What will I learn?
In the first and second year, you absorb a lot of theory. You will learn to apply this theory during the projects of the Modelling course. You will also learn how to work on projects. After all, as an engineer, you need to be able to cooperate, present and communicate. In the third year, you will start with an elective: the so-called minor. Eventually, you will complete the bachelor's programme with a graduation assignment. After completion of the programme, you can add Bachelor of Science (BSc) to your name. Structure of the programme "Mathematics, a subject with infinite dimensions" - Joost de Groot Coordinator of the Bachelor of Applied Mathematics Distribution of courses 7% Optimisation 7% Stochastics 7% Discrete mathematics 10% Bachelor final project 10% Numerics and differential equation 13% Elective courses 13% Modelling 16% Analysis 17% Minor Study Guide Modules The first year The second year The third year The Applied Mathematics degree programme consists of five modules: Modelling and Applications Numerical Methods and Differential Equations Optimisation and Discrete Mathematics Analysis Stochastics The first year of the programme revolves around fundamental mathematics. These courses are a level up from secondary school. You will also learn about something completely new in courses which focus on reasoning. You will apply the theory you learn during the first two years in projects of the Modelling course. In the third year, you will take courses and do a minor. The degree programme is rounded off with the Bachelor’s graduation project. In addition to courses in fundamental mathematics, you will get started this year with mathematical modelling as well as learning how to present a mathematical solution. Other courses include probability theory, algebra and programming. You will also take a technology elective module. And because the mathematics at university is so different from that at secondary school, a lot of attention is paid to personal supervision. You will take part in a mentor group of ten students from the beginning of the first year. A faculty mentor will supervise you on study skills for two hours a week. In the second year, you will take eight compulsory mathematics courses, from fundamental to applied and from broad to in-depth. You will also get to choose an elective from a list of approximately five courses, such as Advanced Statistics and Decision Analysis. So you can customise the Applied Mathematics degree programme a bit. You will also work on a project, by modelling a mathematical physical problem, such as an epidemic.In the second year, you will take eight compulsory mathematics courses, from fundamental to applied and from broad to in-depth. You will also get to choose an elective from a list of approximately five courses, such as Advanced Statistics and Decision Analysis. So you can customise the Applied Mathematics degree programme a bit. You will also work on a project, by modelling a mathematical physical problem, such as an epidemic. Courses and competencies Real Analysis (AM2090) Building on the analysis courses Mathematical Structures and Linear Algebra, this course is an important foundation for later analysis and probability theory courses. The course is divided into two parts: metric spaces, and measurement and integration theory. At the end of the course, you will be able to understand, explain and apply the theory learned. Optimisation (AM2020) Are you interested in the mathematics underneath defining the shortest routes and matchings? In this course you will learn to view and solve these kinds of problems mathematically. For example: 'What are the best ambulance standby locations in a town (and how many are needed) to ensure that all areas of the town can be reached as quickly as possible?' This course deals with numerous algorithms, each of which solves a different general problem. Introduction to Statistics (AM2080) This course applies the knowledge acquired in Introduction to Probability Theory. Its components include making predictions and basing decisions on historical data. This involves being able to write an appropriate probability model in which the unknown parameters have to be estimated on the basis of the given data. Performing statistical analyses requires use of the statistical software package R, which you will learn to work with during this course. Linear Algebra 2 (AM2010) Linear Algebra 2 takes up where Linear Algebra 1 left off and deals with sets of vectors. These sets have special properties. While in Linear Algebra 1 you learn about calculations and all kinds of rules, in Linear Algebra 2 you will also learn the theory and properties, as with Mathematical Structures. Ordinary Differential Equations (AM2030) This course is an introduction to differential equations. A differential equation is an equation for which the solution is a function. The equation involves both the function and its derivative. A differential equation is not as easily solved as a linear or quadratic equation. You will therefore learn the many different ways of solving different kinds of differential equations. There are also several laboratory modules that demonstrate how important differential equations are to mathematically describing and solving practical problems. Modelling 2A and 2B (AM2050-A and AM2050-B) The structure of this course is similar