## Features of the School

In the School of Mathematics and Physics, we conduct research and education which integrate mathematics, physics, and computational science.

Mathematics and physics are fundamental fields of academic study that cover a wide spectrum of modern science, especially natural science. Computational science, however, is an academic field whose subjects cover various phenomena through computer simulations. Recent advances in computers are beneficial for mathematics and physics: it is now possible to elucidate natural phenomena and verify theories that were too complex for previous methods.

Students in the School of Mathematics and Physics devote their first year to basic coursework that forms the foundation of the three fields of academic study. This gives them the opportunity to consider which of the fields they would like to pursue as they enter their second year. There is no fixed quota limiting the number of students in each course. Coursework from the second year onwards emphasizes specialized education specific to each course. Fourth-year students participate in small research groups
under the guidance of faculty advisors to concentrate on individual research. Students are not limited to research within their course, and are free to choose any research group within the School of Mathematics and Physics.

The School of Mathematics and Physics aims to produce highly motivated scientists who can investigate open problems on their own knowledge of mathematics, physics and computational science.

## Introduction

### Outline

In the School of Mathematics and Physics, we conduct research and education which integrates mathematics, physics, and computational science, and aims to cultivate highly motivated scientists who can contribute to the further development of these disciplines, pass their knowledge on to the next generation, and be actively involved in various areas through logical thinking and creativity nurtured by mathematics, physics and computational science.

The School of Mathematics and Physics offers three courses: Mathematics, Physics and Computational Science. Course in Computational Science provides two education rograms, Computational Mathematics and Computational Experiments, which are relatively close to mathematics and physics, respectively. Students devote their first year to the basic coursework that forms the foundation of studies in the three disciplines. This gives them the opportunity to consider which of the three they would like to pursue as they enter their second year. There is no fixed quota limiting the number of students in each course. Coursework from the second year onwards emphasizes specialized education specific to each course, but since there are many lessons that also form part of other courses, students can learn three broad disciplines deeply and widely, and interact with students in the other courses. Fourth-year students participate in small research groups to concentrate on individual research. Students are not limited to research within their course; they are free to choose any research group in the School of Mathematics and Physics that they feel will facilitate their investigation into the specific topic they wish to pursue.

#### Curricula and support systems for teacher certification

By earning credits for specified subjects related to teaching in addition to the required credits, students will be able to obtain a certificate to become junior and senior high school teachers. All students of our school are eligible for a Class 1 junior high school teaching certificate (mathematics/science) and a senior high school teaching certificate (mathematics/science/information) regardless of their course.

#### A wide variety of career paths

The students’ knowledge of basic science opens up many different career paths after graduation; possible careers include production engineer, IT engineer, junior or senior high-school teacher, publisher, and researcher.

## Our Principles and Goals

We foster the skills required to investigate the fundamental questions about our universe using the knowledge gained from mathematics, physics and computational science, and to master scientific creativity and way of thinking.

Mathematics and physics are fundamental fields of academic study that cover a wide spectrum of modern science, especially the natural sciences, and that were developed in parallel over their long history. Computational science is incorporated in mathematics and physics at many universities, but it exists as a course along with Mathematics and Physics at Kanazawa University, and the curriculum is designed in such a way that basic skills such as programming for computer simulation are learned at an early stage in preparation for acquiring practical skills in the fourth year.

In the School of Mathematics and Physics, we conduct research and education in the three disciplines of mathematics, physics, and computational science organized in a comprehensive manner, and aim to train specialists that can contribute to the further development of these disciplines, pass on their knowledge to the next generation, and be actively involved in various areas thanks to their knowledge of mathematics, physics and computational science.

## Course in Mathematics

### Investigating the mysteries of the world through the magic of numbers

Mathematics developed as the extension of logical thought. This field is essential in the description and development of other areas of academic study, the natural as well as the human and social sciences. Course in Mathematics gives students the opportunity to master advanced mathematics through a greater focus on logic than on calculation, an approach that differs slightly from what students learn in high school. Course in Mathematics helps students develop a deeper understanding of mathematics, along with the ability to think logically, with the goal of fostering the ability to flexibly respond to a wide range of challenges.

