Mathematics

■ 2004 Curriculum chart

The number of credits to be earned in each subject is 2 if not otherwise specified in parentheses.

■ Objectives and Key Points of the Curriculum

1st and 2nd years
　1st- and 2nd-year students must take required subjects including lectures and exercise labs that are required later on when studying modern mathematics. Students are required to carefully listen to the instructors during lectures, actively volunteer answers in exercises, create ideas to solve problems, create scenarios to solve the problems, and then submit a complete answer with consistent terminology and symbols.

3rd and 4th years
　There are not many required subjects for 3rd- and 4th-year students, but instead, there are a wide variety of electives in various fields. By offering these electives, the objective of this curriculum is to allow the students to experience as many kinds of fields as possible such that they will be able to widen their views toward math in general and study further advanced math.

Seminar on Mathematics
　4th-year students must take the required subject "Seminar on Mathematics." The prerequisite for this seminar is full understanding of the required subjects that must be taken from the 1st to 3rd year. Therefore, to enroll in this seminar, students must earn credits for most of the required subjects before they enter the 4th year.

Supervisor system
　During the 2001 school year, an adivsor system was implemented. In this system, an instructor is designated for each student and the instructor will give advice on the student's study activities or university life in general.

■ Flow of the Curriculum

New curriculum
　During the 2002 school year, a new curriculum was implemented in order to better respond to the current curricula of educational institutions up to senior high school or to meet the tastes of new students.

(1)	Half a term is spent for implementation of new contents within the conventional curriculum.
(2)	The weight of introductory lectures or exercise labs, such as the "Reading Seminar of Mathematics,""Overview of Mathematics," and "Lecture on Mathematics," has been increased.
(3)	The balance of the curriculum is reviewed so that study loads will be evenly distributed over the four years.

From the 1st year to the first half of the 2nd year
　The curriculum is design to allow students to acquire mathematical knowledge, thinking, and expression, and also to learn the fun and practicality of mathematics. There are required lectures and exercise labs for students to master the basis of mathematical thinking. More specifically, the required lectures are mainly lectures on calculus and linear algebra. Both subjects are essential for mastering basic mathematical thinking and methods. Taking a year and a half, these lectures are given in stages, gradually shifting their targets from concrete objects to abstract discussions, while taking the links with current curricula of senior high schools into consideration. At the same time, lectures such as "Overview of Mathematics" and "Lecture on Mathematics" are provided. These lectures are available to students of any fields or any school years, and students are able use their already obtained knowledge to find interest in mathematics or learn classical theories. Through these courses, students will be mathematically educated, find interest in concrete objects, and become motivated to learn more abstract modern mathematics.

The second half of the 2nd year and after
　From the second half of the 2nd year and on, more abstract theories such as general topology or group theories are introduced, and students start their intensive studies on the basics of algebra, geometry, and analysis that will all be necessary in any field of mathematics. For those who wish to understand modern mathematics in which various mathematical fields influence each other, a wide variety of lectures and accompanying exercise labs are offered. Students will select lectures that meet their abilities and interest, and it is desirable that exercise labs be taken along with lectures for better understanding. In the 4th year, students continue to study various fields of mathematics, but at the same time, they must take the "Seminar on Mathematics" (or "the Seminar"). In this Seminar, each group of several students enters an instructor's office and studies a specific mathematical theme. This will be the completion of four years of study in the Department of Mathematics, and each group will make a presentation at the end of the program.

About the Seminar
　In the 4th year, students take specialized lectures as well as the required Seminar. In the Seminar, students form small groups and, under supervision of the instructor of their choice, they read documents on a specific theme. At the end of the school year, students will then make presentations on what they have learned. In the Seminar, students usually read academic papers or books, explain or illustrate the content of these papers or books to the instructor by using the blackboard, and then solve mathematical problems. The instructor then asks a number of questions such as "What did you understand from what you were assigned to read?" "What does that definition mean? Why is such definition necessary?" "Give some examples in which this hypothesis is proven true," "Please give counter examples," "When you say 'obviously true,' is it really 'obvious'? Please explain," "When you say 'the problem can be solved in the same way as before,' did you actually do it yourself? Please explain," "At which point in the process of proving this does that hypothesis become valid?" "Can you think of other proofs for that theorem?" and "Can you generalize that theorem?" Through these questions and answers, students can better understand the content of their readings and at the same time they can learn mathematical theories. In some cases, students can witness the creation of new mathematics.

■ Features of the department

■ Objectives of the department

　The first objective of this department is to develop individuals who will contribute to society, such as educators who can create educational programs, creative experts with specialized skills, and researchers in basic studies.
　The second objective of this department is to teach the basics of modern mathematics to those who wish to study mathematics and then develop an educational background in which they can further study as sophisticated experts or researchers.
　The third objective is to develop individuals who are beneficial to society, such as those who have mastered mathematical and logical thinking through mathematical education, especially through the Seminar on Mathematics.

■ Lounge

　Since there is no such thing as laboratories for experiments in mathematics, interaction between students and instructors tends to be insufficient. Therefore, one classroom is open for everyone as a lounge, and students ask instructors questions, get together for lunch, and study in the lounge. There are also computers connected via a LAN so that students can use the Internet.

■ Study fields of instructors