Course title
6M0173001
Mathematics for Numerical Computations B

 OZAKI Katsuhisa
Course content
In numerical computation, floating-point numbers and their arithmetic as defined by the IEEE 754 standard are widely used. Since this system is used in various simulations, it is important to know the principles of the system. In this lecture, we will apply this system to the introduction of interval arithmetic and computer-assisted proofs.
Purpose of class
The purpose of this course is to provide a deeper understanding of calculations that have been handled in C, MATLAB, etc. The course covers the understanding of binary floating-point numbers and the problem of rounding errors, and computer assisted proof. The subject will be numerical linear algebra.
Goals and objectives
  1. Understanding the definition of floating-point numbers defined by IEEE 754
  2. Understanding interval arithmetic and its mathematical properties
  3. Understanding the basic of computer assisted proof
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Report Short Reports Total.
1. 20% 10% 30%
2. 25% 10% 35%
3. 25% 10% 35%
Total. 70% 30% -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Floating-point arithmetic (definition) Review of C or MATLAB programming 190minutes
2． Floating-point arithmetic (directed rounding) Review of floating-point arithmetic 190minutes
3． Interval arithmetic (definition) Max. and Min. of a function 190minutes
4． Interval arithmetic (implementation) Review of Basic of MATLAB programming 190minutes
5． Computer assisted proof (1) Review of Dot product of vectors and interval arithmetic 190minutes
6． Computer assisted proof (2) Review of a matrix in linear algebra 190minutes
7． Problems for Report Review of all topics 190minutes
8． None 0minutes
9． None 0minutes
10． None 0minutes
11． None 0minutes
12． None 0minutes
13． None 0minutes
14． None 0minutes
Total. - - 1330minutes
Evaluation method and criteria
The main evaluation is based on a main report, but short reports on the lecture content will also be taken into account as described above.
Students who have passed the unit are expected to be able to understand the problem of errors in floating point arithmetic, and to be able to prove simple mathematical problems using numerical computations.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
Nothing.
All material will be shown in the class.
Prerequisites
Review of basic programming and topics in linear algebra (determinant, inverse matrix).
Office hours and How to contact professors for questions
  • Lunch time on Monday, please send e-mail in advance
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic self-management skills
Active-learning course
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A 該当しない
Education related SDGs:the Sustainable Development Goals
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Tue Mar 12 04:09:50 JST 2024