Mathematics Major 3

・Mathematics Major　1　2　3	・Faculty	・Messages from Graduates
・Curriculum	・Syllabus	・Open Lectures
・Institute of Mathematics

Carl Friedrich Gauss
(1777－1855）The greatest mathematician in the first half of the 19th century. It is said that his discovery that the regular 17-gon was constructible by ruler and compass led him to specialize in mathematics. His significant achievements can be seen in the fields of number theory, mathematical analysis, geometry, and applied mathematics.

David Hilbert
(1862－1943）The greatest mathematician of the 20th century. Noted for his fine achievements in algebraic geometry, algebraic number theory, mathematical analysis, and foundations of mathematics. His 23 problems presented at the International Congress of Mathematicians in Paris have had a decisive influence on the development of mathematics ever since.

Mathematics Major Curriculum
Year 1	Year 2	Year 3	Year 4
Calculus I, II	Analysis	Algebra I A	Algebra II, III
Calculus I, II Exercises	Analysis Exerc.	Algebra I A exerc.	Topology III
Linear Algebra I, II	Adv. Linear Algebra	Algebra I B	Differential Geometry
Linear Algebra I Exerc.	Adv. Linear Algebra Exerc.	Algebra I B exerc.	Differential Equations
Seminar in Mathematics	Intro. to Algebra	Topology I, II	Real Analysis III
Mathematics Special Lectures I	Intro. to Algebra Exerc.	Topology I exerc.	Complex Analysis
	Curves and Surfaces	Intro. to Manifolds	Functional Analysis
	Curves and Surfaces Exerc.	Complex Analysis	Probability Theory II
	Intro. to Set Theory	Complex Analysis exerc.	Mathematical Statistics II
	Intro. to Set Theory Exerc.	Real Analysis I, II	Mathematical Logic II
	Intro. to Topology	Real Analysis I, II exerc.	Computer Mathematics II
	Intro. to Topology Exerc.	Probability Theory� I	Topics in Mathematics I, II, III
	Statistics	Mathematical Statis. I	Special Lectures A, B, C on Mathematics
	Exercises of Computer	Mathematical Logic I	Special Lectures on Algebra
	Reading English Mathematical Books Ⅰ	Computer Mathematics I	Special Lectures on Geometry
		Reading English Mathematical Books II	Special Lectures on Analysis
		Measurement	Special Lectures on Information Mathematics
		Pre-Thesis Research	Graduation Thesis

　The mathematics that you learn in Years 1 and 2 is a warm-up for Years 3 and 4. The lectures in the first two years are for all students of the College of Natural Sciences, called specialized basic subjects, and are a step before the more specialized subjects. You will cover the three categories of calculus, linear algebra, set theory and topology. Year 3 will be the first step in modern mathematics, with lectures in algebra, geometry, and analysis. From the third semester of Year 3, you will begin your preparatory research for the graduation research project, preceding your Year 4 seminar classes. This is when you begin to discover learning not only through lectures and exercise courses, but also by reading papers and books to get a better understanding in your field of interest. It will be one of the most satisfying times as a mathematics major.

　In Year 4, lectures go deeper into the basic theories taught in Year 3, which are combined with more specialized courses. These include function space, Lie group theory, Riemann surface theory, ordinary differential equations, mathematical logic, probability theory, mathematical statistics, and computer mathematics. Students not only learn theories in pure mathematics but also gain a wider perspective in applied mathematics. In Year 4, all students will be working on their graduation theses. There are several seminar groups, and students join one according to their interest. This seminar is the place to present progress of research projects and have discussions with your tutor. It will provide you with a satisfaction different from the ordinary lectures.

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