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- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
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School of Environment and Society
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- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Humanities and social science courses
- Instructor(s)
- Hirano Yoichi
- Class Format
- Lecture (Livestream)
- Media-enhanced courses
- Day/Period(Room No.)
- Wed7-8()
- Group
- -
- Course number
- LAH.S441
- Credits
- 1
- Academic year
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
The history of mathematics does not simply mean the historical development of theories and concepts. Mathematicians have developed mathematics through their own activities, sometimes thinking and sometimes making practical experiments. In fact, the development of mathematics can be seen in various aspects of societies. The lecture focuses on the history of mathematics and mathematical thought, and covers the fundamentals of the epistemological understanding of these disciplines. Specifically, taking various cross-sections of the development of mathematics as examples, the lecture will examine the development of theories and practices of mathematics, and view them in a perspective of total history based on both the internal history of theories and the external history of factors.
The students are required to understand the development of mathematics and science in a broad sense. In this sense, the topics also include the historical development of human thought and activity, with a particular emphasis on understanding how academic disciplines have been formed from their developments. This approach can be applied to a wide range of areas other than the history of mathematics and sciences, and will be helpful for students to understand human thinking and activities. Students are expected to acquire the ability to apply the method learned in the lecture to each problem.
Student learning outcomes
At the end of this lecture, students will be able to:
1) Have an understanding of the existence of various elements in the historical development of mathematics
2) Understand that some mathematical concepts and theories are derived inductively from human activities.
3) Explain that the development of mathematics reflects people’s ideas and values of each era.
4) Acquire ways of thinking about today's problems related to mathematics and science and technology, based on this understanding,
Keywords
history of mathematics, history of mathematical thought, total history, theory and practicality, induction and deduction
Competencies that will be developed
| ✔ Specialist skills | ✔ Intercultural skills | Communication skills | ✔ Critical thinking skills | Practical and/or problem-solving skills |
Class flow
The lecturer summarizes important discourses of the Chapter 3 and 4 and of some sections of chapter 7 of the textbook, using slides.
After the class, students write comments for the class in "Reaction Paper" and submit it to OCWi.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Introduction : Perspective of total history in history oh mathematics - internal history, external history, total history - theory and practicality - eurocentrism in the development of mathematics and ethnomathematics | Students must make sure they understand what significance the course holds for them. Understand, the characteristics of mathematics, and in particular, the significance of total history for the study on history of mathematics. |
| Class 2 | Greek geometry: Structure of demonstrative geometry and Three classical problems of construction - Structure of demonstrative geometry in ancient Greece (found in Euclid’s “Elements”) - Three classical problems of constraction (Trisecting the angle, Doubling the cube, Squaring the circle) - Pythagorean school and its works | Understand the structure of demonstrative geometry (e.g. the problem known as “bridge of assessments” (on the base angles of an isosceles triangle), [Euclid, I, Prop.5]) |
| Class 3 | History of numbers: natural number, rational number, irrational number - Pythagorean figurate numbers (on the sum of natural numbers) - Incommensurability in the ancient Greek mathematics - Regular pentagon and golden ratio | Understand how humans have treated numbers Trough the introduction of the concept of irrational numbers, understand how humans |
| Class 4 | Development of Theory of algebraic equations: Proving the problems of impossibility - Historical development of solutions of equations - Introduction of algebraic expresson and cartesian coordinates - Unsolvability of quintic equation and development of mathematical research (Proof of problems of impossibility) | Understand abstraction in the development of equation theory. Understand that problems related to impossibility develop mathematical concepts and theories. |
| Class 5 | Mathematics in the Renaissance (1): Art and Matnematics - Practicality of mathematics in the Renaisance - Mathematical elements found in artists' activities (perspective, human proportion) | Understand that mathematics seen in the Renaissance period generally had a practical aspect, and examine the characteristics of mathematics through its understanding. At the same time, understand that the practical mathematics then moves toward theory formation. |
| Class 6 | Mathematics in the Renaissance (2): Leonardo da Vinci’s mathematical activities - Mathematical factors seen in Leonardo da Vinci’s manuscripts - Classical disciplines as the roots of Leonardo da Vinci's thinking and activities | Understand that Leonardo da Vinci, a genius of the Renaissance, was involved in mathematical research and that classical works had a great influence on the root of his activities. |
| Class 7 | Conclusive observasion - Mathematics museum (historical exhibits that show mathematics) - Mathematics Museum: mathematical exhibits related to human activities and society - Understanding nature by applying mathematics - Summary of the question of “what kind of science is mathematics?” | Through the theory and practice of mathematics learned in this class, each student will independently consider what kind of academic field mathematics is, and summarize what they have understood. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to course materials.
Textbook(s)
None required.
Reference books, course materials, etc.
Carl B. Boyer & Uta C. Merzbach, A History of Mathematics (John Wiley & Sons, 2011).
Assessment criteria and methods
1) Students will be assessed on their understanding what is taught on each lecture, through their assignments for each class (the deadline for submission of assignments for each class is scheduled to be one week). In addition, a final report will be assigned in the last class.
2) Students course scores are based on the following weights:
Assignments (1st class – 6th class): 10 units each (total 60 units) / Final report: 40 units.
3) The instructor may fail a student if he/she submits assignments (or report) later or resubmits too often.
Related courses
- LAH.S433 ： Essence of Humanities and Social Sciences37:History of Science
- LAH.T102 ： History of Science A
- LAH.T202 ： History of Science B
- LAH.T302 ： History of Science C
Prerequisites (i.e., required knowledge, skills, courses, etc.)
1) No prerequisites (in principle).
2) This lecture will be given in English. However, questions may be asked in English or Japanese.
3) Students are required to study the reference materials (in English) distributed in advance before coming to class.
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
yhirano[at]tsc.u-tokai.ac.jp
Office hours
Contact before and after classes, or e-mail for an appointment.
Other
No classes will be given on April 10(Wed).
Seven total classes will be held for this course: April 17 (Wed), April 24 (Wed), May 1 (Wed), May 8 (Wed), May 15 (Wed), May 22(Wed), May 29(Wed).
