|Teaching methods (Werkvormen)
- 28 hrs lecture
- 28 hrs tutor session
The student learns that the mathematics may be developed in other ways than the usual one, in particular, along the lines indicated by the famous Dutch mathematician L.E.J. Brouwer.
In this course we consider the criticism L.E.J. Brouwer (1881-1966) exercised on many results of classical real analysis, and explain why he refused to use the principle of the excluded middle in his own mathematical proofs. Brouwer not only wanted to restrict the logic of mathematical arguments but also proposed some new axioms. We will see that his new mathematics contains many delightful and convincing results.
We also treat intuitionistic logic as formalized by Heyting and Gentzen.
We will compare Brouwer's point of view with other conceptions of constructive mathematics.
After having completed and submitted a number of excercises, students have to pass an oral examination
A. Heyting, Intuitionism, an Introduction, North Holland Publ. Co., Amsterdam 1971.
E. Bishop, D. Bridges, Constructive Analysis, Springer Verlag, New York etc.,1985.
D. Bridges, F. Richman, Varieties of Constructive Mathematics, Cambridge UP, 1987.
A.S. Troelstra. D. van Dalen, Constructivism in Mathematics, Volumes I and II, North Holland Publ. Co., 1988.