a solid academic programme in which you delve into the nature – or art, some would say – of mathematics.

From day one you will engage in the abstract and formal aspects of mathematics, always keeping in mind its practical applicability. You will become familiar with calculus, linear algebra, probability and much more. At the same time, you will engage in applying the theory. One way of doing this is modelling: using abstraction to reduce complex problems to their essence, as described in mathematical terms, and then using mathematical analysis to identify solutions to the original problem. Modelling requires skills that you will gradually develop through the different learning lines that run through the programme. These learning lines include abstract mathematics, mathematical modelling and practical skills – think of programming, (intercultural) collaboration or presentation.

You will become a mathematician who has mastered to perfection the cycle of abstraction, analysis and solution, and who can easily participate in interdisciplinary teams. This means you will be able to make a substantial contribution to solving tough societal problems.

## Modules Applied Mathematics

During this three-year Bachelor's in Applied Mathematics, you will follow twelve modules: four modules per year. Each module covers a theme and brings together all the main aspects of your studies: theory and practice, research and solution design, self-study and teamwork.

Module 1 | Structures & Models15

This module lays the foundation for you to become an applied mathematician. 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. 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 the courses Analysis 1, Linear Structures 1, and Modelling and Programming 1.

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Module 2 | Structures & Systems15

In this module you expand your skills and deepen your knowledge of the abstract foundation of mathematics in the courses Analysis 2 and Linear Structures 2. You immediately apply your newly acquired abstract knowledge on Systems Theory. Systems Theory involves the control of systems. For example, how can you distribute power over the different rotors of a drone to make it perform a task, while it also maintains its balance.

Module 3 | Signals & Uncertainty15

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 would like to understand or predict can be described as functions of time. 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 data. 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 also this module continues with teaching you effective programming.

Module 4 | Numerical Mathematics and Differential Equations15

Mathematical models often involve dynamics, like in preypredator systems or masses moving in a potential field. These models involve differential equations and are called dynamic, because they show the relationship between the variables and their changes, whereas so-called static models only represent the variables. In this module you will study dynamic models from the perspective of differential equations. Numerical methods are needed if no closedform solution to a mathematical problem exists or if solving the problem by hand is infeasible or even impossible. Consider, for instance, the simulation of an airflow around a formula one car or the fitting of large data sets. Numerically solving such real-life applications introduces several errors: modelling errors, data errors, truncation errors, and rounding errors. In the modelling team project you will apply the knowledge of theoretical parts.

Module 5 | Statistics & Analysis15

In this module you will learn to look for linear relationships in statistical data, using an advanced software package, SPSS. In the Mathematical statistics part of the module, you will learn much of the underlying theory. You will continue to develop your knowledge of basic mathematics in Analysis, Part 2 (having done Part 1 in module 2 of the first year). Also, you will learn in this module how to reflect on different aspects within and outside the field of mathematics. For example, the different approaches mathematicians take and consider to develop a theory, or how the same behaviour can be interpreted differently by different people. In this module you will follow courses like Mathematical Statistics, Analysis II, Prooflab Revisited: Diversity in Cultures.

Module 6 | Statistics & Optimization15

You are introduced to optimization, which appears quite often in real life. Which location to choose, what to decide, how to allocate items, and so on. You learn how to model these problems and solve them and understand the underlying mathematics. This knowledge is applied to a neural network. Besides, you continue your studies of statistics and will learn about regression analysis, estimation and quantification of uncertainty in data and dealing with dependency in data. You use the program R for computations and learn how to draw correct conclusions based on those computations.

Module 7 | Discrete Structures & Efficient Algorithms15

You will be studying so-called discrete structures. As opposed to continuous structures, such as a collection of real numbers, these structures are about finite or countably infinite sets and variations thereon. The focus is on making calculations within such sets, such as finding the shortest path between a certain number of points and the links between those points. The computability and complexity of these calculations are important factors. You will use elements from abstract algebra, such as groups, rings and fields, as well as finite automata and Turing machines. This module is joint with Technical Computer Science. In this module you will follow courses like Algorithmic Discrete Mathematics, Algebra, Implementation Project on Graph Isomorphism.

Module 8 | Modelling & Analysis of Stochastic Processes15

As far as mathematics is concerned, this module is about Markov chains. These are stochastic models, or models in which outcomes depend on chance, and in which you go from state to state according to a given probability distribution, regardless of where you were in the past. These models find all sorts of applications, for example, in modelling queues. They also play a vital role in modelling and simulating complex stochastic systems. In your project group, you will learn how to use such models to make good decisions in practical situations in which chance plays an important role, for example, logistics, a hospital environment or traffic. In this module you will follow courses like Stochastic Models and Markov Chains.

Modules 9&10 | Electives30

In your elective space, you have different options such as: taking subjects of your choice at the University of Twente, for example, from our Bachelor’s Civil Engineering or Computer Science, or at other universities in the Netherlands or abroad. You could also sign up with one of our student teams or complete a pre-master’s in preparation for a Master’s other than Applied Mathematics, such as a technical master’s or one of our social sciences programmes. Is it your ambition to teach? Choose the Education minor Learn to Teach and get a second-degree teaching qualification. This qualification allows you to work as a teacher at secondary schools in the Netherlands. Please be aware that this minor is in Dutch.

Modules 11&12 | Graduation Assignment30

More than half of the second semester is dedicated to your thesis; you spent the remaining time on additional coursework like Graph Theory, Introduction to Partial Differential Equations, and Complex Function Theory

. Your graduation project is a large modelling assignment, often taken from real life. In preparation for this assignment, you will first study and discuss several mathematics articles. This will give you experience in reading and understanding scientific research. Then, you get to formulate your own research question on the basis of your assignment. Afterwards, you are to write a report on your findings. And to finish off your project - and your bachelor's studies - you will present your work at a special student conference.

## FIRST TIME AT UNIVERSITY

When you are a first-year student, you experience many new things. Here we start explaining at least a few of them.

During your three-year bachelor's programme, you will take 12 modules (4 modules per year). Each module, you will address** a theme that is hot in society, business or industry**. This theme will bring together all the components of your study: theory and practice, research, designing solutions, self-study and teamwork.

A fixed part of every module is the team project, in which you and your teammates apply the knowledge you have acquired to a current challenge and design a workable solution. This learning method is part of the Twente Education Model (TOM): an innovative approach to studying that you will only find at the University of Twente.

Study points - how do they work? Student workload at Dutch universities is expressed in EC, also named ECTS (European Credit Transfer and Accumulation System), which is widely used throughout the European Union. In the Netherlands, each credit represents 28 hours of work. You need to acquire 60 credits each year.

Your programme assigns fixed numbers of hours to each assignment, project report or exam. In the first year, you need to get at least 45 out of 60 points to be able to continue to the second year.

Did you obtain 45 or more credit points? Then you can continue to the 2nd year Our aim is to get you in the right place as soon as possible, which is why we use the principle of a binding recommendation. You will receive a positive recommendation if you have obtained 45 or more of the 60 EC in the first year. A negative recommendation is binding and means you have to leave the programme. Under certain circumstances, we may give you a positive recommendation despite a low score. For example, if we are confident that you are in the right place.

Do personal circumstances such as illness or problems interfere with your study performance? Student Affairs Coaching & Counselling (SACC) is there to support you.