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A study that uses equations to consider the structure of figures, points, etc.

Algebra is a study that employs equations to explore the structures of figures, points, and more. In essence, it involves methods for solving equations, expanding its scope to include algebraic geometry, number theory, and active applied research. Within this evolving landscape, Professor Ito specializes in algebraic geometry. He explains, “We use equations to investigate the properties of figures, considering higher-dimensional aspects that cannot be visually depicted. Shapes, when conceptualized using complex numbers alongside real numbers, defy visualization, prompting us to rely on equations for investigation.” On the other hand, Professor Kida is an expert in algebraic number theory. He notes, “Unlike algebraic geometry, which examines the figure itself, we focus on points with integer components on the figure or graph, specifically integer points.” Professor Kida emphasizes the importance of these differences, highlighting the need for collaborative research in mathematics.

Need for Collaborative Research to Combine Two Minds

Encounters between researchers exploring similar subjects with different approaches can be exciting, as it involves thinking with two minds. Beyond listening to lectures at international conferences, creating opportunities for researchers to engage in discussions is crucial. Professor Kida asserts, “Research often reveals our weaknesses. Conversations with those in different research domains can lead to collaborative projects.” Professor Ito adds, “Sometimes, using a different method reveals previously unknown information, solving unsolved problems.” However, the COVID-19 pandemic has hindered face-to-face interactions, impacting the progress of collaborative research.

Division of Modern Algebra and Cooperation with Engineering: Uniting Mathematicians for Enhanced Research

The Division of Modern Algebra and Cooperation with Engineering seeks to bring theory to theory, method to method, and inspire collaboration on a larger scale. It gathers researchers specializing in algebra and those involved in algebra-based applied research. Professor Ito emphasizes the fundamental role of mathematics in science and engineering education, asserting that the Tokyo University of Science boasts many exceptional mathematicians, covering almost all fields of mathematics. Professor Kida highlights the division’s future contribution to society, stating, “Algebra’s abstract nature allows for customization in various fields, demonstrating its strength.” The increasing number of job offers from companies for students who have studied mathematics serves as proof of algebra’s relevance.

Faculty of Science and Technology, Department of Mathematics
Professor Hiroyuki Ito

■ Main research themes

Professor Ito specializes in algebraic geometry and applied algebra. He researches algebraic varieties defined by the common zeros of many multivariate polynomials from various perspectives.

Faculty of Science Division I, Department of Mathematics
Professor Masanari Kida

■ Main research themes

Professor Kida specializes in algebraic number theory, algebra, and computational number theory. His goal is to construct algebraic number fields and/or polynomials with certain properties.

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