Cognitive Subject & Structure of the ΙPMS
Cognitive Object
The purpose of the Ι.P.M.S. is to strengthen Scientific and Technological Research and to cultivate, at postgraduate level, their Mathematical and Technological Applications, which are treated by the collaborating Departments of the Schools of Applied Mathematics and Physical Sciences, Mechanical Engineering and Naval Architecture and Mechanical Engineering of NTUA.
The Ι.P.M.S. includes five streams
The aim of each stream is to create high-level and prestigious Scientists and Researchers who will have the opportunity to work in Research Centers and International Organizations, in Greek and Foreign Universities, in Businesses as executives and in Industry. The number of courses offered per stream, their quality, their appropriate content and their organization, allow for a large number of combinations and options, covering almost every possible desired preference of the student.
Analysis and Differential Equations
Postgraduate students who choose the Analysis and Differential Equations stream are trained in the concepts and methods of modern Analysis and Differential Equations (Ordinary and Partial). They acquire a broad and deep background for the formulation, study, and solution of a wide range of problems in Technology and Applications.
They develop skills and knowledge that enable them to handle and apply in depth the methods of Analysis and Differential Equations, particularly in the Applied Physical and Technological Sciences.
Computational Mathematics
The aim of this stream is to provide high-level education in computational mathematics and in the use of large-scale scientific computations in Technology and Applications. The main mathematical tools taught to postgraduate students, with the purpose of deepening their knowledge in Computational Mathematics, come from the fields of Numerical Analysis and Scientific Computation, Differential Equations (Ordinary and Partial), as well as Mathematical Analysis.
In addition, special emphasis is placed on the use of suitable computational tools in mathematical modelling and in the analysis of problems arising from Technology and Applications.
Statistics – Probability
Stochastic Mathematics holds a central position in mathematical modelling and in solving modern complex problems. This stream aims to teach students techniques of stochastic modelling, analysis, and simulation. It consists of two complementary groups of courses.
The first group focuses on Probability Theory, Stochastic Analysis, and their applications in the Physical Sciences and Finance. During the first semester, students build a strong mathematical foundation in Probability Theory and Stochastic Processes. Then, advanced courses are offered in Stochastic Calculus, Stochastic Differential Equations, and Stochastic Optimal Control. Particular emphasis is given to applications of the theory in Finance and the Physical Sciences, as well as to the development of numerical methods for solving problems in Stochastic Mathematics.
The second group of courses aims to provide students with comprehensive scientific training and specialization in the field of Statistics, enabling them to address and solve problems involving uncertainty. The offered courses present a mathematically grounded methodology of Statistical Inference, along with its applications to problems from various scientific disciplines.
Several courses include the use of statistical software packages, while students gain knowledge and develop skills across a broad range of areas in Statistics, such as Bayesian Statistics, Computational Statistics, Generalized Linear Models, Statistical Quality Control, Reliability, and Statistical Design.
Mathematics of Informatics
The goal of the Mathematics–Informatics stream is to offer very high-level education in the mathematical aspect of Computer Science. The mathematical side of Computer Science constitutes an important methodological tool for numerous applications of the field worldwide.
These Mathematics cover both the bidirectional relationship between Mathematics and Computer Science and their broad range of applications in other sciences and technology. Among the subjects developed are applications of algorithm theory, graph theory (graph representation), and logic in informatics.
A student of this stream will not only understand and handle the particularities of the mathematical techniques used by computers but will also be able to reformulate problems effectively and derive the desired solutions swiftly and accurately.
Algebraic, Geometric and Topological Structures
In this stream, students are introduced to both introductory and advanced knowledge in the fields of Algebra, Geometry, and Topology. They acquire the necessary background to apply these areas to interdisciplinary problems and become familiar with their applications in Mathematics and other sciences.