Course Content (Syllabus)
The course is part of the module of courses that aim to offer dexterities for teaching mathematics in Secondary Education.
The course is concerned with the development of Mathematics from antiquity to 19th century: a special emphasis
will be given to the development of algebra. The following topics will be covered: Egyptian and Babylonian mathematics, the famous three problems of antiquity, the "Elements" of Euclid, the role of Euclid's "fifth axiom" in Euclidean Geometry and the "discovery" of other Geometries in the 19th century, Hilbert's attempt for the axiomatic foundation of geometry. Selections from Archimedes' work and his "Method", topics from the History of Number Theory, mathematics in Islam, mathematics during Renaissance: the solution of cubic and fourth degree equations, the beginnings of calculus, Newton and Leibniz, the discovery of Hamilton's quadratic numbers, the non-solvability of the 5th degree equation, the transition from practical algebra and arithmetic to abstract algebra with Gauss and Galois, E. Noether and the development of algebra.
Course Bibliography (Eudoxus)
ΙΣΤΟΡΙΑ ΤΩΝ ΜΑΘΗΜΑΤΙΚΩΝ, Μια εισαγωγή, V. Katz, Πανεπιστημιακές εκδόσεις Κρήτης
Η ιστορία των Μαθηματικών, Carl B. Boyer; Uta C. Merzbach, εκδόσεις Πνευματικός Γ. Α.,
Συνοπτική ιστορία των μαθηματικών, Dirk Struik, Εκδόσεις ΔΑΙΔΑΛΟΣ