Topics in Philosophy of Mathematical Practice
This highly interactive summer school offers students from mathematics and philosophy of mathematics the opportunity 1) to gain knowledge about the central topics in the philosophy of mathematical practice and 2) to gain the basic skills needed in order to practice empirically informed philosophy of mathematical practice themselves.
The course will be organized in two parts, a four-week asynchronous online part (25 hours per week) and a two week synchronous online part (full time).
The asynchronous online part will include reading of research papers, online discussion of topics raised in the papers, online collaboration and supervision in developing problem formulations for final products. The material will primarily be centered on the following four themes from contemporary philosophy of mathematical practice:
- The role of diagrams in mathematical practice
- Proofs as vehicles of communication in mathematical practice
- Experimental aspects of mathematical practice
- Formal aspects of mathematical practice
Furthermore, the students will familiarize themselves with basic theories of empirical data collection during the online part of the course.
The synchronous online part will consist of the following three elements:
- Lectures following up on the four themes in philosophy of mathematical practice covered in the on-line part.
- Workshops on empirical data collection.
- Practical work preparing an empirically informed product in the philosophy of mathematical practice (such as an essay informed by data from e.g. qualitative interviews, a questionnaire or corpus analysis performed by the student).
Students will receive group supervision on their product during the synchronous online part of the course.
After following the course students should have the following skills, knowledge and competences:
The students should be able to collect and analyze empirical material
The students should be able to account for central topics in the philosophy of mathematical practice.
The students should be able to:
- Reflect on the strengths and limitations of empirical methods.
- Discuss and reflect on central topics in philosophy of mathematical practice.
- Produce empirically informed written products in the area of philosophy of mathematics.
Lectures, online exercises, group work, group supervision, and practical workshops.
Students will be given a collection of research papers and excerpts from text books.
It is recommended that at least one of the following three
qualifications is fulfilled:
1) BSc in mathematics and knowledge about philosophy.
2) BA in philosophy and knowledge about mathematics.
3) knowledge equivalent to one of the following books:
- Johansen and Sørensen (2014): Invitation til matematikkens videnskabsteori
- Mark Colyvan (2012): An Introduction to the Philosophy of Mathematics
The course is a 100% online course.
The student will be given oral feedback of the short presentations made during the synchronous online part of the course, and a short written feedback of the final exam project.
- 7,5 ECTS
- Type of assessment
Written assignmentTake-home assignment consisting of four small exercises posted during the asynchronous online part of the course and a written project to be produced during the synchronous online part of the course and in the following week. All five parts of the assignment must be handed in no later than friday in the examination week. The assignment will be assessed as a collected whole.
- All aids allowed
- Marking scale
- passed/not passed
- Censorship form
- No external censorship
One internal examiner
Criteria for exam assessment
See Learning Outcome
Single subject courses (day)
- Class Instruction
- Project work
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
Asynchronous online part: 4/7 - 29/7 (4 weeks at 25 study hours per week)
Synchronous online: 1/8 - 12/8 (full time/40 study hours per week)
Individual project: 15/8 - 26/8 (26 hours)
Written project exam assignment, hand in: 26/8
- Study Board of Mathematics and Computer Science
- Department of Science Education
- Faculty of Science
- Mikkel Willum Johansen (3-7c86794f787d733d7a843d737a)
- Henrik Kragh Sørensen (12-726f787c737538757c6b71724a73786e38757f386e75)
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Courseinformation of students