Graduate School of Mathematics, Nagoya University
ADDRESS: Furocho, Chikusaku, Nagoya, Japan / POSTAL CODE: 464-8602

Education - Graduate Program for Master’s degree

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Update: 2012/09/28


Education Program

Graduate Program for Master’s degree

I. Basic Principles

A. Mission Statement

The Graduate School of Mathematics aims to cultivate/​nurture self-motivated individuals, who can successfully navigate inquiry, reflection, and discovery based upon scholarly training in mathematics. Our commitment is to maintaining an enlightening environment for problem-conscious students where, together with scholars and fellow students, they can refine their ideas and apply logical reasoning in seeking solutions to problems.

Prospective students should know that in the mathematics department:

  • Research planning, pursuit of research and regular reporting of results are expected.
  • The education in the department is designed to support Students’ self-motivatation.
  • Research is pursued in dialogue with active researchers and fellow students.
B. Study Hints

To ensure academic excellence, students are advised

  • To acquire an excellent command of and full appreciation of the fundamentals of mathematical knowledge.
  • To familiarize themselves with various theoretical and conceptual aspects of different subject areas, and their broader meaning/​applications.
C. Essential Abilities

Students are expected to develop the following research abilities:

  • Learning skills, including advanced reading and literature search capabilities.
  • Problem-solving skills involving the ability to analyze, reflect, synthesize and construct.
  • Ability to apply assembled data and learned material to advance one’s research.
  • Communication skills, including academic discussion, written expression and presentation.
D. Subject to learn

Students are expected to gain a strong command of the following through our curriculum:

  • All areas of mathematics and mathematical science
  • Ability to evaluate what is behind a given subject in the spectrum of mathematical genre
  • Mathematical methodology and its approaches, such as systematic and logical ways of thinking
  • Ways of defining positions and characteristics of mathematics in reference to the scientific method.
    (While mathematical concepts may, at first glance, seem so abstract as to be irrelevant to social realtities, these concepts directly affect our natural surroundings and society. The study of these phenomena is thus called mathematical science, and called mathematics when more universalized.)

II. Academic Support

The main features of our academic support systems are summarized below.

  • Multiple advisory system for all graduate students, offering individual assistance with academic progress
  • Wide-ranging programs in a consistent and systematic curriculum for students’ various scholastic needs (e.g. the Level System and Course Design facilitate that students choose their own courses)
  • Weekly office hours allow students access to all faculty members on a regular basis.
A. Advisor System

Advisors assist students’ study and research. They listen to students individually to learn students needs and advise them accordingly. Advisors also play the part of career counselor. Please do not hesitate to ask your advisor to introduce other professionals or faculty members in other sections if you need. Finding the appropriate faculty member is also the advisor’s role.

The main feature of this system is that “several” advisors advise one student. Students will have a different advisor in each master’s or doctorate program.

0. For admitted students
There is an advising system particularly for those who transfer into to our department from other academic institutions.
1. For the first year of the Master students (M1 students)
Students may select a different advisor for the 1st year and for the 2nd year. Or they may keep the same advisor through both the 1st and the 2nd years. Moreover students may select another subadvisor who can provide an objective perspective on the student’s research and thesis organization.
2. For the Doctoral students
More than one faculty member will serve as advisor to the doctoral students. Besides this multiple advisory system, another advisor for the doctoral thesis will be available.

We recommend you contact not only the personal advisor assigned to you for the academic year, but also other faculty members. If, for instance, you wish to further explore subjects that you studied for the 4th year final report, you are welcome to continue to ask your 4th year advisor for help. Likewise if, in the 2nd year of the Master’s Program, you wish to continue to study the subject of the 1st year Small Group Class your 1st year advisor will help.

Advisors serve only as your guides. Your own motivation is the key to your academic success.

B. Office Hours

All faculty members have weekly office hours during academic terms. There is no need for prior appointments and you should feel free to visit instructors’ offices whenever you have questions or concerns.

Cafe David

There are mainly three types of office hours: regular office hours, office hours for specific courses, and joint office hours called Cafe David, which are held by teaching assistants.

C. The Level System

The Level System is our central mechanism for classifying programs of study into educational purposes, organizing both undergraduate and graduate degree curriculums as a coherent whole. Thus, all lectures and small group classes fall into a certain level.

Level 0

All science major students work together in the initial disciplinary phase of the art of science level 0 classes and learn subjects including calculus and linear algebra.

