Applied Epistemology of Mathematics
Praktisk kunskapsteori för matematik

FMAP01F, 7.5 credits

Valid from: Autumn 2022
Decided by: Professor Thomas Johansson
Date of establishment: 2022-06-14

General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course codes: FMAP01, TFRP80
Teaching language: English

Aim

The course aims to give students an introduction to the philosophy of mathematics from a practical perspective, and to make students aware of some important questions concerning the culture of mathematics, such as good scientific practice, reproducibility and diversity.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• be able to describe and use some basic theories in the philosophy of science, in particular their application to mathematics
• be able to describe and have practised the recovery and usage of primary and secondary sources of knowledge, especially scholarly research published in international journals
• be able to describe and have practised methods for evaluating scholarly work
• be able to give an account of relevant historical and current research questions
• be able to describe current challenges in university culture, e.g. to ensure equal opportunities and diversity.

Competences and Skills

For a passing grade the doctoral student must

• be able to apply the working methods of philosophy of science in order to identify and analyse common types of argument
• be able to write a referee report
• be able to give an account of recently acquired knowledge and insights in both written and oral form, as part of a group or individually
• through a project have been given an introduction to research on different aspects of university research and culture.

Judgement and Approach

For a passing grade the doctoral student must

• be able to argue the value of both philosophical and personal critical reflection, regarding various forms of human knowledge and science
• be able to formulate relevant criticism of both individual philosophical arguments and scientific theories.

Course Contents

The course introduces elements of 1. the philosophy of science and its application to mathematics, engineering mathematics and engineering physics 2. the history and philosophy of mathematics 3. research on diversity and equal opportunities. It discusses some questions concerning good scientific culture practice in mathematics. This includes questions about reproducibility and diversity.

Course Literature

Thomas Kuhn: The structure of scientific revolutions. 1966. There are many editions of this book, e.g. ISBN 9780226458120 from University of Chigaco Press 2012. A. Rodin: Axiomatic Architecture of Scientific Theories, Habilitation Thesis, S:t Petersburg University. 2020. Available at http://philsci-archive.pitt.edu/id/eprint/17600. N. Vavilov: Reshaping the metaphor of proof. 2019. Published in Philosophical Transactions of the Royal Society, vol 377, no 2140. https://doi.org/10.1098/rsta.2018.0279 (18 pages). Maria Chionidou-Moskofoglou (editor): Promoting Equity in Maths Achievement. , The Current Discussion:selected contributions from the proceedings of the Barcelona (25 January, 07) and the Paris (25 April, 07) Workshops. Publicacions i Edicions Universitat de Barcelona, 2008, ISBN: 978-84-475-3225-4.

Instruction Details

Types of instruction: Lectures, seminars

Examination Details

Examination formats: Written report, seminars given by participants. Written project, oral presentation.
Grading scale: Failed, pass
Examiner:

Admission Details

Admission requirements: FMAF01 Mathematics - Analytic Functions and FMAN55 Applied Mathematics and FMSF80 Mathematical Statistics, Basic Course and one of EITF85 Electromagnetic Field Theory or ETEF01 Electromagnetic Field Theory
Assumed prior knowledge: Assumed prior knowledge: Some experience of academic writing within mathematics or the natural sciences, for instance, reports or essays.

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page: https://www.maths.lth.se/course/MathCult