In this module you will study mathematics from different angles. You build on the mathematics you studied in secondary school, but you will also immediately start exploring new areas, too. The methodology is also different than those used at most secondary schools. You will delve deeper into the material, and there will be a strong emphasis on mathematical reasoning as well as the formal and abstract sides of mathematics. Another area we focus on at the University of Twente is mathematical models. These are vital for applying mathematics. You will spend part of your time working in a team on a project-based assignment. This involves working independently on a practical problem, in which calculating mathematical models is a vital part of the right solution. Sometimes you will discover that you need extra knowledge or techniques to resolve the issue at hand, but mostly you will find you can rely on what you have learnt in the other areas of the module.
In this module you will delve even deeper into mathematics. You will learn about matters that every mathematician needs to understand and that will constantly recur in the course of your studies. Some of these topics are not really that simple and you may not understand everything in one go. Again, it helps that you will be working on projects as a team, as it means you can easily talk issues over with the members of your team. This will help you develop into an applied mathematician who can communicate about his field and, therefore, identify solutions more quickly. Learning to think in mathematical structures is important for a future applied mathematician, because it helps you to see connections more quickly and to perceive that apparently completely different problems are actually mathematically related, so they can be approached using the same techniques. In your project, you will look for the best solution in relation to a predefined criterion, for example 'as cheap as possible', or 'as fast as possible'. It will involve a lot of mathematics.
Many phenomena from daily practices can be described in graphs. Like the range of temperatures during 24 hours, the water level in certain places, or stock prices. By examining these graphs in a certain way, you will learn to discover certain regularities – something that in mathematics is called periodicity. Sometimes these types of graphs describe more than one periodicity at a time. Mathematics will help you unravel them.
In modelling, uncertainty plays an important part. Think of weather forecasts. In order to make sensible statements and predictions, a strong foundation in probability and statistics is essential. Combine those with the graphical representation of signals and you will have an important mathematical tool for solving complex problems. Again, computers are vital here, which is why this module also covers the programming of mathematical techniques.
The last module of your first year focuses on an important subject: vector calculus. Much of what you have already learnt in the previous modules will come together here. You will learn to integrate over curved surfaces. Seemingly complicated calculations will suddenly become simple through the use of integrations theorems. Vector calculus is important because of its many applications, for example in flow measurement. We will approach this in conjunction with electromagnetic fields theory. Together with Physics students, you will perform experiments and tests that will sometimes cause sparks to fly - both literally and figuratively! You will see mathematics at work with your own eyes. In this module, you will also learn how the theory originated and how mathematicians and physicists approach it differently.