Level 1

Level 1 classes deal with basic concepts, which all science-majored students need to comprehend. This level corresponds to curricula for undergraduates in the second and third years. These classes encourage students to apply and connect mathematical concepts with other fields of science, such as physics, and to develop intuitive, logical and abstract thinking.

Level 2

The scope of level 2 classes embraces various areas of advanced concepts. These classes provide scholarly training in logical, abstract and systematic approaches commonly used in mathematics through a wide diversity of subjects. This level is intended for fourth year undergraduates and graduate students. It is advisable to complete the set of classes within two years.

Level 3

Level 3 classes serve as an advanced courses, and are designed based upon the elemental portions of curriculum up to level 2, the so-called core program. These are intended for all graduate students of 2nd year or above graduate students and should be completed over three or four years.

Level system and education program

The level concept focuses on students’ individual needs and level, not on students’ actual grade. As a result, students can both challenge to higher-level study and reinforce what they lack of as following 2 examples (both are in their second year):

A’s Case

A finished level 2 in his 1st year of his Master’s Program, and has found a subject for his master’s thesis. Thus he can advance to level 3 (the contents of which apply to both the Master’s and doctoral programs) and he will participate in workshops.

B’s Case

B felt that he lacked comprehension of some level 1 contents that should be mastered by the end of the 3rd year of undergraduate work. To correct this he takes a level 1 course in addition to his normal 2nd year Master’s Program.

Most students will take level 2–3 courses during their Master’s Program. But we encourage both those who wish to improve their abilities and those who plan to pursue further research to design an individualized study plan regardless of the academic year.

Further details can be found III-A.

D. Course Design

In order to provide a comprehensive guide of course work, all instructors renew their Course Design each academic term, including the latest and detailed information about their courses. Thus, students are asked to refer to the course design for all information needed for course selection. Students may find such entries as course title, outline, instructor and contact information, course level, purpose and goals, content and teaching style, textbooks and references, prerequisites, grading scales, and study tips, etc.

III. Program Details

Requirements for Master’s Degree:

  • 12 credits for the ordinary course (Group-A),
  • Credits for the Small Group Class (Group-B and C*),
  • Submission of a Master’s thesis.

* 16 credits from B-group, 4 credits from C-group

The Master’s Program is composed of 3 types of courses and other activities below:

Ordinary Course*,
Small Group Class*,
Annual Report and Master’s thesis,
Comprehensive Examination,
First Year Study Report and Presentation,
Teaching Assistant,
LATEX Seminar.

* Credits are awarded only to Master students, but doctoral students may also participate in class.

A. Ordinary Course

The ordinary course, which is presented in Group A (see also the Student Handbook for details), includes year-long and intensive courses. These courses are ranked in level 2 or 3. If you want to strengthen basic skills, you can take a level 1 course with your advisor’s approval. In this case, you may earn no more than 4 credits (2 credits per course).

Students will be required to submit summaries of the courses they take at the end of the session. Students who take more than 3 courses may select 3 courses to summarize.

Check carefully when you register because some courses, especially courses in level 3, are not always offered every year.

We recommend you finish taking all courses by the end of the first semester of the second year in order to leave enough time for writing your master’s thesis.

Students are allowed to pursue other department’s courses, and credits can be transferred. We propose you to participate in a variety of classes to expand your interests.

You can also ask more details at Office of Academic Affairs.

B. Small Group Class (Seminar)

Small Group Class is a two-semester seminar intended to develop reading, critical thinking and discussion skills. In the seminar class students expand upon their learning from faculty lectures and identify their specific focus of interest/​research from within areas presented in lectures.

Within the chosen subject area, classes offer multifaceted lectures guided by student interest. The pace of the lectures is tailored to participating students’ needs. As seen from the chart above, students can both improve their skills and explore their chosen field in the small group class.

Master students will belong to a credit-earning seminar each/​per year. At the same time they are strongly advised to attend another seminar. Students who attend regularly and submit successful assignments will be awarded at most 1 credit over 2 years in addition to the credits from other classes for which they are registered.

All small group classes are open to both 1st and 2nd year students. The content of these classes ranges across level 2 and level 3 areas of inquiry. Read the course design carefully and consult with the lecturers of the classes in order to choose a class appropriate to your interest.

Students are required to submit a report at the end of first semester, a Final report at the end of the 1st year, and a Master’s thesis at the end of the 2nd year.

In addition to these requirements, 2nd year students must either pass or be exempted from the Comprehensive Examination at the end of first semester.

Since the curriculum is organized by level rather than year, students are strongly advised to read the course design carefully and consult teaching staff before choosing a class.

