Graduate School of Science and Technology(Master's Program)>Department of Science>Mathematics Division
The target of the Mathematics Division is to unravel phenomena and structures in the natural world and societies by using “mathematics.” This division undertakes education and research of pure mathematics for pursuing original results such as generalization and refinement of previous research, configuration of specific examples, reconsideration, etc., in various fields such as algebra, geometry, and mathematical analysis, and their fused fields. This division also undertakes, as an application, education and research into natural informatics for developing natural and social sciences
Quadratic formula are learned in high school, and in fact there are formulas for equations of the third and fourth orders. However, it is known that formulas do not exist for equations of the fifth degree and higher order equations. To prove it, we need to consider a mathematical object called a "group". Algebra is the study of groups. In algebra, there are also important research objects called "rings" and "fields". In the field of algebra, we mainly study groups and rings, but we also study computer algebra and combinatorics.
There are no boundaries in the academic world, and also in nature surrounding us. Classification of knowledge, such as, mathematics, physics, chemistry, and computer science is made by humans for convenience sake. On the other hand, there are many figures called fractal figures, in which a part of the whole is the reduced copy of itself, like trees and cauliflowers. A branch of a tree can be seen as a reduced copy of the tree, and a cluster of a cauliflower can be seen like a small cauliflower. Fractal figures can be researched both in physics and in mathematics. In such research, using computers is very effective. This is an example of knowledge exceeding the boundaries of academic fields. The target of natural informatics is to handle complex problems found in mathematics, physics, and computer science, and to research them as an organized combination.
Geometry is the field of mathematics that analyzes the properties of figures. The first thing that comes to mind when you hear the word "figure" is a triangle or a circle, and whether two triangles are "the same" (congruent) or not can be determined by examining the lengths and angles of their sides. In general, it is modern geometry that examines whether two figures are "the same" or not. Complex figures are impossible to classify with such simple data as triangles, and there are many different methods and criteria for classification. For example, when classified according to the criteria of the field of topology, triangles and circles are "the same," or donuts and coffee cups are "the same," which at first glance may seem strange.
In the field of geometry, various figures are studied using algebra tools and mathematical analysis.
The foundation of mathematical analysis is undoubtedly calculus. University students learn it in more detail, and also learn differential equations and complex-function calculus, which provides a completely new world.
“Differential” was devised to analyze the movement of an object. “Integral” was devised to calculate the area of a figure. Like this, there are some motives to advance mathematical analysis. Theories based on such motives are not only interesting by themselves but also provide unexpected power by applying them. Actually, mathematical analysis is widely applied to natural science, engineering, economics, etc.
Your requests will be satisfied because the staff of Mathematical Analysis covers both theoretical and applied fields.
Mathematical Analysis