Graduate School

Thank you for your interest in graduate studies at Univesity of Tsukuba.

Several recent developments in mathematics have contributed greatly to advances in the natural sciences. Research in this program covers the five main fields of pure and applied mathematics: (1) algebra, (2) geometry, (3) analysis, (4) information science, and (5) mathematical science (applied mathematics).

Graduate students in this program will select one research project in modern mathematics and conduct research under the supervision of one of the faculty advisors.

Students will learn mathematics through advanced lectures and seminars given by faculty advisors. They will be challenged with fundamental general problems as well as more focused, specific problems and become able to produce high-level research findings on pure and applied mathematics.



For those who are considering studying at our graduate school, the followings are some information that will be useful.


Archive of Past Entrance Exams

For international students, Master's Program in Mathematics provides English translation of the exam questions upon request.

The followings are questions of "Specialized Subjects" (Mathematics) which have been delivered in past entrance exams.



To research algebra, it is advisable that you have an understanding of Jordan normal forms in linear algebra and the fundamentals of groups, rings, and fields.

To research topology, it is advisable that you have an understanding of the fundamentals of sets and topology and, to research differential geometry, it is advisable to be aware of the basics of the geometry of curved lines and surfaces and the fundamentals of manifolds.

To research mathematical analysis, it is advisable that you have an understanding of calculus and linear algebra and the fundamentals of complex analysis and Lebesgue integration.

To study mathematical logic, you need to be aware of the meaning of ordinal numbers, cardinal numbers, and transfinite induction. A fundamental knowledge of naive set theory is also necessary; however, if you have had no opportunity to study these topics, we ask that you at least be familiar with rigorous mathematical arguments.

To study mathematical statistics, you should have a sound knowledge of basic statistical ideas, such as distributions, estimation and hypothesis testing, and acquire competence in calculus and linear algebra. 

For researching computational mathematics, knowledge on basic mathematics is more important than that on computer technology. Calculus, Linear Algebra, and Algebra (at least fundamentals of groups, rings, and fields) are indispensable. Analysis and Geometry may be also necessary depending on research topics. Moreover, you may be required to have some knowledge on algorithms from the viewpoint of computational complexity.