C. Master’s Thesis (Self-study/Research)

Master students must submit a Master’s thesis to earn their degree. (See I-C, I-D.) The goal of the thesis is to demonstrate your learning and your research discoveries. The Master’s thesis is not judged on the level of the focus of inquiry but on depth and breadth of your reflection.

The thesis must include the following:


A brief outline of the thesis structure; a clear statement of the research subject and question; the main results of the theory surveyed. Students may write one Introduction for the whole dissertation or a separate Introduction for both the Self Designed Study Report and Research Report.

Self Designed Study Report/Research Report

This part should be devoted to your Self-Study Report. Students in the Master’s program select one area of inquiry—their area of interest—and study this on their own. This research is the core of the master’s thesis.

Small Group Class’ Report

In this part, please include the report of your Small Group Class.

However if the topic of Self Study report and Small Group Class are similar to one another, or you want to try to find an original result referring to both two reports, you do not need to necessarily get sections separated.

When you begin writing your thesis, we suggest you to check the following three points:


First of all, make a good plan so that your thesis is well organized. Write in your own words to demonstrate your understanding.

3 key questions to ask & answer for yourself:

  • What it is the core issue or main point of your thesis?
  • What is the background of your area of inquiry?
  • What is the expected result or conclusion?

Reference to the work of other scholars is required in an Master’s thesis. Whether you aim to present your original findings or to survey theory, quotations and references are expected. In other words, you must demonstrate that you know where your work fits into the existing body of knowledge by reference to relevant existing research.


It is important to write your thesis so that others who study in different fields can understand, because not only your advisor, but also other faculty members and students will read your thesis. In particular, you must be able to read your thesis yourself.

After submitting the Master’s thesis, students have an oral defense in which are required to explain their thesis. The oral defense is open to the faculty and students in the Graduate School of Mathematics. Students are evaluated on both the written thesis and the oral defence. The first year study report may be taken into consideration if needed.

D. Other Activities
Comprehensive Examination

The Comprehensive Examination is designed to determine whether students have sufficient mathematical literacy for graduate studies. Students who fail the comprehensive examination must attend the supplementary class. Participation in class, submission of reports, and passing the final examination are required.

Students will be required to answer questions that Department of Mathematics undergraduate 2nd years have mastered. Comprehension of and skills in the following are tested:

  • Basics of calculus and linear algebra,
  • Ability to articulate mathematical concepts and logic.

Each question is graded on a scale of 3. Students’ answers will be graded on total comprehension in every fundamental point.

The evaluation standard is as follows:


Has demonstrated appropriate level of comprehension and skill.


Some gaps in comprehension/​skill.


Comprehension and skills insuffiently demonstrated in some areas.


Comprehension and skills inadequate.

Table: Grading Policy of the Comprehensive Examination

The examination consists of 4 questions. Students are required to earn at least 9 of the 12 total points.*

* 2nd year Small Group Class credits will not be awarded to students who fail the Comprehensive Examination.

Study Report and Presentation

At the end of the session, 1st year Master students submit a Study Report and give a presentation on their study as preparation for 2nd year research. The aim is to review first year studies. We recommend students design a report that reconstructs what they have studied, especially in the Small Group Class.

Students must follow the “Master’s Thesis Guideline” in preparing the Study Report.

The presentation should include a summary of courses taken, the main issues learned, a discussion of the student’s main area of interest, and a plan and goals for the second year. After the presentation, teaching staff will comment.

Teaching Assistant

In the Graduate School of Mathematics, we recruit, mainly from Master students, Teaching Assistants (TAs), who assist in the following activities:

  • Calculus, linear algebra classes
    (for the first-year at Schools of Science and Engineering);
  • Lectures and Exercises
    (for the second-year and the third-year at the Department of Mathematics);
  • Cafe David;
  • General Work
    (Correction of reports, writing answers, correction of exercises, summarize and collate answers);
  • Q & A,

Advantages of TA work:

  • Learn how to organize lectures,
  • Re-learn fundamentals by observing the beginners’ mistakes Teaching experience,
  • A chance to apply experience in study/​fieldwork.
LATEX Seminar

Graduate students are required to write more and longer reports than are undergraduates. This includes the master’s thesis. When writing a thesis or other formal report, you will need to make a plan at first and elaborate it to the end. Moreover, in mathematics, reports often contain many formulas and/​or graphics. LATEX is document preparation software that facilitates professional and effective preparation of formal mathematical documents. Students are strongly encouraged to familiarize themselves with this software though participation in the LATEX seminar early on.