Prospects of Mathematics II

Hidetoshi AWATA Associate Professor

Department: School of Science / Graduate School of Science

Class Time: 2006 Fall
Recommended for: School of Science

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Course Overview

Looking into the history of mathematics and physics, it is clear that both disciplines have exerted a huge influence on one another. We can see a typical example of this via the concurrent evolution of pre-twentieth century mathematical concepts such as differential and integral calculus, as well as topology, alongside the physics-based study of Newtonian mechanics. Another good example would be the evolution of vector analysis alongside the study of electromagnetism. Since the twentieth century, this connection has deepened. For this reason, it is impossible to disregard the study of physics if we want to better understand mathematics. In this course, we will study the relationship between mathematics and physics, introducing twentieth century concepts such as quantum theory and the theory of relativity, which are not commonly taught in high school or in liberal art courses.

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Important notes on satisfying the course requirements

In order to take this course, students must have a high competence in differential and integral calculus, as well as linear algebra. A high level of knowledge in physics is not required, although a familiarity with high school-level physics would be beneficial in understanding the course contents.

Textbooks and Reference Books

No textbooks are assigned for this course.

Course Schedule

The following schedule has been proposed for this course. We will look at mathematical concepts related to the theory of relativity and quantum theory.

Session Contents
1 Part 1: The Theory of Relativity
  • Lorentz Transformation
  • Space-Time Diagram
  • Minkowski Space(time)
2
3
4
5
6 Part 2: Quantum Theory
  • Dual nature of light
  • Wave Function
  • Hilbert Space
  • Fourier Series
  • Linear operator
  • (Heisenburg) Uncertainty Principle
  • Duality
7
8
9
10
11
12
13
14
15

Grading

Students will be evaluated based on papers submitted throughout the course. The reports will be comprised of exercise problems from the lectures. Students with a low grade may resubmit papers multiple times in order to improve their score, but plagiarism of other student's work is strictly forbidden.

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Lecture Handouts

All files are in Japanese.

Session #1
Session 1 lecture notes (PDF, 834KB)
Session #2
Session 2 lecture notes (PDF, 1062KB)
Session #3
Session 3 lecture notes (PDF, 615KB)
Session #4
Session 4 lecture notes (PDF, 616KB)
Session #5
Session 5 lecture notes (PDF, 730KB)
Session #6
Session 6 lecture notes (PDF, 701KB)
Session #7
Session 7 lecture notes (PDF, 656KB)
Session #8
Session 8 lecture notes (PDF, 642KB)
Session #9
Session 9 lecture notes (PDF, 292KB)
Session #10
Session 10 lecture notes (PDF, 724KB)
Session #11
Session 11 lecture notes (PDF, 601KB)
Session #12
Session 12 lecture notes (PDF, 793KB)
Session #13
Session 13 lecture notes (PDF, 697KB)

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Page last updated June 28, 2011

The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.

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