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In the first half of the lecture, students will learn basic concepts such as sets and maps, which are the common language of mathematics, and aim to master their use. In the second half, students will learn elementary concepts that will lead to future studies using problems such as integers, counting, and recurrence relations, while also acquiring and solidifying a sense for mathematical inspiration and logical thinking skills. The course is also linked to the content of analysis and linear algebra, which students will study in parallel, and students will be able to experience the joy of thinking while strengthening their legs and back for mathematics.

This is an introductory class on algebra. Starting with elementary number theory, students will learn basic concepts of algebraic systems, such as rings and fields, with examples. In algebraic systems, the theorems are often stated in an abstract form, so a certain degree of familiarity is required to understand them. In this class, students will perform actual calculations using familiar objects such as integers and polynomials, and through this experience, they will become familiar with the basic concepts of rings and fields. On top of that, students will improve their ability to digest abstract theorems, such as Euler's theorem, one of the most fundamental theorems in elementary number theory.

This lecture will be an introduction to differential geometry using curves and surfaces. Curvature is a tool used to show how curved a curve or surface is. By calculating the curvature of actual curves and surfaces, you will gain a geometric image of how things are curved. The sum of the interior angles of a triangle on a plane is 180 degrees. On a sphere with positive curvature, the sum of the interior angles of a triangle is greater than 180 degrees. The Gauss-Bonnet theorem links the sum of the interior angles of a triangle to the integral of curvature. The sum of the interior angles of a triangle, which you learn in junior high school, actually represents a geometric property of a plane.

From the third year, students will begin taking lectures on the application of mathematics. "Financial Mathematics" is one of these. Students will learn about finance theory, which plays an important role in the real economy, focusing on its mathematical aspects. Through the study of capital asset pricing models, derivative pricing models, and financial data analysis, students will come to realize that the mathematics they learn in their first and second years, such as calculus, linear algebra, and probability statistics, is essential for discussions on finance.

This is an exercise in which students are divided into small groups and make presentations themselves. In the first half, students carry out problem exercises to review and develop what they have already learned, and they also touch upon topics that span multiple subjects and fields, cultivating the ability to grasp problems from multiple perspectives. In the second half, students hold a text seminar in which they read a text in advance and make a presentation on the content. By making an effort to make their presentations easy to understand, students can develop the ability to deeply understand and explain the content. In addition, being involved in topics from a variety of fields can also serve as a reference for selecting a theme for their "graduation research."

Group theory and representation theory are fields that mathematically study symmetrical objects and phenomena, such as figures that overlap even when flipped or rotated. The lack of a formula for solving a quintic equation can be explained using group theory by focusing on the symmetry of the solution. Furthermore, the human ear breaks down sound into basic, beautiful waves, and this decomposition of sound can also be understood from the perspective of representation theory. The goal is to clearly understand seemingly complex phenomena by finding hidden symmetries in various phenomena and investigating the beautiful ways in which these symmetries manifest themselves.

We aim to understand population dynamics and infectious disease epidemics using differential equations, dynamical systems theory, and computer simulations. Infectious disease epidemics are complex nonlinear phenomena, and their mechanisms are often not fully understood. We aim to understand the phenomenon by considering and developing mathematical models that represent infectious disease epidemics and investigating the structure and properties of the mathematical models. In the course of our research, we sometimes come across differential equations with interesting properties, and clarifying these properties mathematically is also an important research topic.

Probability theory is the field that mathematically studies uncertain phenomena that are influenced by chance. A major theme of probability theory is grasping the mathematical characteristics behind chance phenomena. The simplest probability problem is the "throw of a dice" learned in high school mathematics, but the ideas of probability theory are used in a variety of real-world situations, from familiar topics such as "how many times is it enough to shuffle a deck of cards?" to highly specialized topics such as "how should the price of financial derivatives be determined?".