Curriculum
The IDPP
The IDPP awards a Postgraduate Diploma (PGD) in the area of Mathematical Modeling in Modern Technologies and Financial Engineering upon successful completion of the relevant course of study.
The title of the IDPP is: “Mathematical Modeling in Modern Technologies and Financial Engineering” (MathTechFin)
The translation of the IDPP title into Greek is: “Μαθηματική Προτυποποίηση σε Σύγχρονες Τεχνολογίες και τη Χρηματοοικονομική» (ΜΠΣΤΧ)”
Subject of the IDPP:
In recent decades, an intense research activity has developed, internationally and also in Greece, to study both natural processes and technological, economic and social problems using the tools of modern Mathematical Science.
The ever-increasing complexity of both technological processes and industrial and business activities requires the substantial contribution of applied mathematics and in particular the so-called industrial mathematics, mainly in the form of mathematical modeling and computational mathematics. Mathematical analysis – deterministic or stochastic – and numerical simulation as well as the learning of mathematical models from data can, in many cases, replace long-term experiments for the design of new materials, devices and complex systems. They thus contribute substantially to the development and implementation of procedures that provide greater flexibility of choices, economy and safety in the execution of experimental controls, as well as to the understanding of dynamic behavior in the ever-expanding spectrum of human activities, as well as to enable a new form of cooperation and interaction between humans and systems. Today, it is now common knowledge that, in all of the above, modern theories of linear and nonlinear systems, deterministic and stochastic approaches, discrete techniques, and finally mathematical tools of the continuum as well as advanced statistical methodologies capable of utilizing the available abundance of data of all forms can play a pioneering role. However, their utilization requires systematic development of basic research and extensive experience (and feedback) from the application of theoretical results to the corresponding problems.
Mathematical modeling is a very important branch of the positive, technological and economic sciences for several reasons:- It often leads to the discovery of particularly important new phenomena, which arise due to the complexity of systems and the non-local nature of the interactions that take place in them.- It requires a combination of knowledge from different branches of mathematics and their harmonization with the understanding at the physical, technological, biological, social and economic (depending on the case) level of the processes that take place in the system under study. – Mathematical models allow the inexpensive and systematic investigation of the behavior of the systems and processes that they model, by varying a series of free control parameters, as well as the finding of optimal values and behaviors through numerical simulations and/or analytical observations.
Purpose of the IDPP:
The aim of the IDPP is to provide students with high-level resources from the field of Mathematical Science and in particular from the areas of Mathematical Analysis (Deterministic and Stochastic), Differential Equations and Dynamical Systems, Numerical Analysis and Statistics. Resources which, over time, are increasingly proving to be a common meeting place for Mathematical Modeling techniques, both for the processes that take place in natural phenomena and technological systems, and for the basic phenomena of the evolution of social and economic systems.
The Direction of Modern Technologies:
The objective of the MSc Program in Mathematical Modeling in Modern Technologies and Finance is to produce highly esteemed scientists and researchers who will work at Greek or foreign universities, research centers, and international organizations, as well as high-level executives who will be engaged in management and research in the fields of industry and business. Specifically, for students interested in the specialization of “Modern Technologies”, the MSc Program aims to:
- Provide comprehensive knowledge with a unified methodological approach to the fundamental tools of mathematical modeling of continuous and discrete systems and processes, both microscopic and macroscopic, deterministic and stochastic.
- Through examples (both in the laboratory and in real-world settings), reinforce the capabilities of modeling across a wide range of systems for the design of products and processes in the fields of biosciences (drug design, structure-activity relationships of biological macromolecules, biomedical engineering) and materials science (structure-property-processing-performance relationships, polymers, nanostructured materials and devices for applications in microelectronics, telecommunications, energy technologies, and environmental protection).
Students will be trained in creating mathematical models based on the physical sciences to describe the behavior of the aforementioned systems at various length and time scales (multiscale modeling) and in solving these models analytically or numerically using methods that ensure high reliability and low computational cost. They will understand how different levels of description and simulation (molecular, mesoscale, and macroscopic) can be interconnected to achieve an in-depth understanding and quantitative prediction of phenomena and the optimization of products and processes for specific applications. Graduates of this specialization will be able to transform complex problems, encountered daily in the aforementioned fields, into functional models. The mathematical investigation and numerical simulation of these models will significantly impact the technological, scientific, and economic progress of our country. The great importance of this specialization is evidenced, among other things, by the awarding of the 2013 Nobel Prize in Chemistry to Martin Karplus, Michael Levitt, and Arieh Warshel for the development of multiscale models for complex chemical systems. Additionally, large-scale research programs such as the Materials Genome Initiative in the USA aim to discover, produce, and utilize advanced materials twice as quickly and at a fraction of the current cost. The structure of the Postgraduate Programme is based on the three fundamental categorizations of systems-models in general: macroscopic-microscopic, deterministic-stochastic, and continuousdiscrete. Special emphasis is also placed on the importance and necessity of nonlinear perspectives. Efforts are made to reflect all three main priorities, at least at the European and national level, namely environmental-life-quality technologies, materials, and information and communication technologies in their broadest sense.
The Direction of Mathematics of Data Science:
The objective of the MSc Program in “Mathematical Modeling in Modern Technologies and Finance” is to produce highly esteemed scientists and researchers who will work in Greek or foreign 5 universities, research centers, and international organizations, as well as high-level executives who will be engaged in the management and research in the fields of Industry and Business. Specifically, for students interested in the Specialization of Data Science, the MSc Program aims to:
i. Provide comprehensive knowledge with a unified methodological approach to rapidly evolving tools of mathematical modeling based on the broader field of statistics, focusing on model learning from data, or “data analysis”, capable of adapting to continuous change and scaling to large volumes.
ii. Through examples (in the Computational Systems Laboratory), reinforce the capabilities of modeling across a wide range of systems, covering the broad spectrum of life technologies (environment, quality of life and services, biology, biotechnology, and biomedical engineering), the information society (informatics, spatiotemporal signal processing, communications), and materials science.
