here.

Moreover, the student is introduced in the field of probability theory, which plays an important role in many topics of Econometrics & OR. We introduce basic concepts of probability theory and focus on both discrete and continuous univariate distributions. Emphasis is not only on the computational aspects, but also on the underlying mathematical structures and techniques.

Topics that are discussed:

• Algebraic skills: including solving (in)equalities, partial differentiation and calculation of integrals.
• Elementary proof techniques, for example the principle of induction and proof by contradiction.
• Mathematical model of probability, including outcomes and events
• Geometry, combinatorics and set theory, including applications in probability theory.
• (Conditional) probabilities and independence
• Random variables and univariate discrete and continuous probability distributions, including specific classes of commonly used univariate distritbutions.
• Expectation, variance, moments and moment generating functions of random variables.

Type of instructions

Type of exams

1. H. Norde, Reader Introduction Analysis. This reader will be available in Canvas at the start of the course.
2. L.J. Bain & M. Engelhardt, Introduction to probability and mathematical statistics, Duxbury, 2nd edition (1992). Hoofdstuk 1-3.