Mathematics and Statistics

Aims

This introductory/refreshment course provides basic knowledge of mathematics and statistics needed in the other courses in statistics and methods curriculum at ERIM. Students are asked to participate actively, especially in the tutorials. The course is based on the principle that in mathematics and statistics we should view every error as an invitation to learn. In particular, students are asked to present their solutions of the tutorial exercises.

Information

The course consists of four parts.

1. Calculus.
• Functions and limits.
• Differentiation.
• Integration.
2. Matrix algebra.
• Vector spaces and linear maps.
• Matrix and vector multiplication..
• Rank of a matrix,
• Eigenvalue decomposition, matrix norms.
3. Probability theory.
• Random events and random variables.
• Working with distributions. Common distributions.
• Expectation, Moments and moment generating functions.
• Transformations of random variables.
4. Statistics.
• Estimators and estimates. Bias and variance of estimators.
• Hypothesis testing. Type I and Type II errors. Power.
• P-values and effect sizes.
• Some chi-square tests. Some t-tests.

Assessment

Instructional method: each meeting consists of a lecture (approximately 2 hours) followed by a tutorial (approximately 1 hour).

Test: written (re-)examination with essay questions (100%)

Materials

Recommended

• James Stewart. Calculus Early Transcendentals. Brooks-Cole, Cengage Learning, Australia, 7th edition, 2012. ISBN 978-0-538-49887-6. International Metric version. http://www.stewartcalculus.com/media/11_home.php.
• David Poole. Linear algebra: a modern introduction. Cengage Learning, Stamford CT, 4th edition, 2015. ISBN 9781285463247.
• Bain, Engelhardt. Introduction to Probability and Mathematical Statistics, Cengage, 2010. ISBN 9781408092149. Custom Edition.

These books are recommended literature in the first year of the bachelor Econometrics and Operational Research. Stewart (2012) and Poole (2015) are older editions. In the course only selected parts of these books are discussed, the other parts may later serve as material for self-study.