Tokyo Metropolitan University Graduate School Education Curriculum
Diploma Policy and Curriculum Organization and Implementation Policies
Program: Graduate School of Science — Mathematical Sciences

1. Diploma Policy (DP)(1) Degrees to be conferred[Master's Program]
Master's degree (Master of Science): Awarded upon successful completion[Doctoral Program]
Doctorate (Doctor of Science): Awarded upon successful completion(2) Certifications to be granted
i. Certifications to be granted upon completion:
Junior High School Advanced Teacher's License in Mathematics, High School Advanced Teacher's
License in Mathematics
Students who have obtained the Junior High School Class 1 Teacher's License in Mathematics and/orHigh School Class 1 Teacher's License in Mathematics can apply for the above teacher’s license uponcompletion of the master's program at the University.
ii.

Examination eligibility to be granted upon completion:

Not applicableiii. Certifications to be granted upon completion of a separately specified program:Not applicable
iv. Programs that waive the examinations of some courses upon completion (Major certifications only):
Not applicable(3) Educational goals
The Department of Mathematical Sciences aims to develop competent individuals with advanced
knowledge of mathematics and applied mathematics as well as flexible and original mathematical andscientific thinking skills. It also seeks to develop those who can solve various issues in natural science andmodern information society while being aware of the importance of mathematical science as a foundationof science. Upon completing the program, students will acquire:[Master's Program] Advanced technical knowledge in mathematical sciences and flexible mathematical thinking skills.
 The ability to initiate projects and conduct research in a systematic manner independently or under theguidance of the graduate advisor.
 The ability to clearly express the research findings and discuss with other researchers.
[Doctoral Program] Advanced technical knowledge in mathematical sciences and flexible and original mathematical thinking
skills.
 The ability to conduct original research activities as independent researchers with an international
perspective.
 The ability to objectively evaluate the significance of own research and its position in society.

(4) Program features
The Department of Mathematical Sciences has a well-balanced faculty in the four fields: algebra,
geometry, analysis, and applied mathematics. Instructors teach systematic theories in algebra, geometry,
and analysis; and link them organically to the various areas of applied mathematics. Under this approach,students will be trained to think flexibly and will be invited to take part in cutting-edge research in themathematical sciences, including interdisciplinary aspects. The Department also develops individuals who
recognize the importance of mathematical science as a foundation of science and who can solve various
problems in natural science and modern information society through interaction with physics, chemistry,and biological sciences major students.
(5) Specialized knowledge, R&D skills, and other skills
Students are expected to acquire specialized knowledge in the fields of algebra, geometry, analysis, andapplied mathematics and the skills necessary to perform research activities as specifically described in (3).
In addition, students will develop the ability to teach specialized knowledge as teachers and thecommunication and information literacy skills required in companies and research institutions to a levelappropriate for a doctoral program.
(6) Completion requirements
The requirements for the program completion are as follows: The students currently enrolled are advised torefer to the Graduate Program and Course Outlines issued in the first year of enrollment to check thecompletion requirements of the enrolled program.
[Master's Program]Students must be enrolled in the program for two years, earn 30 or more credits, take required courses forMathematical Sciences, including mandatory Exercises in Mathematical Sciences and Seminar in
Mathematical Sciences 1, 2, 3, and 4, submit a thesis, and pass the final examination. In this case, if thegraduate advisor considers it academically beneficial, up to 10 credits out of the 30 credits may be earnedby taking the following courses as prescribed by the graduate school:• Non-major courses provided by the same graduate program• Major courses provided by other graduate schools, or• Undergraduate courses
For those who are recognized as delivering excellent research results, enrollment in the master's programfor one year or more shall satisfy the requirement.
○ Thesis evaluation process and criteria

