Meiji University

By elucidating complex systems appear in nature, society and biological world, together with fulfilling social innovation by benefitting it to the society, we, the Graduate School of Advanced Mathematical Sciences are able to contribute improvement of humankind’s welfare. Under this ideology, we intent to foster human resources who will acquire highly‐sophisticated broad element of mathematical sciences, who will be able to work and research internationally, as an interface against various phenomena, with ability of bridging mathematics and sciences. At master’s program, our aim is to educate students to become researchers or professionals who acquired conceptions and skills of mathematical sciences based on modeling and analysis which scheme is a fusion of mathematics and sciences. At doctor’s program, in addition to cultivation of human resources from the master’s program, we will guide those to be able to carry further research of theirs individually.

Therefore, at Mathematical Sciences Based on Modeling and Analysis, we offer educational research of mathematical sciences based on the construction of an extraction model to clarify the essences of phenomena. With the knowledge of highly sophisticated broad element of mathematics, we are eager to train young researchers to be able to contribute to our society extensively, with the bases of educational policy at Graduate School of Advanced Mathematical Sciences. For example, researching phenomena in nature, society and biological world with mathematical sciences’ point of view as an important part of its study, we organize curriculums with main structures of ‘Modeling’, ‘Mathematical Analysis’ and ‘Simulation’. Moreover, by practicing combined, cross‐fields type education on both natural science and cultural, social sciences, students are expected to cultivate the ability to clarify the phenomena in various fields, using mathematical sciences. Furthermore, students will have opportunity to visit not only domestic but international institutions abroad as exchange programs (ex, credit transfer system) in order to develop world’s top level Mathematical Sciences Based on Modeling and Analysis and become researchers who have abilities to be active internationally.

The education and research guidance at Graduate School of Advanced Mathematical Sciences will be further evolved based on the achievement of MIMS Ph. D. Program.

As Doctoral program curriculum, Project Study of Proposal Style of Mathematical Sciences Ⅰ&Ⅱ will be available in which students will chose research projects to plan and manage by themselves, and MIMS fellow will supervise them while supporting the researches. Moreover, ‘Project Based Analysis and Research Cluster’ and ‘Inter-Departmental Course’ at the Graduate School of Meiji University can be chose as optional subjects for this course. In the ‘Project Based Analysis and Research Cluster’, four subjects – Advanced Study of Mathematical Sciences A&B, and Advanced Mathematical Sciences C&D – are provided, which are coordinated by MIMS fellows and research fellows. These subjects are taught in both English and Japanese together with the latest topics of mathematical sciences. The Inter-Departmental Course offer a number of ‘Multilingual Graduate Research’, such as ‘Fundamentals of Communication and Seminar Skills in English’ and ‘Fundamentals of Academic Writing Techniques in English’. These subjects, which are taught by English native speaking professors specializing in academic English teaching, are aimed to cultivate highly skilled researchers able to be active internationally.

Moreover, as an optional curriculum, students are encouraged to study at the graduate school of partner universities (Hiroshima University, Ryukoku University, Shizuoka University) where the credit transfer system and research guidance consignment agreements are available.

As to explain research guidance style, one of supervisors who is in charge of Doctoral program as the main fellow, together with MIMS fellow or research fellow will be selected from each MIMS research group (Modeling, Simulation and Mathematical Analysis) to form a research guidance team. Each individual Students will be provide comprehensive supervision depends on their researches. The examples of phenomena entitle for the research guidance are, life and biological phenomena, economical, financial and natural ones.

Students who complete all the courses mentioned above and receive necessary guidance, therefore achieved a certain level, will receive permission to submit a dissertation (Doctoral Thesis). Students who have successfully passed the examination of the thesis will be awarded a Doctoral Degree.

The focal point of the Graduate School of Advanced Mathematical Sciences is the structure research guidance provided to students. Providing students with consolidated instruction, appropriate to each individual research theme and consisting of a fusion of modeling (the mathematical description of phenomena), simulation (the analysis of phenomena) and mathematical analysis, is crucial for the effective study of mathematical modeling and analysis. The multiple guidance structure introduced for the MIMS Ph.D. Program is based on this very principle. Unlike the more traditional model, in which one supervisor oversees the research of a number of students, MIMS fellows and research fellows will be selected according to the specific needs of each research project, and form a strong guidance teams consisting of three supervisors, with each fellow specializing in modeling, simulation and mathematical analysis respectively. This will let students to learn the kind of mathematical modeling and analysis that will allow them to synergize mathematics and the sciences. Particularly outstanding is the fact that amongst MIMS fellows and research fellows there are many leading academics in the field of mathematical modeling and analysis, gathered not only from Meiji University but from other various institutions. Therefore students wil, come into contact with a wide scope of academic staff.

Examples of research topics that would be supervised by Team Fellows are as below;

・Example 1 : Theoretical Analysis of Cellular Information Processing Systems
Modeling supervisor: mathematical biology specialist in biological phenomena modeling to his/hers credit
Simulation supervisor: specialist in large-scale numerical modeling
Mathematical analysis supervisor: specialist in network geometric analysis

・ Example 2 : An analysis of the dynamics of share prices and the possibility of its accurate predictions
Modeling supervisor: a specialist in financial engineering with strong history ofcollaborative research with finance professionals
Simulation supervisor: a specialist in computer assistance / image enhancementanalysis
Mathematical analysis supervisor: a specialist in probabilistic logic / time series Analysis

・Example 3 : Spontaneous structural formations in nature
Modeling supervisor: a specialist in the mathematic theories of self-organization
Simulation supervisor: a specialist in modeling simulation analysis
Mathematical analysis supervisor: a specialist in the mathematical analysis of spontaneously occurring patterns in nature

・Example 4 : Visual illusion and pattern recognition, practical use of structures
Modeling supervisor: specialist in large degrees on freedom, non-linear and non-equilibrium modeling
Simulation supervisor: a specialist in simulation sciences
Mathematical analysis supervisor: a specialist in non-liner / non-equilibrium theory

Research themes related to mathematical modeling and analysis in addition to those mentioned above would be supported in the same way by a team comprising of institute fellows and/or research fellows, all engaged at MIMS which acts as the pillar organization for the Ph.D. program education.