College of Mathematics

 

Curriculum


First and second year mathematics are preparatory steps toward the specialized topics delivered in the third and later years.  In particular, a familiarity with the calculus and linear algebra covered in the first year and the basic set theory covered in the second year is required in all mathematical fields and provides the foundation for mathematical research.  The basic topics taught in the first year provide a smooth transition from high school-level to university-level mathematics.  In the second year, students are introduced to preliminary specialized topics such as advanced linear algebra, introduction to algebra, vector analysis and geometry, introduction to topology, introduction to differential equations, function theory, statistics, and programming.

The first half of the third year is when students start learning more specialized modern mathematics.  In the latter half of the third and fourth year, students address advanced theorems and conduct their own research in specialized areas.  The topics covered in the third and fourth year can be roughly categorized into four groups: algebra, geometry, analysis, and information mathematics.  Algebra includes group theory, ring theory, field theory, additive group theory, Galois theory, and Lie algebra.  Geometry covers topological topics such as geometric topology and algebraic topology and differential geometry based on the theory of surfaces and on manifold theory.  Analysis covers the Lebesgue integral, partial differential equation theory, probability theory, functional analysis, and complex analysis.  Information mathematics discusses mathematical logic including set and model theories, mathematical statistics such as estimation and verification theories, and computer mathematics such as numerical calculation and algorithms.  Students can study topics in pure mathematics, such as algebra, geometry, and analysis, as well as mathematical applications in the sciences, including information mathematics.

Students work toward their graduation in the latter half of the third year and engage in research in the fourth year.  For pre-seminar and graduation seminar, the students are divided into groups according to their research interests and hold seminars under the supervision of faculty members. Seminars involve reading specialized documents, presenting research, and holding discussions with faculty members.  You will experience the joy and profundity of mathematical studies through your graduation seminar.  In the final presentation for the graduation seminar at the end of the fourth year, you will present a comprehensive account of your work over the last four years, which will give you a sense of accomplishment and fulfillment.