Course Outline

National Taiwan Normal University Course Outline
Fall , 2020

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I.Course information

Serial No.	2799	Course Level
Course Code	MAC9028	Chinese Course Name	數學史（IB）
Course Name	History of Mathematics (IB)
Department	Department of Mathematics
Two/one semester	1	Req. / Sel.	Sel.
Credits	1.0	Lecturing hours	Lecture hours: 1
Prerequisite Course	Prerequisite course(can be taken in the same semester): 【MAU0077 History of Mathematics】
Comment
Course Description
Time / Location	Tue. 7 Gongguan MA2-11
Curriculum Goals		Corresponding to the Departmental Core Goal
1.　To demonstrate the ability to see the mathematical structure behind certain problems or procedures in history		College: 　1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint Master: 　1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint
2.　To apply critical thinking skills through the reflexion on the philosophical standpoints of mathematics		College: 　3-2 Possessing the abilities to think independently, criticize, and reflect Master: 　3-2 Possessing the abilities to think independently, criticize, and reflect
3.　To have the ability to present a group project to the class		College: 　3-2 Possessing the abilities to think independently, criticize, and reflect 　3-3 Being willing to work collaboratively Master: 　3-2 Possessing the abilities to think independently, criticize, and reflect 　3-3 Being willing to work collaboratively
4.　To form one’s own ideas and to be able to describe why mathematics is “interesting”, the reasons of which can be internal or external to mathematics such as the influence of cultural reasons		College: 　1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 　3-2 Possessing the abilities to think independently, criticize, and reflect 　3-5 Having good taste for mathematics 　4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning Master: 　1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 　3-2 Possessing the abilities to think independently, criticize, and reflect 　3-5 Having good taste for mathematics 　4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning
5.　To demonstrate one’s beliefs that in different contexts there can be different standards for “good” or “useful” mathematics		College: 　1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 　3-2 Possessing the abilities to think independently, criticize, and reflect 　4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning Master: 　1-6 Possessing the capacities to view elementary mathematics from an advanced viewpoint 　3-2 Possessing the abilities to think independently, criticize, and reflect 　4-3 Possessing a variety of beliefs regarding mathematics values and mathematics learning
6.　To know that mathematics has its cultural elements, and learn to have inter-cultural understanding and respect for others		College: 　4-4 Possessing global views from both scientific and humanistic perspectives, and being able to appreciate the values of other knowledge fields Master: 　4-4 Possessing global views from both scientific and humanistic perspectives, and being able to appreciate the values of other knowledge fields

II. General Syllabus

Instructor(s)

HORNG, Wann-Sheng/ 洪萬生

Schedule

Session 1	Topic: Introduction to the humanistic side of mathematics l What is mathematics, really? l Is there a history for mathematics? Activities: Lecture and class discussion
Session 2	Topic: Plato and Aristotle Activities: Lecture, group discussion and class discussion
Session 3	Topic: Logicism, intuitionism, and formalism Activities: Lecture, group discussion and class discussion
Session 4	Topic: Quasi-empiricism Activities: Lecture, group discussion and class discussion
Session 5	Topic: Different philosophical standpoints of mathematics Activities: class discussions about the mid-term essays
Session 6	Topic: Babylonian and Egyptian mathematics l Is there something we may call mathematics in the ancient world? Activities: Lecture, group discussion and class discussion
Session 7-8	Topic: Hellenistic mathematics Activities: Lecture, group discussion and class discussion
Session 9-10	Topic: Group presentations on the mathematics in the ancient world Activities: group presentation and class discussion
Session 11	Topic: East Asian mathematics in the first millennium Activities: Lecture, group discussion and class discussion
Session 12	Topic: East Asian mathematics in the early second millennium Activities: Lecture, group discussion and whole-class discussion
Session 13-15	Topic: Group presentations for the Chinese mathematics Activities: group presentation and class discussion
Session 16-17	Topic: Early modern mathematics Activities: Lecture, group discussion and class discussion
Session 18	Activities: Final written examination

Instructional Approach

Methods

Notes

Formal lecture

Group discussion

Grading assessment

Methods

Percentage

Notes

Assignments

30 %

Final exam

30 %

Presentation

40 %

Required and Recommended Texts/Readings with References

1. Victor Katz (2008). A History of Mathematics (3rd Edition). New York: Pearson.

2. Stewart Shapiro (2000). Thinking about Mathematics: The Philosophy of Mathematics. Oxford: Oxford University Press.

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