## Department of Physics and Mathematics

##### The Department of Physics and Mathematics provides quality education in a wide range of disciplines, ranging from applied physics and its technology-related fields to pure mathematics. A wide variety of career opportunities can be found for graduates of physics and mathematics degree programs who benefit from the quantitative and analytical skills of mathematics and from an understanding of the fundamental law of nature behind science and technology.

Physics research areas of particular strength at Aoyama Gakuin University include condensed matter physics and astrophysics. Numerous novel superconducting materials such as MgB2 and the exotic ladder materials have been found. Our campus is located near the Institute of Space and Astronautical Science (ISAS) of Japan Aerospace Exploration Agency (JAXA). World class astrophysicists at the department emphasize close collaboration between theory and experiment, and explore an extensive variety of high-energy astrophysical phenomena, involving black holes, neutron stars, gamma-ray bursts and origin of cosmic rays and promote various space missions such as MAXI, Astro-H and CALET in international collaborations. The other strength of the department is also covering interdisciplinary physics research areas such as biophysics and atomic physics that relate to wide range of sciences.

Research topics in mathematics cover the entire field of the subject.

Areas of particular strength include theory of nonlinear systems, topology, representation theory, probability theory and numerical analysis. Nonlinear integrable systems such as soliton equations, Painlev'e equations and ultra-discrete systems, aim to explain a variety of mathematical and physical phenomena. Mathemataical modeling and analysis are also applied to understand nonlinear phenomena in life sciences. Topology is a powerful tool to analyze dynamical systems, which often exhibit complicated phenomena such as chaos, fractal and complex system. Representation theory is used crucially in the field of differential equations, geometry, combinatorics and spectral analysis. Probability theory mathematically deals with randomness and is applied to many fields in natural science and also in social science. Numerical analysis concerns the development of algorithms for solving problems of continuous mathematics, appearing in all fields of engineering and sciences.

Our undergraduate curriculum in Physics and Mathematics provides the student with a base of fundamental science and mathematics as well as specialization through a broad selection of technical electives. By taking advantage of joining mathematics and physics into a single department, students are able to seek teacher certification for middle and high school either Mathematics or Physics with extra specific requirements for teacher education.

From the first year to the second year, students take Seminars and Laboratory subjects, including computer programming in small groups as well substantial coursework including both physics and mathematics core curriculums shown in the table below.

At the same time, students are required to select one course from Mathematics Course and Physics Course to complete the degree. Each focused course offers its specialized elective requirements designed for students to assist in their positive career explorations and to prepare for Senior Thesis Research during their senior year. The Senior Thesis Research is a physics or mathematics research project carried out under the guidance of a faculty member and the advanced research experience provides a great opportunity for students to discover their individual talents and to demonstrate practical skills and knowledge.

##### Campus of Attendance

First Year to Fourth Year :

#### Curriculum (physical science course)

Lists lecture subjects (mandatory and required electives)

##### Required Credits for Graduation / 138 Credits

##### Mathematics・Common subjects

Subjects | |
---|---|

Required |
■1st year Linear Algebra IＡ・IＢ Analysis IA・IB Mechanics Ⅰ・Ⅱ Fundamental Mathematical Physics/Fundamental Mathematical Physics |

##### Specialized Experiments・Practical Work

Subjects | |
---|---|

Required |
■1st year Basic Experimental Physics Ⅰ・Ⅱ Basic Experiments in Chemistry Basic Experiments in Electric Engineering Practical Work of Monozukuri (Shop-floor Technology) Introduction to Computer Programming ■2nd year Computer Programming Exercise ■3rd year Computer Application Exercise Problem Solving Seminar in Mathematics Ⅰ・Ⅱ Practicum in Science and Technology Ⅲ・Ⅳ |

##### Seminar・Graduation Thesis

Subjects | |
---|---|

Required |
■4th year Seminar in Mathematics Ⅰ・Ⅱ Graduation Thesis Research Ⅰ・Ⅱ Advanced Practical Research in Science and Technology Ⅰ・Ⅱ |

##### Subject Group 1

Subjects | |
---|---|

Required |
■2nd year Linear Algebra Ⅱ Differential Equations I |

Required Electives |
■2nd year Analysis Ⅱ・Ⅲ Elementary Algebra and its Applications Probability Theory and Statistics Linear Algebra Ⅲ Set Theory and General Topology Computational Mathematics ■3rd year Complex Analysis I Differential Equations Ⅱ Geometry Ⅱ Analysis Ⅳ Mathematical Statistics |

##### Subject Group 2

Subjects | |
---|---|

Required Electives |
■1st year Exercises in Mathematics A・B Exercise in Physics Ⅰ ■2nd year Exercise Session (Differential Equations I) Exercise Session (Analysis Ⅱ) Exercise Session (Elementary Algebra and Applications) Exercise Session (Linear Algebra Ⅱ) Electromagnetism Analytical Mechanics Waves Algebra Ⅰ Geometry Ⅰ Mathematics Ⅱ Exercise Session (Set Theory and General Topology) Exercise Session (Analysis Ⅲ) Exercise Session (Algebra Ⅰ) Exercise Session (Geometry Ⅰ) Exercises in Mathematics Ⅱ Quantum Mechanics Ⅰ Thermal Physics ■3rd year Fundamentals of Computer Science Exercise Session (Analysis Ⅳ) Exercise Session (Complex Analysis I) Algebra Ⅱ Complex Analysis Ⅱ Geometry Ⅲ Financial Mathematics Differential Equations Ⅲ Exercise Session (Algebra Ⅱ) Exercise Session (Geometry Ⅲ) ■4th year Geometry Ⅳ Analysis Ⅴ Algebra Ⅲ |

##### Elective Subjects

Subjects | |
---|---|

Electives |
■1nd year Chemistry Ⅰ・Ⅱ ■2nd year Chemistry Ⅲ ■3rd year Quantum Mechanics Ⅱ・Ⅲ Relativity Solid State Physics Statistical Mechanics Ⅰ Seminar in Physics and Mathematics(in English) Fundamentals of Mechanical Engineering Fundamentals of Industrial and Systems Engineering Fundamentals of Electrical Engineering Internship Practical Research in Science and Technology Ⅰ・Ⅱ ■4th year Philosophy of Science |

##### The Aoyama Standard Subjects

##### 1st - 4th year :

School-wide universal education system where experts in wide-ranging academic fields transcending the framework of colleges/schools and departments stimulate interest in learning and provide guidance.

