[MUSIC] This lecture has presented the basic concept of an equation. We have seen that, although the business, the financial and economic model is a theoretical construct, or a theoretical set of statements, we can use very often mathematics as the most suitable tool to model these statements. If the model is represented through mathematical expressions, it will typically consist of a set of equations. These in turn describe the structure of the model. The mathematical representation of financial, business, and economic models we adopt often include one or more equation, which solutions determine the magnitude of the variables we would like to understand, and the behavior of those variables under a set of particular hypotheses. In this first week of the quantitative foundations for international business, we have seen why it is important to learn some key mathematical concepts. These must be considered as preliminary steps, that in turn will allow us to deal with more complex topics in mathematical modelling, for the models we will meet later on. In detail, we have discussed and studied how to relate a number of variables to one another in order to build up the equations, which will give us the mathematical shape of the set of analytical assumptions that the model has needed and used. After this, we have seen how to use some mathematical transformations for these equations with the aim of deriving conclusions. These conclusions will follow inescapably from these assumptions. In particular, we studied the concept of a constant, a variable, and the parameter. From this very basic concept, we move on to the idea of the equation, the identity. We have seen how to manipulate and solve basic equations. Finally we have moved on to study practical application of all these concepts focusing of course, especially on equations. We have studied some relevant business formulas. And finally, we have introduced the idea of the ratio and the proportion. Now building on the material we presented this week, the next week, we'll introduce you the concept of a function. Thank you very much. [MUSIC]