Max-plus (or min-plus) algebras are algebras called idempotent semirings, which have various origins in applications and have
developed independently in each field of application. In recent years, a research area called tropical geometry has been actively
studied in mathematics. Tropical geometry is an algebraic geometry on max-plus algebras. On the other hand, many properties
and theorems well known in linear algebra are known to have similar properties in max-plus algebra, and are sometimes called
tropical linear algebra.
In this class, we will discuss the basic properties of the max-plus algebra and its relation to graph theory, as well as eigenvalues and eigenvectors in max-plus algebras and their applications.
In this class, we will discuss the basic properties of the max-plus algebra and its relation to graph theory, as well as eigenvalues and eigenvectors in max-plus algebras and their applications.
The purpose of this class is to understand the basic properties of max-plus algebras and their relation to graph theory, as
well as eigenvalues and eigenvectors in max-plus algebras and their applications.
- Students can understand the definition and basic properties of max-plus algebra
- Students can understand linear algebra over max-plus algebra, properties of eigenvalues and eigenvectors, and their applications.
- Students can understand the mim-plus analogy of the qd algorithm
| report | Total. | |
|---|---|---|
| 1. | 30% | 30% |
| 2. | 40% | 40% |
| 3. | 30% | 30% |
| Total. | 100% | - |
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1． | Guidance Definition of max-plus algebra, basic properties |
Review of linear algebra | 190minutes |
| 2． | Polynomials and factorizations on max-plus algebra | Review of previous classes | 190minutes |
| 3． | Functions on max-plus algebras and their graphs | Review of previous classes | 190minutes |
| 4． | Linear algebra over max-plus algebras | 前回までの復習 | 190minutes |
| 5． | Matrices and graphs over max-plus algebra | Review of previous classes | 190minutes |
| 6． | Eigenvalues, eigenvectors, and graphs over max-plus algebra | Review of previous classes | 190minutes |
| 7． | Min-plus analogy of the qd algorithm | Review of previous classes | 190minutes |
| 8． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 9． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 10． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 11． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 12． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 13． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| 14． | (Ends at the 7th class due to being a 1-credit course) | (Ends at the 7th class due to being a 1-credit course) | 0minutes |
| Total. | - | - | 1330minutes |
Evaluation will be based on a short report on each lecture and a final report at the end of the term.
A student will pass the course if he/she is judged to have understood at least 60% of the content of the lectures.
A student will pass the course if he/she is judged to have understood at least 60% of the content of the lectures.
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class |
Basic knowledge of linear algebra I/II, numerical analysis I/II, and algebra is preferred.
- Tuesday, 4th period; it is advisable to contact in advance when visiting the lab..
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Wed Oct 02 04:04:02 JST 2024