An applicant shall decide a thesis title with the prior approval of their graduate advisor and submit thecompleted thesis to them. The applicant shall submit a degree application with a document certifyingthat the thesis has been accepted by their graduate advisor. Acceptance/rejection of the degreeapplication shall be decided by the Graduate Faculty Committee. If the application is accepted, theGraduate Faculty Committee shall establish a Review Committee consisting of three or more faculty
members, including the chief examiner, with extra examiners from other graduate schools oruniversities/institutions if necessary. The Review Committee shall rigorously review the content of thesubmitted thesis. The applicant shall write and submit the master's thesis in Japanese or one of the major
languages in Mathematical Sciences (English, German, or French). The applicant shall give a publicpresentation on the research findings in Japanese or English and answer questions. The Review
Committee shall determine pass or fail on the thesis and presentation based on the criteria below andreport the result to the Graduate Faculty Committee through the Department Meeting. The Graduate
Faculty Committee shall make the final decision on whether to confer a degree.
(1) Did the applicant show sufficient understanding of the research topic?
(2) Did the applicant conduct research activities sufficiently during the period of the standard two-year
program?
(3) Did the applicant perform an appropriate analysis of the research findings?

(4) Was the thesis written in logical and clear language?
(5) Were the presentation and response to questions in the Master's thesis presentation logical andclear?
[Doctoral Program]Students must be enrolled in the program for three years and earn 20 or more credits, take required courses
for Mathematical Sciences, including mandatory courses "Advanced Seminar in Mathematical Sciences 1,
2, 3, 4, 5, and 6," and submit a dissertation and pass the final examination. For those who are recognized asdelivering excellent research results, enrollment in the doctoral program for one year or more shall satisfy
the requirement. However, for those who have completed the master's program with one-year enrollment,
two-year enrollment in the doctoral program satisfies the completion requirement. The process and criteriaof dissertation evaluation are as follows:○ Dissertation evaluation process

A prospective applicant shall undergo a preliminary examination in the Department (closed to the public)
before proceeding to write a dissertation. If a degree application is approved, the applicant shall decide thedissertation title with the prior approval of their graduate advisor. The applicant shall write a dissertation in
one of the major languages in Mathematical Sciences (English, German, or French) and submit thecompleted dissertation to their graduate advisor and a degree application to the Graduate FacultyCommittee. If the application is accepted, the Graduate Faculty Committee shall establish a Review
Committee consisting of three or more faculty members, including the chief examiner, with extra
examiners from other graduate schools or universities/institutions if necessary. The Review Committee
shall review the content of the submitted dissertation. The applicant shall prepare the final version of thedissertation reflecting the advice of the Review Committee and submit it to the Graduate FacultyCommittee. The applicant shall give a public presentation on the research findings in English or Japaneseand answer questions. The Review Committee shall determine pass or fail on the dissertation andpresentation based on the criteria below and report the result to the Graduate Faculty Committee throughthe Department Meeting. The Graduate Faculty Committee shall make the final decision on whether toconfer a degree.

○ Dissertation evaluation criteria

In principle, a doctoral dissertation shall be a comprehensive report of the applicant's ongoing research.
All of the following criteria must be satisfied to pass the final examination.
(1) Is the dissertation original with new findings and insights?
(2) Were the presentation and response to questions in the dissertation presentation logical and clear?
(3) Is the level of completion of the dissertation appropriate?
(4) Has a part of the dissertation been published or will it be published in a peer-reviewed journal as an
academic paper (written in the primary language)?
(5) Are appropriate ethical considerations given to planning and conducting research, presenting the
research findings, and storing the data?

2. Curriculum Policy (CP): Policy on curriculum organization and implementation(1) Basic policy on curriculum organization
The curriculum shall be appropriately organized to provide students with a high level of expert
knowledge and competence in their field of study and to develop basic knowledge in related fields asfollows.
[Master's Program]
The Department of Mathematical Sciences provides systematic theories in algebra, geometry, andanalysis and links them organically to the various areas of applied mathematics. With this approach,students will be invited to take part in cutting-edge research in the mathematical sciences, includinginterdisciplinary aspects. In order to achieve this, the following courses are offered as the core curriculumfor each field.
• Special Lectures in Algebra (1), (2), (3)• Special Lectures in Geometry (1), (2), (3)• Special Lectures in Analysis (1), (2), (3)• Special Lectures in Applied Mathematics (1), (2), (3)• Intensive Lectures in Algebra 1, 2
• Intensive Lectures in Geometry 1, 2

