SylabUZ
| Course name | Elements of the History and Philosophy of Mathematics |
| Course ID | 11.1-WK-MATP-EHFM-W-S14_pNadGen0DBZX |
| Faculty | Faculty of Mathematics, Computer Science and Econometrics |
| Field of study | Mathematics |
| Education profile | academic |
| Level of studies | First-cycle studies leading to Bachelor's degree |
| Beginning semester | winter term 2019/2020 |
| Semester | 4 |
| ECTS credits to win | 2 |
| Course type | optional |
| Teaching language | polish |
| Author of syllabus |
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| The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
| Lecture | 30 | 2 | - | - | Credit with grade |
Students should be familiar with an outline of history of main fields of mathematics, in particular, with evolution of the most important concepts and ideas in mathematics . Moreover , students should know the main directions in modern philosophy of mathematics.
Standard graduate courses in : logic and the set theory, geometry , mathematical analysis.
1. Outline of history of logic and the set theory. ( 2 hours )
2. Foundations of mathematics. Formalized theories. Hilbert’s program . Models of mathematical theories. Godel’s theorems and their philosophical implications. (2 hours)
3. The classical directions in the modern philosophy of mathematics. Platonism, formalism, intuitionism, constructivism. ( 2 hours)
4. The problem of the truth and existence in mathematics. The cultural basis of mathematics. ( 2 hours)
5. Different concepts of reconstruction of mathematics. Reconstruction of mathematics on the base of the set theory. Structuralism in mathematics: Bourbaki. Theory of categories ( 2 hours)
6. Elements of history of mathematics. Mathematics in the Ancient Orient.( 2 hours) Mathematics in Greece.( 2 hours) Arabic Mathematics (2 hours) Mathematics in XVI century.(2 hours) Mathematics in XVII century.(2 hours) Mathematics in XVIII century.(2 hours) Mathematics in XIX century.(2 hours)
7. Evolution of the most important mathematical concepts and ideas. Outline of history of geometry, algebra and mathematical analysis.(4 hours)
8. Outline of history of mathematics in Poland. The Lvov and the Warsaw mathematical schools.(2 hours).
Traditional lecture , open to a discussion and expressing opinions by students.
| Outcome description | Outcome symbols | Methods of verification | The class form |
Students write an essay on a chosen subject in the history or philosophy of mathematics.
1. D. Struik, A Concise History of Mathematics, Dover Publications ,Inc., New York,1948.
2. R. Murawski, Filozofia matematyki. Zarys dziejów, Warszawa 1995.
3. P. Davis, R. Hersh, Świat matematyki, PWN , Warszawa 1994.
4. James, Remarkable Mathematicians, Cambridge University Press 2002.
1. M. Kordos, Wykłady z historii matematyki, Wyd. II, SCRIPT, Warszawa 2006.
2. M. Murawski, Współczesna filozofia matematyki, Wybór tekstów, Wydawnictwo Naukowe PWN , Warszawa 2002.
Modified by dr Robert Dylewski, prof. UZ (last modification: 20-09-2019 09:51)
