University of Canberra

Dr. Sergey Sergeev

Masters Projects.

- Projects in Calculus

1.1 Complex calculus and foundations of the modern theoretical Statistics [TAKEN]

1.2 Complex calculus and and its application to multidimensional Euclidean Geometry and to the theory of special functions - Projects in Analysis

2.1 Notion of Analysis, its difference from the Calculus. Example: derivation of

∑_(n=1)^∞▒1/n^2 =π^2/6,

and many other equations - Projects in Discrete Mathematics

3.1 Modern analytical cryptography

3.2 Exotic mathematical induction - Projects in History of Mathematics/History of Mathematical Education

4.1 Napoleon theorem (how the Napoleon Theorem can be/can not be proven by the methods of Euclidean Geometry)

4.2 History of Tsiolkovsky equation (Moore 1813, Taight and Stils 1856, Leitch 1861, Tsiolkovsky 1903), modern situation. - Projects in Modern Geometry

5.1 De Rham complex and the coordinate free formulation of Maxwell theory.

5.2 Foundations of Riemann Geometry. Example: the Poincare space, 3-wave equations, volumes of ideal polyhedra.

5.3 Foundations of Riemann Geometry. Example: the general and special relativity. Applications to GPS.