Undergraduate Major

Specialized education built on a broad foundation
— a solid footing for researchers and engineers

The curriculum is designed to develop students with strong mathematical foundations in the first three years of study. During these years, close guidance coupled with problem-solving sessions that encourage active learning are central to the students' education. In their fourth year, students will participate in seminars where they will read and examine technical literature in depth. As such, they not only learn the skills needed to acquire knowledge through the seminars, but they also learn to present this knowledge to others in their own words.

To be more specific, students, during their second year and the first half of their third year, will study subjects that are fundamental to mathematics based on their understanding of calculus and linear algebra that were taught in the first year. Many courses involve problem solving. In the latter half of the third year and the fourth year, course material will cover specific areas of algebra, geometry, and analysis. Furthermore, the Independent Research Project will give students training on in-depth reading of technical texts. Students will also be required to present content using their own words during seminar sessions.

The curriculum is designed not only to provide students with mathematical knowledge, but is also arranged to enable students to acquire mathematical thinking in a stepwise fashion.

  1. 1st Year

    100-Level Courses

    Students in their first year of undergraduate studies receive basic education that centers on Institute-wide compulsory courses regardless of their discipline. The 100-level courses are designed to teach common, basic skills that are required of science and technology students. The aims of these courses are to provide knowledge and cultivate versatile intellect necessary for studying at the Institute.

  2. 2nd Year
    3rd Year

    200-Level and 300-Level Courses

    Students who complete their 100-level courses advance to study their undergraduate major. Courses at the 200- and 300-levels specific to the Mathematics Major are taken in accordance with the curriculum.

    • Algebra Courses
      Topics that are fundamental to the understanding of modern algebra are covered.
      Keywords: linear space, groups, rings, fields, modules, homomorphism theorem, Galois Theory
    • Analysis Courses
      Finite and infinite dimensional analyses based on calculus are taught.
      Keywords: vector analysis, complex function theory, Fourier analysis, functional analysis, Lebesgue integral, ordinary differential equations, probability theory
    • Geometry Courses
      Topics that are fundamental to the understanding of modern geometry are covered.
      Keywords: topological spaces, manifolds, differential forms and vector fields, homology groups, fundamental groups, Riemannian metric, curvature
  3. 4th Year

    200-Level and 300-Level Courses

    At the final stage of the 300 level is the Independent Research Project (equivalent to the Undergraduate Thesis Research that was in place previously). The project is intended to serve as a capstone for students to consolidate and reinforce all of the skills acquired in their Mathematics Major. Furthermore, they may choose to enroll in the Advanced Independent Research Project. The purpose of this course is to enhance students' interest in scientific and technological research that began with the Independent Research Project. The course provides students with the opportunity to actively engage in their interests by taking part in science- and technology-related activities.

    * The timeline depicts a standard case where students complete their bachelor's degree program in four years.

  4. Entrance Examination

    Students need to pass an entrance exam to advance from a bachelor's to master's program. To advance from a master's to a doctoral program, students must pass an advancement assessment.

  5. Graduate Major
    Master's Program
    Doctoral Program

    400-Level, 500-Level, and 600-Level Courses

    Students who complete the Mathematics Undergraduate Major may continue to study the discipline in more depth by taking the Mathematics Graduate Major.

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