to that of the first-year courses Modelling A and B. In the second year, part A involves working on a mathematical model for probability and statistics. In part B you will work on a mathematical-physical problem. One example of such a project could be creating a model of a flu epidemic. This would involve researching how the number of people affected increases and decreases over time as well as how the epidemic spreads in spatial terms. Numerical Methods 1 (AM2060) Some mathematical problems cannot be solved exactly, or not easily. This is where numerical methods come into the picture. These are methods that approach the solution of a problem rather than solving it exactly. An important part of this is the laboratory module, during which you will implement these methods in MATLAB. Partial Differential Equations (AM2070) This course also concerns methods of solving differential equations, but a different type of equation. The problems discussed in this course are practical ones and include, for example, a simple model of traffic congestion. It is important to consider not only the mathematical solution but also its interpretation. When you calculate the heat distribution of a bar, for instance, it is impossible to determine an infinite temperature. It might be possible mathematically, but is physically impossible. Complex Function Theory (AM2040) Complex Function Theory is actually another analysis course. In this case it concerns the application of functions to complex numbers and images that are also complex numbers. In effect, you will expand your understanding of the basic concepts of analysis to the complex domain. What's great about this is that these functions have very special properties. They can help you integrate functions that you were not yet able to integrate in Analysis 1 or 2, for example. Elective There is scope for a mathematical elective in the third quarter. The second-year electives are: Decision Theory (the application of probability theory and statistics to make decisions about problems with a degree of uncertainty), History of Mathematics (the history of mathematics is studied in work groups), Philosophy of Mathematics (the philosophy of mathematics is studied in work groups), Mathematical Models in Biology, Advanced Statistics (theory and application of generalised linear models, such as linear regression models), Applied Algebra: Codes and Cryptosystems (a course on the use of algebra to encrypt data and break codes, etc.) and Markov Processes (This is an introductory course on Markov chains, where time-discrete and continuous time Markov chains will be introduced, and their most fundamental basic properties studied). You will begin the first half of the third year with a minor. In the third quarter, you will take two electives, helping you to set your own course. You will also take an intensive course in presentation skills. The degree programme is rounded off with the Bachelor’s graduation project. This involves working on a mathematical or practically oriented problem, such as creating a strategy for the Nuna solar car in South Africa or modelling wound healing. This project lasts three months and enables you to demonstrate that you can tackle a problem independently, and present your finding adequately both orally and in writing. Minor Your minor is an opportunity to gain more in-depth knowledge of mathematics or another subject. This could be computer science or physics, for example, but could just as easily be medicine, law or indeed any other field of study. You are completely free in your choice of minor, which need not be relevant to your Bachelor's degree programme in Applied Mathematics. Electives Besides your minor, you also have freedom of choice in the form of electives. In the third year, you can choose two. The third-year electives are: Mathematical Physical Models (the application of the Partial Differential Equations course to such physical phenomena as heat conduction), Inverse Problems, Numerical Methods 2 (which follows on from Numerical Methods 1), Graph Theory (this course is about the mathematical theory of networks), Advanced Probability (theoretical treatment of analysis concepts that play a part in the calculation of probability), Fourier Analysis (theory and applications of Fourier series), Differential Geometry (The focus of this course will be on Riemannian geometry, the study of metric spaces in a smooth context), Topology (studies notions from previous subjects - such as open collections, convergence and compactness - in a broader context than that of metric spaces) and Mathematics Seminar. Bachelor Colloquium The Bachelor Colloquium forms a relatively small part of the Bachelor's final project. Here, students develop skills in the verbal presentation of a mathematical subject. Bachelor Project (TW3050) Your Bachelor's degree programme concludes with a Bachelor Project, which involves working on a mathematical or practically oriented problem. You choose a problem from one of the various research groups of the Mathematics department. The next step is to search for the relevant background literature and to translate the problem into a mathematical form. You will then solve the mathematical problem and subsequently translate the solution back into the practical situation. The project concludes with the submission of a thesis and delivery of a presentation.
