General Description (概要)
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Introduction to modern algebra. Includes group theory and ring theory. One period of lecture and two periods of recitation weekly. Prerequisite: Linear Algebra II. Recommended to be taken after BASIC CONCEPTS IN MATHEMATICS I.
現代代数学の基礎を学ぶ。群論，環論など。 毎週講義1時限，演習2時限。線形代数学 II を既修のこと。さらに数学通論 I の既修が望ましい。
We will study an introduction to Group Theory in Algebra I. A group is a beautiful fundamental algebraic structure with one binary operation. We will study rings with two algebraic operations in Algebra II, and we will apply Group Theory to rings.
代数系のうち最も基本的で最も美しい群の理論を学ぶ。 代数学 I では群、代数学 II では環および体の理論が中心である。
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Learning Goals(学習目標)
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Understanding definitions, contents of theorems and proofs of them are essential in studying Mathematics.
Through this course students will learn how to read and write proofs of basic properties of groups by starting from only definitions and/or appropriately quoting theorems.
Students will know several examples of groups and will be able to apply theorem of groups in concrete examples.
群とその基本理論を理解し、その基本的な性質については自分で導き出せるようにする。
定義を満たす例と、満たさない例を確認することで、定義の意味を理解し、さらに、定義の中のどの性質を使って、群のそれぞれの導き出されるのかをチェックしながら、定理を学び、さらに、実例でその性質を確認し、さらにどのような性質が成立するかを考え、一般には成立しない性質についても例で確認していくプロセスを経験する。
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Contents(内容)
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Introduction to Groups
Finite groups; Subgroups
Cyclic Groups
Permutation Groups
Isomorphisms
Cosets and Lagrange's Theorem
External Direct Products
Normal Subgroups and Factor Groups
Group Homomorphisms
Fundamental Theorem of Finite Abelian Groups
Sylow Theorems
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Language of Instruction(教授言語の詳細)
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Grading Policy(成績評価基準)
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Homework (35%、Final Exam (50%)、and class participation by solving and explaining exercises (15%) . Details will be posted in Algebra I homepage.
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Expected study hour outside class(授業時間外学習)
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References(参考文献)
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Textbook: Joseph A. Gallian, Contemporary Abstract Algebra -- 8th Edition (Expositions are similar to 7th edition but with more exercises)--
International Version --- Paper backs ISBN-13: 978-1133606758
(640 pages)
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Learning Support Resources for Students (学生のための学修支援リソース)
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If there are learning support resources that are especially recommended for this course, they will be listed below.
Here (ICU Internal page) is the list of learning support resources available at ICU.
このコースで特に利用を推奨する学修支援リソースがある場合、以下に記載されます。
ICUで利用可能なリソースの一覧は こちらです （学内ウェブサイト）。
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Notes(注意事項)
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Textbooks are available at ICU Bookstore in mid April. (expected price 7,593 yen) 教科書は大学書店で販売します。（４月中旬入荷予定、予価：7,593円）
My home page below contains useful information of this course. 下のホームページを参考にして下さい。
基本的には、１単元１週間で、１回授業、１回例などを共に考え、1回は解いた演習問題を発表し、最後にTake-Home の小テストという形式で進む予定です。課題が多く忙しく感じるかも知れませんが、授業を理解し、例を自分で考え、演習問題を解いていくことで、身について行きます。
Language of Instruction:
Most of the lectures may be given inEnglish and, textbook, blackboard writings, assignments, final will be in English. At recitations, homework and final, students are strongly recommended to write in English. However, students are allowed to ask questions in Japanese and the instructor may add extra explanation in Japanese.
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Schedule(スケジュール)
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2/M,(2/W,2/F)
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URL
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subsite.icu.ac.jp/people/hsuzuki/science/class/algebra1/index-j.html
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