Quest for Mathematics I-E2

科目ナンバリング U-LAS10 10023 LE55 開講年度・開講期 2021 ・ 前期
単位数 2 単位 授業形態 講義
配当学年 主として1・2回生 対象学生 全学向
使用言語 英語 曜時限 火2
教員 Arseniy Aleksandrovich,Kuzmin (工学研究科 講師)
授業の概要・目的 In the "Quest for Mathematics", complex numbers and their applications are introduced. At first, we will follow some of the steps of their invention and learn to understand their basic properties. This numbers are very important in many different fields, such as quantum mechanics or electric engineering. In this course we explore geometrical applications of complex numbers, geometrical transformations, and complex functions.
到達目標 - To understand the origins and importance of complex numbers
- Understanding of the geometric representation of complex numbers
- Learn the complex numbers arithmetic
- Learn the relation between trigonometric and exponential functions
- Acquire the ability to use complex numbers
授業計画と内容 In this course the following topics are covered:

1. Introduction and history of complex numbers. Geometric definition of complex numbers.
2. From geometric definition to Bombelli's "wild thought". The Argand plane and modern definitions.
3. Simple complex arithmetic and De Moivre's formula.
4. Equivalence of symbolic and geometric arithmetic.
5. Euler's formula: moving particle argument.
6. Euler's formula: power series argument.
7. Applications: trigonometry.
8. Applications: geometry.
9. Applications: calculus.
10. Applications: algebra.
11. Applications: vector operations.
12. Complex numbers and Euclidean geometry: transformations.
13. Motions and reflections.
14. Similarities and complex arithmetic. Spatial complex numbers.

14 lectures in total and one feedback class.
成績評価の方法・観点 Evaluation will be based on:
10% attendance and participation
20% homework
20% quiz
50% final exam
履修要件 No knowledge of complex numbers is required to join this class. All necessary concepts are introduced during the lecture.
授業外学習(予習・復習)等 Preparation for lectures will include revision of class materials and homework assignments. The work during the semester is most important, it helps to build up the understanding. If you have no problems with homework, there will be no problem solving the tests.
参考書等 Mathematics and its history, John Stillwell, (Springer), ISBN:978-1-4419-6052-8