History of Mathematics

The origins. Ancient Mathematics (Egypt, Mesopotamia, China and India). Early Greek Mathematics: Thales and Pythagoreans. Plato’s Academy. Euclid, Introduction to the Elements. The role of axioms in a theory. The mathematical proof. Geometric constructions by using straightedge and compass. Ratio and proportion. Irrational magnitudes. Archimedes and Apollonius. Conic sections (an introduction to geometric loci). Mathematical methods in Hellenistic times. Astronomy. Ptolemy, Nicomachus, Diophantus, Pappus and Hypatia.

Mathematics in the Middle Ages. China and India. Indeterminate Analysis. Mathematics in the Islamic world, Mathematics in the West. The role of the Byzantine Empire in History of Mathematics. Mathematics of the civilizations of Inca and Maya.  Mathematics around the world.

Early Modern Mathematics. Algebra in the Renaissance. The Italian Abacists. The work of Viète and Stevin. Perspective, Geography and navigation. Astronomy and Trigonometry, Logarithms, Kinematics.

Mathematics in the 17th and 18th century. Analytic and Projective Geometry. Fermat and Descartes. Finding geometrical loci. The theory of equations. Elementary probability theory. Number Theory. The beginnings of Calculus (Newton and Leibniz – First Calculus texts). Differential equations.

Mathematics in the 19th century (era of specialty): Evolution and formal foundation of Calculus (Euler, Lagrange, Cauchy, Riemann, Weierstrass). Sets of numbers. Non-Euclidean geometries (Bolyai, Lobachevsky, Gauss). Modern algebra and Cayley-Klein geometries. Matrices. Geometric transformations on a plane.

• Boyer, C. B. & Merzbach, U. C. (2011). A History of Mathematics (3^rd Edition). N.J.: John Wiley & Sons.
• Katz, V. J. (2009). A History of Mathematics. An Introduction (3^rd Edition). Boston, Ma: Pearson Education, Inc.