• Intensive Lectures in Analysis 1, 2
• Intensive Lectures in Applied Mathematics 1, 2
In addition, the following courses cover interdisciplinary topics.
• Intensive Lectures in Mathematical Sciences 1, 2
The group of highly specialized courses below are taught by full-time faculty members or external
lecturers and offers leading-edge research topics.
• Advanced Topics in Algebra 1, 2
• Advanced Topics in Geometry 1, 2
• Advanced Topics in Analysis 1, 2
• Advanced Topics in Applied Mathematics 1, 2
Exercises in Mathematical Sciences is a mandatory course to develop practical skills, including searching
and collecting information on mathematical science, writing synthesis reports and research papers, andgiving presentations.
The following mandatory courses help students to discover research topics, conduct research activities
and complete the research results in a master's thesis under the guidance of the graduate advisor.
• Seminar in Mathematical Sciences 1, 2 (for first-year students)• Seminar in Mathematical Sciences 3, 4 (for second-year students)[Doctoral Program]
The following courses are the core curriculum for each field of study, and each is offered concurrently
with the corresponding master's course.
• Intensive Lectures in Algebra 1, 2
• Intensive Lectures in Geometry 1, 2
• Intensive Lectures in Analysis 1, 2
• Intensive Lectures in Applied Mathematics 1, 2
The following courses are taught by full-time faculty members or external lecturers and offer leadingedge research topics, each is offered concurrently with the corresponding master's course.
• Advanced Topics in Algebra 1, 2
• Advanced Topics in Geometry 1, 2
• Advanced Topics in Analysis 1, 2
• Advanced Topics in Applied Mathematics 1, 2
In addition, Special Exercises in Mathematical Sciences is offered concurrently with Exercises inMathematical Sciences in the master's program.
The following mandatory courses help students to discover research topics, systematically conduct
research activities and complete the research results in a doctoral dissertation under the guidance of thegraduate advisor.
• Advanced Seminar in Mathematical Sciences 1, 2 (for first-year students)• Advanced Seminar in Mathematical Sciences 3, 4 (for second-year students)• Advanced Seminar in Mathematical Sciences 5, 6 (for third-year students)(2) Policy on teaching and learning methods in the curriculum
The courses shall be taught with various methods and forms, such as lectures, exercises, and practicaltraining, in accordance with the objectives and learning goals of each course so that students can learn
independently and actively and acquire the qualities and abilities appropriate to the objectives of humanresources development and the degree awarding policy.
Research guidance shall be provided to improve students' research skills and methods under the researchguidance plans defined separately.
(3) Policy on the assessment of learning outcomes
All courses shall be assessed according to the level of achievement of the course objectives, based on theassessment methods and criteria specified in the syllabus. Theses/dissertations shall be assessed
according to the following process and criteria.

[Master's Program]○ Thesis evaluation process and criteria

An applicant shall decide a thesis title with the prior approval of their graduate advisor and submit thecompleted thesis to them. The applicant shall submit a degree application with a document certifyingthat the thesis has been accepted by their graduate advisor. Acceptance/rejection of the degreeapplication shall be decided by the Graduate Faculty Committee. If the application is accepted, theGraduate Faculty Committee shall establish a Review Committee consisting of three or more faculty
members, including the chief examiner, with extra examiners from other graduate schools oruniversities/institutions if necessary. The Review Committee shall rigorously review the content of thesubmitted thesis. The applicant shall write and submit the master's thesis in Japanese or one of the major
languages in Mathematical Sciences (English, German, or French). The applicant shall give a publicpresentation on the research findings in Japanese or English and answer questions. The Review
Committee shall determine pass or fail on the thesis and presentation based on the criteria below andreport the result to the Graduate Faculty Committee through the Department Meeting. The Graduate
Faculty Committee shall make the final decision on whether to confer a degree.
(1) Did the applicant show sufficient understanding of the research topic?
(2) Did the applicant conduct research activities sufficiently during the period of the standard twoyear program?
(3) Did the applicant perform an appropriate analysis of the research findings?
(4) Was the thesis written in logical and clear language?
(5) Were the presentation and response to questions in the Master's thesis presentation logical andclear?