Graduates of this program will be able to transform complex problems encountered daily in the aforementioned fields into operational standards, shaped by the vast availability of data in various formats. This will reflect external emerging reality in a way that is estimated to have a significant impact on the technological, scientific, and economic progress of our country. Within this specialization, the most modern trends in the development of tools will be presented, capable of adequately analyzing data of any format and size, leading to representative models and intelligent systems. According to both earlier and recent recommendations of internationally renowned scientists in Applied Mathematics and particularly in Statistics (such as John Tukey, John Chambers, Jeff Wu, Leo Breiman), the international academic community of applied mathematicians is expanding its boundaries beyond its existing fields. This aims to emphasize the preparation and presentation of data in mathematical models with improved predictive capabilities as well as inference provision, incorporating these tools into a recommended scientific example entitled “Data Science”. Drawing conclusions from the methodology of discovering scientific findings in different fields, it becomes apparent that the overwhelming majority of science is already, and will continue to be, in the foreseeable future, initiated from data, which can be extracted in various ways, as well as the application of tools for their appropriate analysis and mathematical modeling. Furthermore, internationally, the provision of a robust mathematical background in models that also have the capability to learn from data, originating from other scientific fields such as computer science, is deemed of paramount importance. This approach helps avoid the sterile and beyondtheir-limits use of these models with the “black box” logic, which can easily lead to their misuse. The aforementioned argument strengthens the adoption of such a specialization by academic schools whose discipline is mathematics. In line with international developments in academia, particular reference should be made to similar initiatives undertaken by distinguished universities. Specifically, a recent and continually expanding phenomenon is the emergence of “data science” programs at major universities, including UC Berkeley, NYU, MIT, and the University of Michigan, which, in September 2015, announced an initiative called the Data Science Initiative, making significant investments with the aim of hiring several new faculty members. Similar initiatives have recently been announced by distinguished European universities. Teaching in these new programs has significant overlaps with the curriculum 6 of traditional statistics programs. Although many academic statisticians perceive the new programs as a potential “cultural cohabitation”, they nonetheless make significant efforts to develop new methods suitable for application in large-scale data and execution by modern computational systems. Thus, according to international practice, efforts are made to leverage advanced computing techniques in statistical methods for data collection, processing, and analysis, such as process monitoring. Additionally, indicative of this emerging direction is the launch of a new journal, SIAM Journal on Mathematics of Data Science (SIMODS), with submissions starting from April 25, 2018, covering fields such as numerical algorithms, statistical inference, optimization and control, machine learning, theoretical computer science, signal processing and information theory, applied probability, and functional analysis. This journal aims to reflect contemporary academic and research advancements in the field. https://www.siam.org/journals/simods.php?utm_source=mbr_blurb&utm_medium=email_pre&u tm_campaign=SIMODS_2018 Beyond the aforementioned paragraphs, which justify the establishment of this new Specialization based on modern academic and research developments, it is pertinent to provide a brief but illustrative description of the industry’s advancements, which similarly underscore the same need. In the context of the 4th industrial revolution (Industry 4.0), which reflects the current trend of automation and data exchange in manufacturing plants, there is a prominent emphasis on the analysis and modeling of large-scale data, as well as the necessity for the development of robotics and intelligent systems. Furthermore, the emergence of startups offering artificial intelligence as a service to the general public and other companies is noted, creating a significant number of new job positions and mobilizing substantial investments in many countries, including Greece. From the above, it becomes evident that the field of Data Science, proposed herein as a new Specialization in the MSc Program, is a cutting-edge domain of mathematical standardization characterized by the integration of new technologies that enable model learning from data, which can be scaled to “big data”.
The Direction of Financial Engineering:
For students interested in the “Financial Engineering” Specialization, the MSc Program aims to offer advanced knowledge, primarily in analytical and stochastic mathematics, as well as in fundamental tools of finance, alongside economic theory relevant to the field.
The aim of the MSc Program is to “produce” high-caliber scientists and researchers who will work in Greek or foreign universities, research centers, international organizations, as well as high-level executives who will be employed in financial advisory firms, financial institutions, or the financial departments of large companies. Special emphasis will be placed on the modeling of financial instruments through the application of stochastic processes, as well as on the evaluation of financial products within the framework of complete and incomplete markets. Modern rearrangements have either led economic systems to liberalization or their inclusion in supranational formations. This framework has intensified international competition and created an environment characterized by intense challenges and high levels of uncertainty.
These high levels of uncertainty decisively affect businesses, making timely and accurate assessment of their prospects critical for economic development 7 The analysis of the financial sector, one of the most critical pillars of the economy, includes, among other things, the evaluation of financial transactions of households and businesses. To achieve this goal, tools from microeconomics, econometrics, mathematics, and organizational theory are utilized.
The financial sector, aided by stochastic mathematics, has developed highly advanced models that are applied to address uncertainty and risk, both for investors-savers and businesses. This progress in finance, accompanied by corresponding scientific specialization, leads us to a better understanding of the phenomena observed in markets and businesses. Scientific analysis of these phenomena and their approach in the optimal manner, for all market factors, consequently leads the economy to optimal allocations. Moreover, technological advancements in recent years are intertwined with corresponding rearrangements in the economic field, often making the technological and economic sectors interdependent.