Applied mathematical thinking

The course is a single-subject course at Gothenburg University.

To enter the course, 7,5 hec in mathematics (calculus, linear algebra, mathematical statistics and/or discrete mathematics) are needed.

Applicants must prove knowledge of English: English 6/English level 2 or the equivalent level of an internationally recognized test, for example TOEFL, IELTS.

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 therefore includes occasional running and understanding of simple given computer programs.

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.

On successful completion of the course the student will be able to:

Knowledge and understanding

• Explain different aspects of mathematical thinking: mathematical reasoning, problem solving, modelling.
• Explain how mathematical thinking can be applied in different areas.
• Explain common mathematical knowledge and how it can be used (including functions, equations, derivatives and integrals, probabilities, sets, graphs).

Competence and skills

• Show a basic ability to use mathematical concepts such as definitions, theorems, as well as different kinds of mathematical reasoning and proofs (mathematical reasoning).
• Show a basic ability to solve complex and unknown problems with a structured and investigative approach (mathematical problem solving).
• Show a basic ability to investigate real problems, determine if they can be seen from a mathematical perspective and translate to mathematical problems, and adapt mathematical conclusions to the real problem (mathematical modelling).
• Communicate about and with the help of mathematics.
• Use different computational tools as a natural part of thinking and working mathematically.

Judgement and approach

• Identify how own thinking can be used to solve a problem, and to what extent previous knowledge can be used.
• Show a reflective attitude to the course contents and to their own thinking.
• Show care for precision and quality in all work.

The course is mainly organized in modules. For every module there is an introductory lecture and a compulsory follow-up lecture providing feedback on the problems of the module.

The learning is supported by an interactive way of teaching with a lot of contact between students and teachers. This occurs during supervision hours where students work with the problems and regularly discuss with the supervisors. They will then receive individual feedback and guidance in their own problem solving, and develop
their independent abilities.

Language of instruction: English

The course is examined through written assignments in weekly modules and through an oral discussion that is included in the last module. All activities are normally done in groups of two persons. To pass the course, attendance of selected lectures is also required.

If a student who has been failed twice for the same examination element wishes to change examiner before the next examination session, such a request is to be granted unless there are specific reasons to the contrary (Chapter 6 Section 22 HF).

If a student has received a certificate of disability study support from the University of Gothenburg with a recommendation of adapted examination and/or adapted forms of assessment, an examiner may decide, if this is consistent with the course’s intended learning outcomes and provided that no unreasonable resources would be needed, to grant the student adapted examination and/or adapted forms of assessment.

If a course has been discontinued or undergone major changes, the student must be offered at least two examination sessions in addition to ordinary examination sessions. These sessions are to be spread over a period of at least one year but no more than two years after the course has been discontinued/changed. The same applies to placement and internship (VFU) except that this is restricted to only one further examination session.

If a student has been notified that they fulfil the requirements for being a student at Riksidrottsuniversitetet (RIU student), to combine elite sports activities with studies, the examiner is entitled to decide on adaptation of examinations if this is done in accordance with the Local rules regarding RIU students at the University of Gothenburg.

Sub-courses

1. Assignments, 7.5 credits
   Grading scale: Pass with distinction (5), Pass with credit (4), Pass (3) and Fail (U)

To pass the course, you must pass all assignments and attend mandatory sessions. For a grade higher than passing for the entire course, you need to obtain a higher total score on the graded components.

The course is evaluated through meetings both during and after the course between teachers and student representatives. Further, an anonymous questionnaire is used to ensure written information. The outcome of the evaluations serves to improve the course by indication which parts could be added, improved, changed or removed.

The course is a joint course together with Chalmers.

The course replaces the course DIT025, 7.5 hec. The course cannot be included in a degree which contains DIT025, DIT991, DIT992, DIT855 or DIT856. Neither can the course be included in a degree which is based on another degree in which the course DIT025, DIT991, DIT992, DIT855 or DIT856 is included.