## Course in Physics

### Scientific thinking and problem-solving skills are developed through the study of physics.

In this course, students can study physics deeply and acquire the basic skills required for cutting-edge research and development. Exercises that correspond to lectures, group seminars, and physics experiments carried out in pairs are included in the curriculum. In addition to acquiring basic knowledge of physics, students learn methods of scientific communication and logical discussion by expressing their own views and interpretations and discussing them. A fourth-year student usually participates in one of eight research groups to carry out a research project under individual guidance, and will play a part in modern research in physics. Our educational aim is the nurturing of talented engineers who can discover and solve problems based on their technical knowledge of physics, and who can succeed in a new field. Our graduates are active in various areas of society as professionals with a solid scientific background.

### Explore physics to the limit, and investigate every matter in the universe and the principles and laws that govern it.

Course in Physics consists of eight research groups in the fields of theoretical physics and experimental physics. From elementary particles to the universe, from low temperatures extremely close to the absolute zero to super-hot plasma, from the quantum state of an atom or a molecule to the nano science of atomic ensembles, and from nonlinear phenomena to biophysics, students can study the fundamentals of various areas of physics. In cooperation with students, each research group takes on the challenge of developing a new theory or an analysis method, establishing an experiment technique for the realization and observation of an ultimate state, or developing an innovative equipment with high accuracy and high sensitivity. The goal of the research in physics is the fundamental understanding of the nature of all matter and interaction (including dark matter and dark energy) for the complete elucidation of the mechanism of various phenomena in nature.

## Course in Computational Science

### (1) Introduction to the Course

With the advent of computers, an innovative research method called computer simulation was devised. This method made it possible to analyze phenomena that could not be adequately investigated previously. Computer simulation is the third research method following the theoretical and experimental research methods, and the academic field related to computer simulation is called "computational science".

The terms "Computer Science" and "Computational Science" sound similar, but they are rather different disciplines. While computer science is the science in which the hardware and software of computers are studied, computational science is the science of studying scientific problems using computers. Computer
simulation is an indispensable research method in many fields of modern science, and computational science is developing in conjunction with the work in these fields.

In this course, we conduct research from an interdisciplinary perspective. Mathematics and physics are the pillars of the education and research that are carried out, as mathematics provides the theoretical foundation, and physics is the basis for understanding with natural phenomena. Students of the Course in Computational Science learn a
wide range of developmental content; they acquire a strong foundation in mathematics and physics, perform computer simulations, and study the theory behind them.

### (2) Introduction to the Computational Mathematics Program

"Mathematical science" is an academic field that connects mathematics and interdisciplinary fields such as natural science, engineering, and economics. Computational mathematics is an academic field that arose from the relationship between mathematical science and computational science.

Most importantly, numerical analysis, one area of mathematics, is the foundation of numerical simulation. Encryption and data compression techniques
are essential for computational science and modern society. Algebra is in the background of these technologies.

By solving mathematical science problems using computers, mathematicians can now conduct research in fields that they were not previously involved in. Mathematicians are increasingly active not only in basic fields such as physics, chemistry, biology, geology, and astronomy, but also in applied fields such as engineering, as well as economics and finance.

In the computational mathematics program, education and research are conducted for “basic mathematical science,” which is a mathematical science that supports computational science, and “computational mathematics,” which involves the study of various mathematical science problems using computer simulation.

### (3) Introduction to the Computational Experiment Program

This program covers the academic field that elucidates the phenomena of nature through computer experiments (computer simulation). Simulation is a method for determining principles and laws in various fields of natural science (physics, chemistry, biology, etc.) using a computer. For example, by solving the equation of motion using a computer and visualizing the result, phenomena and motion can be expressed in a form that is easy to understand intuitively. Investigating the results of computer
simulation enables us to understand the essence of a complex phenomenon, for which principles and laws can be clarified.

Computer simulation arose as the third research method following the theoretical and experimental methods of science, and it benefitted the industrial world, particularly the field of state-of-the-art technology. Computer simulation is a research method that meets the needs of modern society and has become a powerful and indispensable tool for research in the field of advanced technology.

In the computational experiment program, education and research are conducted to elucidate various phenomena of nature, especially complex systems, using computer simulation. In the course, we conduct education and research on interdisciplinary and diverse fields such as material physics, nano science, molecular science, bioscience, and high-performance computing.