National Taiwan Normal University Course Outline
 Fall , 2025

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I.Course information
Serial No. 2704 Course Level Undergraduate / Master
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 3.0 Lecturing hours Lecture hours: 3
Prerequisite Course
Comment
Course Description
Day & Class Period/Location Fri. 6-8 Gongguan M211
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) CHANG, Ping-Ying/ 張秉瑩
Schedule

I. Introduction

II. The transmission of Western mathematics in Qing China

  • Jesuit missionary and Ming-Qing calendar reform
  • The Kangxi Emperor's imperial mathematics
  • The Biographies of Mathematics and Astronomers
  • Late Qing reform movements and the learning of Modern Mathematics

III. East Asian mathematics

  • Counting rods and abacus
  • From Suanshu shu to Ten Computational Canons
  • Tianyuan shu
  • Sangaku and Wason

IV. Western mathematics

  • Medieval Europe and the development of Islamic mathematics
  • Renaissance mathematicians
  • Mathematics and the scientific revolution
  • Mathematics in French revolution and the Enlightenment

V. Origin of mathematics

  • Plato and Aristotle
  • Greek and Hellenistic mathematics 
  • Egyptian and Babylonian mathematics
Instructional Approach
Methods Notes
Formal lecture  
Group discussion  
Grading assessment
Methods Percentage Notes
Assignments 25 %  
Class discussion involvement 50 %  
Case study reports 25 %  
Required and Recommended Texts/Readings with References
  1. 洪萬生等 (2024). 《數之軌跡》I, II, III, IV，台北：三民書局。
  2. Bunt, Lucas N. H., Phililip S. Jones, Jack D. Bedient (1988). The Historical Roots of Elementary Mathematics. New York: Dover Publications, INC.
  3. 台灣HPM團隊翻譯 (2008).《溫柔數學史》(Math through Ages: A gentle history for teachers and others)，台北：博雅書屋。
  4. 郭書春、劉鈍校點 (2001).《算經十書》，台北：九章出版社。

 

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