[Doctoral Program]○ Dissertation evaluation process

A prospective applicant shall undergo a preliminary examination in the Department (closed to the
public) before proceeding to write a dissertation. If a degree application is approved, the applicant shalldecide the dissertation title with the prior approval of their graduate advisor. The applicant shall write adissertation in one of the major languages in Mathematical Sciences (English, German, or French) andsubmit the completed dissertation to the graduate advisor and a degree application to the Graduate
Faculty Committee. If the application is accepted, the Graduate Faculty Committee shall establish a
Review Committee consisting of three or more faculty members, including the chief examiner, withextra examiners from other graduate schools or universities/institutions if necessary. The Review
Committee shall review the content of the submitted dissertation. The applicant shall prepare the final
version of the dissertation reflecting the advice of the Review Committee and submit it to the Graduate
Faculty Committee. The applicant shall give a public presentation on the research findings in English or
Japanese and answer questions. The Review Committee shall determine pass or fail on the dissertationand presentation based on the criteria below and report the result to the Graduate Faculty Committee
through the Department Meeting. The Graduate Faculty Committee shall make the final decision onwhether to confer a degree.

○ Dissertation evaluation criteria

In principle, a doctoral dissertation shall be a comprehensive report of the applicant's ongoing research.
All of the following criteria must be satisfied to pass the final examination.
(1) Is the dissertation original with new findings and insights?
(2) Were the presentation and response to questions in the dissertation presentation logical and clear?
(3) Is the level of completion of the dissertation appropriate?
(4) Has a part of the dissertation been published or will it be published in a peer-reviewed journal asan academic paper (written in the primary language)?
(5) Are appropriate ethical considerations given to planning and conducting research, presenting the
research findings, and storing the data?

Curriculum Structure of the Department of Mathematical Sciences

Advanced Topics in Analysis 1 (1)Advanced Topics in Analysis 2 (2)Special Lectures in Applied Mathematics (1), (2), (3) (2)Intensive Lectures in Applied Mathematics 1 (1), Intensive
Lectures in Applied Mathematics 2 (2)Advanced Topics in Applied Mathematics
1 (1)Advanced Topics in Applied Mathematics
2 (2)Intensive Lectures in Mathematical Sciences (1), (2) (2)Courses for dissertation preparation
Exercises in Mathematical
Sciences (1)Seminar in
Mathematical
Sciences 1 (3)Master's Year 1, 1st

Seminar in
Mathematical
Sciences 2 (3)Seminar in
Mathematical
Sciences 3 (3)Master's Year 1, 2ndMaster's Year 2, 1stMaster's program

Seminar in
Mathematical
Sciences 4 (3)Master's Year 2, 2ndDoctoral program

Submission and presentation of the doctoral dissertation

Special Lectures in Analysis (1), (2), (3) (2)Intensive Lectures in Analysis 1 (1), Intensive Lectures inAnalysis 2 (2)Preliminary evaluation of the doctoral dissertation

Advanced Topics in Geometry 1 (1)Advanced Topics in Geometry 2 (2)Advanced Seminar in Mathematical Sciences 5, 6 (2)Special Lectures in Geometry (1), (2), (3) (2)Intensive Lectures in Geometry 1 (1), Intensive Lectures inGeometry 2 (2)Advanced Seminar in Mathematical Sciences 3, 4 (3); Enrollment
in specialized courses

Advanced Topics in Algebra 1 (1)Advanced Topics in Algebra 2 (2)Advanced Seminar in Mathematical Sciences 1, 2 (4); Enrollment
in specialized courses

Special Lectures in Algebra (1), (2), (3) (2)Intensive Lectures in Algebra 1 (1), Intensive Lectures in
Algebra 2 (2)Submission and presentation of the master's thesis

A wide range of specialized
courses