Ph.D. (Mathematics)University of Madras
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The University of Madras offers number of courses one of the course is Ph.D. (Mathematics)
This Course is offered by the Department of Mathematics
This University Department, was then the first, and for the some time the only center where some of these topics of basic importance were studied. The topics included: Modern Algebra, Symbolic Logic, Boolean algebra and its relation to Logic, Elements of Set Theory, Topology of Points Sets, Study of Linear Spaces, of Spectral Theory in a Hilbert space, Convergence questions in topology, Partial order lattice theory, etc. Among the publications of the period are articles by Dr. R.Vaidyanathaswamy and students on such topics as: The Algebra of Quadratic Residues, the Group operations of a Boolean algebra, Quasi-Boolean Algebras and Open sets of a Topological Space, Localization Theory in Set Topology, etc., The students published articles on Tauberian theorems, Systems of non-linear integral equations, Legendre functions, Semi-convergent series, Expansions in Eigen functions, Multiplicative functions, Structure of the propositional calculus, Bessel summability of series, Rieszian summability, Intuitionistic theory of linear order, the last residue class in a Distributive Lattice, Ramanujan's trigonometric sum, Congruences and Homorphisms on partially ordered sets, Desarguesian geometries, the Grassman cubic and the Wallance line, Duality of linear complexes in affine spaces, etc. In 1947 Dr.Vaidyanathaswamy published his 'Treatise on set-topology', in which much valuable material on the subject is brought together, and lattice methods are systematically used.