Be ready for this Master

This page provides a set of recommendations, tools and references, in order to allow students to prepare as good as possible and to achieve some previous knowledge relevant for the Master. The page contains (a) a presentation of some important academic aspects of the master (in spanish), (b) a list of references for each subject, and (c) a short test that permits to evaluate if your current mathematical skills are good enough to face our master programme with a high probability of success.

MCTS academic information presentation 

• You can watch this video (in spanish) here.

References for each subject

• (480051) Fundamentals of Geosciences and Geographic Information Systems. We recommend that students have minimum knowledge of chemistry and biology for this course. It is possible to check it on the following links:
• Chemical reactions and stoichiometry (Khan Academy)
• Chemical equilibrium (Khan Academy)
• Introducción a la Geología (Universidad Austral de Chile)

• (480011) Fundamentals of Economics, Environmental Economics and Ecological Economics. It is suggested to familiarise with the following references, in order to do this course:
• Mankiw, N.K. (2002): Principios de economía, Ed. McGraw-Hill (Madrid).
• Mochón Morcillo, F. (2008): Economía. Principios y aplicaciones, Ed. McGraw-Hill (Madrid).

• (480021) Fundamentals of Mathematical and Systemic Sustainability Modelling. Knowledge of differential equations and mathematical functions is recommended for this course. It is possible to test your knowledge on the following links:
  • Differential equations (Khan Academy)
  • Functions (Khan Academy)

• (480022) Fundamentals of Applied Statistics and Sustainability and Development Measurement. For this subject we recommend basic knowledge of informatics and univariate statistics. It is possible to test it on the following links:
• Bass, R.F. (2013): Undergraduate probability.
• Grinstead, C. M., Snell, J.L. (1997): Introduction to Probability (2 Edition), American Mathematical Society. Capítulos 1-10.
• Venables, W.N., Smith, D.M. & R Core Team (2017): An Introduction to R, v3.3.3. Capítulos 1-8, 12-13.
• Introductory courses and open access to R and RStudio. (R Basics) (Introduction to R)
• Playlist (R-Tutorials).

Assessment test of previous knowledge of mathematics

On the link below, you can do a placement test, in order to assess your maths skills. Try to answer the 24 questions and check your successes. A prepared student should be able to answer most of them correctly.

• Calculus Placement Test (Diagnostic Examination) (University of California, Berkeley)