Algebra

Course Information

College	Tsuyama College	Year	2021
Course Title	Algebra
Course Code	0156	Course Category	Specialized / Elective
Class Format	Lecture	Credits	Academic Credit: 2
Department	Department of Integrated Science and Technology Electrical and Electronic Systems Program	Student Grade	5th
Term	Year-round	Classes per Week	1
Textbook and/or Teaching Materials
Instructor	YAMANAKA Satoshi

Course Objectives

Learning purposes : Acquire basic knowledge about Galois theory, which is the basis of modern mathematics.
1. To understand the basic properties of group theory.
2. To understand the basic properties of field theory.
3. To understand the basic properties of Galois theory.

Rubric

	Excellent	Good	Acceptable	Unacceptable Level
Achievement 1	Basic knowledge of group theory is well understood.	Understand about 70% of the basic knowledge of group theory.	Understand about 60% of the basic knowledge of group theory.	Not reached left.
Achievement 2	Basic knowledge of field theory is well understood.	Understand about 70% of the basic knowledge of Field theory.	Understand about 60% of the basic knowledge of filed theory.	Not reached left.
Achievement 3	Have a good understanding of the concept of Galois theory and the basic theorems of Galois theory.	Understand the concept of Galois theory and the basic theorems of Galois theory about 70%.	Understand the concept of Galois theory and the basic theorems of Galois theory about 60%.	Not reached left.

Teaching Method

Outline:

General or Specialized : Specialized

Field of learning : Mathematics / Physics (Specialized Subjects)

Foundational academic disciplines : Mathematical science / Mathematics / Basic analysis

Relationship with Educational Objectives : This class is equivalent to "(3) Acquire deep foundation knowledge of the major subject ares

Relationship with JABEE programs : The main goals of this are "(A) , A-1.

Class outline : Galois theory, the foundation of modern mathematics, will be explained.

Style:

Course method : In this course, we will use lectures as a basis, but we will also use exercises to deepen our understanding.

Grade evaluation method : Evaluation is based on the results of two regular examinations (60%) and the exercise report (40%). In addition, depending on the grade, an additional report may be assigned.

Notice:

Precautions on the enrollment : Students who choose this lecture must take this class (no more than one-third of the required number of class hours missed) in order to complete the 5th year course. This is a class that requires study outside of class hours. A total of 45 hours of study is required per credit, including both class time and study outside class time. Follow the instructions of the instructor regarding study outside of class hours.

Course advice : Review mathematics learned up to the 4th year.

Foundational subjects : Mathematics learned up to the 4th year.

Attendance advice : If a student is tardy too many times, he or she may be given a warning and then be marked absent.

Characteristics of Class / Division in Learning

Active Learning

Aided by ICT

Applicable to Remote Class

Ｅｌｅｃｔｉｖｅ　ｍｕｓｔ　ｃｏｍｐｌｅｔｅ　ｓｕｂｊｅｃｔｓ

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Guidance, solving equations (quadratic, cubic, and quaternary)	Understand how to solve quadratic, cubic, and quaternary equations
		2nd	Symmetry formulas and symmetry groups	Understand symmetry formulas and symmetry groups
		3rd	Irreducible polynomials over a field and Euclidean algorithm	Understand irreducible polynomials over a field and Euclidean algorithm
		4th	Linear algebra over a field and order formulas	Understand linear algebra over a field and order formulas
		5th	Plottable numbers and double product problems	Understand plottable numbers and double product problems
		6th	Determination of irreducible conditions, angle trisection problem, circle product problem	Understand the determination of irreducible conditions, angle trisection problem, circle product problem
		7th	1st semester mid-term exam
		8th	Answers and explanations for 1st semester mid-term exam, homomorphisms and automorphisms of field	Understand homomorphisms and automorphisms of field
	2nd Quarter
		9th	Fundamental theorem of Galois theory	Understand fundamental theorem of Galois theory
		10th	Examples of Galois expansions and Galois groups	Understand examples of Galois expansions and Galois groups
		11th	Cyclotomic polynomial and drawing a regular 17-sided polygon	Understand cyclotomic polynomials and how to draw a regular 17-sided polygon
		12th	Rational function fields and fundamental theorem of symmetric equations	Understand rational function fields and fundamental theorem of symmetric equations
		13th	Formula for solving equations of degree 5 or higher	Understand formula for solving equations of degree 5 or higher
		14th	Galois theorem	Understand Galois theorem
		15th	1st semester final exam
		16th	Answers and explanations for 1st semester final exam

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Other	Total
Subtotal	60	0	0	0	0	40	100
Basic Proficiency	0	0	0	0	0	0	0
Specialized Proficiency	60	0	0	0	0	40	100
Cross Area Proficiency	0	0	0	0	0	0	0