# First year of Applied Mathematics

During the first year of the Bachelor’s Applied Mathematics, we will help you establish a firm foundation in formal mathematics, while also familiarising you with conditions and possibilities for application.

• Year 1Year 1
• Structures & Models
• Mathematical Proof Techniques
• Fields & Electromagnetism
• Signals & Uncertainty

## Module 1: structures and models

This module lays the foundation for you to become an applied mathematician. In this module you will study mathematics from different angles. Building on the math you learned in secondary school, you will also immediately start exploring new areas, going deeper than you ever did at secondary school. You will spend a lot of time on mathematical reasoning, abstract mathematics and modelling. In your team project you get to tackle a practical problem, in which modelling and calculating are a vital part of the solution. In this module you will follow courses like Calculus I & Prooflab I, Linear Structures I, Project Programming, Modelling and Cultural Differences.

## Module 2: mathematical proof techniques

In this module you will tackle some of the tough matters every mathematician needs to understand and that will keep coming back in the course of your studies. You will discuss these topics with your team members and carry out assignments together. This will help you grow into an applied mathematician who can communicate about his work and thus identify solutions more quickly. Learning to think in mathematical structures is important for a future applied mathematician. It helps you to see connections more quickly and to perceive the mathematical relations between seemingly very diverse problems. This means you will be able to approach them 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! In this module you will follow courses like Analysis I, Linear Optimisation, Project Prooflab II.

## Module 3: fields and electromagnetism

The third module of the first year focuses on an important subject: vector calculus. You will learn to integrate over curved surfaces, and 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 fluid flows. We deal with this subject in conjunction with electromagnetic fields theory. Joining forces 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 right before your eyes. You will get familiar with the origin of the theory you explore and with the different approaches mathematicians and physicists use. In this module you will follow courses like Vector Calculus, Electromagnetics, Presenting a Mathematical Subject.

Also, you will learn how to orally present a mathematical topic. You will practice this with a mathematical topic that is new to you and to your audience, receiving feedback from your teacher and fellow students. The presentation topics are not related to any modules, or even to the curriculum, so everyone  can really judge how clearly you present.

Femmy is working on her Module 3 final project. Read about her experiences here

## Module 4: signals and uncertainty

In modelling, uncertainty plays a huge part. Think of predictions, such as the weather forecast, or deviations in a certain process. A solid foundation in probability and statistics is essential if you want to be able to make sensible predictions. Many of the phenomena we like to make statements or predictions about can be described graphically. Think, for example, of the range of temperatures over 24 hours, the water level in certain places, or stock prices. In this module you will learn to recognise regularity, or periodicity, in graphs. Sometimes, graphs describe more than one periodicity at a time. Mathematics will help you unravel them. Combined with modelling, this expertise will give you an important mathematical tool for solving many complex problems. Computers are vital here, which is why this module also covers programming of mathematical techniques.

Read about David’s experience in his first year of Applied Mathematics at the UT, or take a look at the second-year modules.