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2023　Essence of Humanities and Social Sciences48:History of Mathematical Sciences

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Academic unit or major
Humanities and social science courses
Instructor(s)
Takuma Naoki 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Wed5-6(G1-106 (G112))  
Group
-
Course number
LAH.S441
Credits
1
Academic year
2023
Offered quarter
1Q
Syllabus updated
2023/3/20
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

Predictions of complex system like weather and economy are widely conducted today. Among them, prediction based on mathematical modeling plays an important role.
By reading some chapters of the textbook written by David Orrell: Apollo’s Arrow: The Science of Prediction and the Future of Everything (2007), the lecture examines the history of the science of prediction with mathematical modelling, especially on weather and climate.
By tracing the concrete history of prediction science, the lecture aims at deepening the students' understanding about the effectiveness and the limitation of prediction science from mathematical point of view, as well as the difficulty of arguing against the the established theory, namely, the "Paradigm."

Student learning outcomes

1) To grasp roughly the historical development of prediction science of complex system, especially of weather and climate, by referring to some mathematical concepts like "sensitivity to initial condition," "modeling error," and "computational irreducibility."
2) To learn that a prediction of phenomena described by deterministic equation was considered easy at first, but later it turned out to be more difficult than expected.
3) To understand that it is difficult for a new proposition which challenges the existing "paradigm" (i.e. the established theory) to be accepted.

Keywords

Complex system, Chaos, Science of prediction, Sensitivity to initial condition, Sensitivity to parameterization, Model error, Computational irreducibility, Paradigm, Research schools, Acceptance of a new proposition.

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 Orientation and Introduction. After explaining the lecture plan and the evaluation of grades, the lecturer makes elementary explanation of chaos and complex system. To understand roughly the concept of chaos and complex system. As preparation for the next class, students are required to read Appendix I to III, in addition fo Chapter 3.
Class 2 Reading of Chapter 3 ("Divide and Conquer: The Gospel of Deterministic Science") (1st half) We trace the successful and straightforward progress of deterministic science before the recognition of “chaos” and “complex system.”
Class 3 Reading Chapter 3 (2nd half). We tarce the anguished history of science of prediction after the recognition of “chaos” and “complex system (with emergent properties).” Students understand what is “chaos” where prediction is difficult due to sensitivity to initial conditions. They also understand what is “complex system (with emergent properties)” whose exact prediction is “essentially impossible.”
Class 4 Reading of Chapter 4 ("Red Sky at Night: Predicting the Weather") (1) (Early sections) We trace briefly the development of mathematical modeling in the early history of weather forecast.
Class 5 Reading of Chapter 4 (2) (Middle Sections). We trace the history of weather forecast in the age of computer. We look back the beginning of GCM (General Circulation Model or Global Climate Model), Edward Lorenz' emphasis on chaos nature, etc.
Class 6 Reading of Chapter 4 (3) (Late sections). We trace the history of efforts to identify the cause of the prediction error. We learn that the error of the weather forecast is less due to the sensitivity to initial condition than the error of the modeling itself (“model error”). We also understand why meteorologists were prone to attribute the cause of prediction error to the sensitivity to initial condition.
Class 7 Reading of some sections of Chapter 7 which are related to Global Warming. We deepen our understanding of what and to which extent we can tell about the future Climate Change.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for relevant sections of the textbook and related course materials before each class, and to spend another 100 minutes reviewing class contents (and completing assignments) after each class.

Textbook(s)

David Orrell (2007), Apollo’s Arrow: The Science of Prediction and the Future of Everything, Harper Perennial.
Students are not forced to buy it. For those who don't buy it, photocopy of Chapter 3 and 4, and a part of Chapter 7 will be distributed through T2SCHOLA. (Redistribution is prohibited.)
We don't make a bulk purchase of the textbook through the university's COOP. If you want to buy textbook, purchase it by yourself personally.

Reference books, course materials, etc.

Reading relevant literature referred in the textbook is highly recommended. Precise information of the literature is listed in the bibliography of the textbook.

Assessment criteria and methods

Class participation 50%, Term Essay 50%.
Class participation score is evaluated mainly based on "Reaction Paper" submitted after each class.
Rough instruction of the Term Essay will be given in the 1st class. The detailed instruction of it will be given in a later class.

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.)

Students need to have experience of learning calculus and linear algebra.

Other

No classes will be given on April 12 (Wed).
Seven total classes will be held for this course: April 19 (Wed), April 26 (Wed), May 10 (Wed), May 17 (Wed), May 24 (Wed), May 31 (Wed), June 7 (Wed).

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