Famous problems of elementary mathematics MAT3501

Course content:
1.-2. Quaternions. Wedderburn theorem on finite division rings.
3.-5. Irrational, algebraic and transcendental numbers. Set theory arguments (Cantor), Liouville theorem, irrationality of fundamental constatnts (e and \pi),
6.-7. Brouwer fixed point theorem and its applications.
8.-9. Euler formula and its applications. Sylvester-Gallai theorem, Pick theorem on lattice points.
10.-11. Classical inequalities and their applications.
12.-13. Theorems on complex polynomials. Fundamental theorem of Algebra, Polya Theorem on polynomials, Tschebyschev polynomials.
14-15. Last Fermats Theorem; selected cases

Learning outcomes: Exended knowledge of selected problems important in the history of mathematics