Course information

Introduction. Euclid's Elements. The Background. The first four Books and the non-Euclidean Geometry (Arabs, Saccheri, Lambert, Legendre, Lobatchevskii, Einstein's theory of relativity. Book V, Eudoxus theory of proportions and the theories of real numbers during the 19th century. Quadratures. Eudoxus' theory of exhaustion. The quadrature of circle. The nature of number . The proof of as transcendental number. Infinitesimal methods f integration and differentiation in Archimedes' work. The development of these methods in Middle Ages and Renaissance. The creation of Calculus by Newton and Leibniz. The Reform of Analysis: Bolzano-Cauchy -Weierstrass. The problem of the foundations of Mathematics: Zeno paradoxes, B. Bolzano, Fourier. Georg Cantor. Problems and Paradoxes in Set Theory. Axiomatic Foundation of Set Theory. The Conics of Apollonius. Kepler- Newton. Apollonius and analytic geometry Fermat-Descartes. Diophantus and Diophantine equations. Pierre de Fermat. Fermat’s little theory and cryptography. Timaeus and the first program of mathematical physics. Euclid Elements and the mathematical introduction in such physics. Galileo- Newton. W. Heisenberg.