Course title
代数学   [Algebra]
Course category technology speciality courses  Requirement   Credit 2 
Department   Year 24  Semester 3rd 
Course type 3rd  Course code 022653
Instructor(s)
原 伸生   [HARA Nobuo]
Facility affiliation Faculty of Engineering Office 12-214  Email address

Course description
We will learn about the basic notions of algebra with respect to concrete examples such as the ring of integers and a group of permutations.
Expected Learning
1. To understand the algebraic structure of groups through concrete examples
2. To be able to solve linear congruences using Euclidean algorithm
3. To understand the notions of equivalence and residue classes via congruence
4. To be able to perform computaions in linear algebra over a finite field and understand applications thereof
Corresponding criteria in the Diploma Policy: See the Curriculum maps
Course schedule
I. Integers
(1) Euclidean algorithm and prime numbers
(2) Congruence
(3) A few theorems in Elementary number thoery
(4) Application to cryptography
II. Equivalence and finite fields
(1) Residue classes and the ring Z/nZ
(2) Finite fields
(3) Vector spaces over a finite field
(4) Application: linear codes
III. Groups
(1) Definition and examples
(2) Order, subgroup
(3) Residue classes and Lagrange's theorem
(4) Normal subgroups and residue class groups
(5) Theorem on group homomorphisms


Prerequisites
Linear Algebra I, II
Required Text(s) and Materials
None
References
To be indicated in the lectures
Assessment/Grading
Due to a Term Exam (2/3) and Reports (1/3)
Message from instructor(s)
Course keywords
Office hours
Arranged taking into account of students' requests
Remarks 1
Remarks 2
Related URL
Lecture Language
Japanese
Language Subject
Last update
12/17/2019 1:09:56 PM