2023 Students Enrolled in or before 2015 School of Science Mathematics
Advanced courses in Geometry A
- Academic unit or major
- Mathematics
- Instructor(s)
- Hidetoshi Masai
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Fri (M-157(H1102))
- Class
- -
- Course Code
- ZUA.B331
- Number of credits
- 100
- Course offered
- 2023
- Offered quarter
- 1Q
- Syllabus updated
- Jul 8, 2025
- Language
- English
Syllabus
Course overview and goals
To understand 3-dimensional hyperbolic geometry via computational methods. The main topic of this lecture is so-called verified computation, which enables us to prove mathematical theorems by using numerical computation.
Course description and aims
Understand the basics of verified computation.
Keywords
Verified computation, interval arithmetic, Newton's method, fixed point theorems
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction to python programming | Details will be provided during each class session |
| Class 2 | Floating point arithmetic and Interval arithmetic | Details will be provided during each class session |
| Class 3 | Verified computations on linear algebra I | Details will be provided during each class session |
| Class 4 | Verified computations on linear algebra II | Details will be provided during each class session |
| Class 5 | Verified computations of elementary functions | Details will be provided during each class session |
| Class 6 | Verified computations on non-linear equations I | Details will be provided during each class session |
| Class 7 | Verified computations on non-linear equations II | Details will be provided during each class session |
Study advice (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 textbooks and other course material.
Textbook(s)
non required
Reference books, course materials, etc.
・Verification methods: rigorous results using floating-point arithmetic, Siegfried M. Rump
Evaluation methods and criteria
Assignments (100%).
Related courses
- MTH.C201 ： Introduction to Analysis I
- MTH.A211 ： Advanced Linear Algebra I
Prerequisites
Undergraduate-level knowledge of Calculus and Linear Algebra