The following is an incomplete list of topics covered in the course.

• Scientific knowledge
• Hypothesis testing
• Observations and measurements
• Experiments
• Models
• Statistical reasoning
• Causes and explanations
• Philosophy of social science
• Algorithmic reasoning and its limitations.
• Risk and risk assessment
• Research ethics
• Philosophical theories about the nature of mathematical objects
• Representational theorems in measurement theory
• Theoretic values of mathematical models

After having completed the course, the student should, with regards to the theory and methodology of science, both orally as well as in writing, be able to:

• Identify definitions and descriptions of concepts, theories and problem areas, as well as identify the correct application of these concepts and theories.
• Account for concepts, theories and general problem areas, as well as apply concepts and theories to specific cases.
• Critically discuss the definitions and applications of concepts and theories as they applies to specific cases of scientific research.
• Translate sentences of ordinary mathematical English into a formal language.
• chart the main lines of thought in some different philosophical theories about the nature of mathematical objects and our knowledge of them;
• describe the content of some representation theorems from the theory of measurement, and discuss the import of these theorems concerning the relationship between mathematical structures and the material world; and
• compare different mathematical models of one and the same phenomenon with regard to theoretical virtues such as simplicity, agreement with observations, etc.

Lectures

This course includes the following eleven lectures. They are all available as videos on Canvas to watch whenever you want. Their place in the schedule is a suggestion of when you might view it. The exception is the lecture “Algorithmic reasoning and its limitations” which is given as a campus lecture.

1. Introduction and scientific knowledge (26 minutes)
2. Scientific inferences (59 minutes)
3. Observation and measurement (76 minutes)
4. Experiments (49 minutes)
5. Models (62 minutes)
6. Statistics (62 minutes)
7. Explanations and causes (81 minutes)
8. Qualitative methods (93 minutes)
9. Algorithmic reasoning and its limitations
10. Research Ethics (103 minutes)
11. Anticipating Risk in Science and Engineering (85 minutes)

From the second lecture onward, there is an associated quiz of 15 questions. If you complete the quiz with at least 14 points, you will get 0,5 bonus points for the exam. You can attempt to complete the quiz as many times as you like until it closes. This quiz closes at the end of the week where the lecture is scheduled (Sunday, 23:59, of each week). (The exception is “Algorithmic reasoning and its limitations”, which has its own deadline, see Canvas.) This is to incentivise studying throughout the course, rather than only at the end. Bonus points collected during this period are valid for the exam and the re-exam belonging to this period.

In addition to these, there are two “flipped classroom” sessions. In these sessions, the lecturer answers your questions. In this period, they are given only as discussion forum interaction on Canvas. You need to have asked the question before the dates specified for the flipped classroom on Canvas, but you do not need to be present on any lecture nor do you have to watch any video. You can read the answers in the discussion forum at any time after the session.

Seminars, 1,5 credits

This course includes these four mandatory seminars.

1. Definitions, operationalizations and hypotheses
2. Designing a scientific study
3. Interpretation, analysis, and evidence
4. Research ethics

For each seminar, there are texts to read and a quiz to complete before you take the seminar. You need 14 points on the quiz before attending. If you attend without having scored 14 points on the quiz, you are not sufficiently prepared, and you will not be marked as attending. You can take the quiz as many times as you want before your seminar.

You will take one seminar each seminar week. You join a seminar group on Canvas, under the heading “People”. If you cannot see the heading, make sure you have registered. You will then take the rest of the seminars with this group, the same day and time, each week. You are welcome to switch seminar group during the course, as long as there are vacant spots in the groups under “People”.

There is more information about the seminars in the document “Seminar information”.

Project, 3 credits

In this part you will discuss the relationship between mathematics and reality. The part will consist of four lectures and one final assignment, graded pass, fail or revise. More information can be found on Canvas.

Schema HT-2021-PERIOD-1-4
Schema VT-2021-PERIOD-3-4

There are two main course texts:

• Experiments, models and methodology by Till Grüne-Yanoff.
• The Art of Doing Science by Sven Ove Hansson.

In addition, there are three supplemental texts:

• On Being a Scientist: Responsible Conduct in Research, which is an excerpt from a text by the National Academy of Sciences.
• Ethical Thinking by Jesper Ahlin.
• Algorithmic Reasoning and its Limitations by Tor Sandqvist.

Students at KTH with a permanent disability can get support during studies from Funka:

Funka - compensatory support for students with disabilities

A, B, C, D, E, FX, F

• PRO1 - Project, 3.0 credits, Grading scale: P, F
• SEM1 - Seminars, 1.5 credits, Grading scale: P, F
• TEN1 - Examination, 3.0 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

A student may request a home exam, with the maximum grade of E, if two requirements are fulfilled: (1) This is the last remaining exam left before graduation. (2) It is not possible for the student to attend the written exam because the student is, at the point of the request, residing outside of Sweden and will be residing outside of Sweden for at least twelve months following the request. The examiner approves or denies these requests.

Examination ( TEN1 )

There is an online exam at the end of the course. It will be available on a separate Canvas course page during the scheduled exam hours. To take this exam you need to register for it on kth.se during the exam registration period.

The exam consists of three parts. Part 1 is a multiple-choice part, primarily examining the first learning outcome. For each question there can be 1-4 correct options and you need to select all correct options and only the correct options to get 1 point. Partial points are not given. Whenever you start part 1 during the exam, you then have one hour to complete it. The bonus points collected during the period are then applied to the score on part 1 in 0,5 increments up to a score of 15.

Part 2 consists of two essay questions. You are here asked to explain and discuss, in your own words, the meaning of some of the course concepts and apply them to specific situations. This part tests the second and third learning outcome, up to grade level C. Each question is graded between 0-5 points, in 0,5 increments.

Part 3 tests learning outcome two and three, on the grade level between C and A. Here you are asked to explain and critically discuss the course terminology in an independent way. You do not have to complete part 3 to pass the exam, but the maximum grade is then C. Completing part 3 cannot increase your grade from below C. This part is graded C, B and A without the use of points, and bonus point cannot increase the grade above C. You have three hours to complete parts 2 and 3.

During the exam you are allowed to access the course material. Each submission will be reviewed for plagiarism. Note that you will not have enough time to complete the exam unless you have studied during the course. You can give your answers in English or Swedish.

Fullfilled seminar requirements, project requirements and written exam.

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.