Course title
代数学   [Algebra]
Course category	technology speciality courses	Requirement		Credit	2
Department		Year	2～4	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