##### Foreign Language Subjects

##### [ 1st Foreign Language ] 1st year :

English Core I-a, I-b, I-c, I-d

##### 2nd year :

English Core II-a, II-b, II-c, II-d

##### 3rd year :

Active Speaking Skills A, B , Advanced Skills A, B , English Comprehension A, B , English for Engineers A, B , Study Abroad A, B

##### Free Elective Subjects

##### 1st - 4th year :

Students can freely select from departmental subjects, Aoyama Standard Subjects, Foreign Language Subjects (take at least minimum credits required), subjects of other departments in the College of Science and Engineering, as well as subjects offered by other colleges.

#### Curriculum (mathematical science course)

Lists lecture subjects (mandatory and required electives)

##### Required Credits for Graduation / 138 Credits

##### Mathematics・Common subjects

Subjects | |
---|---|

Required |
■1st year Linear Algebra IＡ・IＢ Analysis IA・IB Mechanics Ⅰ・Ⅱ Fundamental Mathematical Physics/Fundamental Mathematical Physics |

##### Specialized Experiments・Practical Work

Subjects | |
---|---|

Required |
■1st year Basic Experimental Physics Ⅰ・Ⅱ Basic Experiments in Chemistry Basic Experiments in Electric Engineering Practical Work of Monozukuri (Shop-floor Technology) Introduction to Computer Programming ■2nd year Computer Programming Exercise ■3rd year Computer Application Exercise Problem Solving Seminar in Mathematics Ⅰ・Ⅱ Practicum in Science and Technology Ⅲ・Ⅳ |

##### Seminar・Graduation Thesis

Subjects | |
---|---|

Required |
■4th year Seminar in Mathematics Ⅰ・Ⅱ Graduation Thesis Research Ⅰ・Ⅱ Advanced Practical Research in Science and Technology Ⅰ・Ⅱ |

##### Subject Group 1

Subjects | |
---|---|

Required |
■2nd year Linear Algebra Ⅱ Differential Equations I |

Required Electives |
■2nd year Analysis Ⅱ・Ⅲ Elementary Algebra and its Applications Probability Theory and Statistics Linear Algebra Ⅲ Set Theory and General Topology Computational Mathematics ■3rd year Complex Analysis I Differential Equations Ⅱ Geometry Ⅱ Analysis Ⅳ Mathematical Statistics |

##### Subject Group 2

Subjects | |
---|---|

Required Electives |
■1st year Exercises in Mathematics A・B Exercise in Physics Ⅰ ■2nd year Exercise Session (Differential Equations I) Exercise Session (Analysis Ⅱ) Exercise Session (Elementary Algebra and Applications) Exercise Session (Linear Algebra Ⅱ) Electromagnetism Analytical Mechanics Waves Algebra Ⅰ Geometry Ⅰ Mathematics Ⅱ Exercise Session (Set Theory and General Topology) Exercise Session (Analysis Ⅲ) Exercise Session (Algebra Ⅰ) Exercise Session (Geometry Ⅰ) Exercises in Mathematics Ⅱ Quantum Mechanics Ⅰ Thermal Physics ■3rd year Fundamentals of Computer Science Exercise Session (Analysis Ⅳ) Exercise Session (Complex Analysis I) Algebra Ⅱ Complex Analysis Ⅱ Geometry Ⅲ Financial Mathematics Differential Equations Ⅲ Exercise Session (Algebra Ⅱ) Exercise Session (Geometry Ⅲ) ■4th year Geometry Ⅳ Analysis Ⅴ Algebra Ⅲ |

##### Elective Subjects

Subjects | |
---|---|

Electives |
■1nd year Chemistry Ⅰ・Ⅱ ■2nd year Chemistry Ⅲ ■3rd year Quantum Mechanics Ⅱ・Ⅲ Relativity Solid State Physics Statistical Mechanics Ⅰ Seminar in Physics and Mathematics(in English) Fundamentals of Mechanical Engineering Fundamentals of Industrial and Systems Engineering Fundamentals of Electrical Engineering Internship Practical Research in Science and Technology Ⅰ・Ⅱ ■4th year Philosophy of Science |

##### The Aoyama Standard Subjects

##### 1st - 4th year :

School-wide universal education system where experts in wide-ranging academic fields transcending the framework of colleges/schools and departments stimulate interest in learning and provide guidance.

##### Foreign Language Subjects

##### [ 1st Foreign Language ] 1st year :

English Core I-a, I-b, I-c, I-d

##### 2nd year :

English Core II-a, II-b, II-c, II-d

##### 3rd year :

Active Speaking Skills A, B , Advanced Skills A, B , English Comprehension A, B , English for Engineers A, B , Study Abroad A, B

##### Free Elective Subjects

##### 1st - 4th year :

Students can freely select from departmental subjects, Aoyama Standard Subjects, Foreign Language Subjects (take at least minimum credits required), subjects of other departments in the College of Science and Engineering, as well as subjects offered by other colleges.