Applied mathematical thinking

The course is mainly intended to strengthen the students’ mathematical thinking, and their ability to apply such thinking in applications, and in their continued studies. The focus is not on mathematical knowledge in the traditional sense, but on the often implied abilities needed to effectively be able to apply the mathematics you already know, and efficiently be able to learn new mathematics. The most important parts are mathematical reasoning, problem solving and modelling. Important aspects such as using the computer as a part of your mathematical thinking, and to be able to communicate with and about mathematics are also integrated in the course. The course also in a natural way introduces basic mathematical knowledge useful in computer science and other areas, including a selection of Swedish upper secondary courses Mathematics 4 and 5. By developing the ability to think mathematically, the course complements other more traditional courses in mathematics, and by providing the student with experience of different areas of application, the gap between mathematical theory and relevant applications is bridged. The core of the course is a number of carefully selected problems, used as starting points for the student’s own learning, where student by working in an investigative way develop their own abilities. We also have lectures which provide a broader understanding, follow-up and perspective. The problems illustrate many different areas of application, and their level of difficulty is adapted to efficiently practice the abilities to think and work mathematically in different situations. In connection with the exercises, we also discuss different problem solving strategies, reflect on solutions, and compare different ways to solve the same problem. We also give an orientation about the role of mathematics in various applications and demonstrate the importance of mathematical computer models.