1991 件ヒット (0.029秒)：
「代数学概論B」の講義に対応する演習の授業です。自力で証明をおこなったり具体例を計算したりする経験を通じて、講義内容を深く理解することを目的としています。
This is the exercise session for the corresponding lecture. Via writing down proofs and handling concrete examples by themselves, students are supposed to develop a deeper understanding of the material.
「代数学序論B」の講義に対応する演習の授業です。自力で証明をおこなったり具体例を計算したりする経験を通じて、講義内容を深く理解することを目的としています。
This is the exercise session for the corresponding lecture. By writing down proofs and handling concrete examples by themselves, students are supposed to develop a deeper understanding of the material.
Google Classroomのクラスコードは工学部Webページにて確認すること。
学部シラバス・時間割(https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html)
計算機を活用して数学の問題を解く方法を学ぶ．そのためのソフトェアとしてMATLAB・Octaveを用いて行うが，その使い方よりも，数学的な技術を身に付けることに重きを置く．
最初にOctave（あるいはMATLAB）の基本的な使い方と簡単なプログラム作成方法を学んだ後，様々な問題を対象に，簡単なプログラミングによって数理的問題を解決する方法を学ぶ．講義時間は前半を問題およびその解法の説明に費やし，残り時間で，各自でレポート課題に取り組んでもらう．微積分，微分方程式，線形代数などの既習の数学だけでなく，数値計算，信号処理，数理統計や機械学習など未習の数学も対象とする．
本演習の目標は，Octave（あるいはMATLAB）を用いて，各演習で扱った各問題を解く能力を習得し，さらに，新しい問題に対してもどのように計算機を活用し得るかの心構えを得ることにある．
Google Classroom class code: dgm3ih7
The class code for Google Classroom can be found on the Web site of
the School of Engineering:
https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html (JP Only)
Students will learn how a computer can be used to solve mathematical problems. Although the course will use MATLAB or Octave for this purpose, its focus is more on mastering mathematical skills rather than learning how to use it.
Starting with the basic usage of Octave (or MATLAB) and how to write a program on it, students will learn how they can solve various mathematical problems by writing and executing simple programs. The first half of each class day will be spent for explaining problems and their solutions. Students will try to solve exercise problems the rest of the time. The course will cover not only mathematics that students have already learned, such as calculus, differential equation, linear algebra, etc., but also those that they have not learned, such as numerical computation, signal processing, statistics, machine learning, etc.
The goal of this course is to have students master skills of solving the specific problems considered in this course using Octave (or MATLAB) and futher obtain a concept of how they can utilize a computer to deal with novel problems.
Google Classroomのクラスコードは工学部Webページにて確認すること。
学部シラバス・時間割(https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html)
計算機を活用して数学の問題を解く方法を学ぶ．そのためのソフトェアとしてMATLAB・Octaveを用いて行うが，その使い方よりも，数学的な技術を身に付けることに重きを置く．
最初にOctave（あるいはMATLAB）の基本的な使い方と簡単なプログラム作成方法を学んだ後，様々な問題を対象に，簡単なプログラミングによって数理的問題を解決する方法を学ぶ．講義時間は前半を問題およびその解法の説明に費やし，残り時間で，各自でレポート課題に取り組んでもらう．微積分，微分方程式，線形代数などの既習の数学だけでなく，数値計算，信号処理，数理統計や機械学習など未習の数学も対象とする．
本演習の目標は，Octave（あるいはMATLAB）を用いて，各演習で扱った各問題を解く能力を習得し，さらに，新しい問題に対してもどのように計算機を活用し得るかの心構えを得ることにある．
Google Classroom class code: kmuaau7
The class code for Google Classroom can be found on the Web site of
the School of Engineering:
https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html (JP Only)
Students will learn how a computer can be used to solve mathematical problems. Although the course will use MATLAB or Octave for this purpose, its focus is more on mastering mathematical skills rather than learning how to use it.
Starting with the basic usage of Octave (or MATLAB) and how to write a program on it, students will learn how they can solve various mathematical problems by writing and executing simple programs. The first half of each class day will be spent for explaining problems and their solutions. Students will try to solve exercise problems the rest of the time. The course will cover not only mathematics that students have already learned, such as calculus, differential equation, linear algebra, etc., but also those that they have not learned, such as numerical computation, signal processing, statistics, machine learning, etc.
The goal of this course is to have students master skills of solving the specific problems considered in this course using Octave (or MATLAB) and futher obtain a concept of how they can utilize a computer to deal with novel problems.
整数論は数学において最も古い分野の一つであり、現在に至るまで盛んに研究されている。特に、19世紀から20世紀前半にかけて，代数体の整数論は大きく発展しその基礎が完成した。さらに、20世紀になると有限体上の幾何学と代数体の整数論の類似が注目され、重要なイアデアをもたらしました。それらを基本として現在の整数論は展開されている。本講義は、代数体や関数体（有限体上の代数曲線の関数体のこと）の整数論について、その基本的事項を学ぶことを目的としている。具体的には、素イデアル分解、イデアル類群、単数群、有理点、合同ゼータ関数などを話題にする。
Number theory is one of the oldest subjects in mathematics, and it has been studied very much until now. Especially, during the 19th century and the first half of 20th century, the foundation of number theory had been completed. Moreover, in the 20th century the analogies between number theory of algebraic number fields and geometry of algebraic curves over finite fields were attracted, and it brought a lot of important ideas. The modern number theory is studied under the development. The purpose of this course is to learn the foundation of number theory in algebraic number fields and function fields (function fields of algebraic curves over finite fields) . For examples, prime ideal factorization, ideal class groups, unit groups, rational points, zeta functions, and so on.
Google Classroomのクラスコードは工学部Webページにて確認すること。
学部シラバス・時間割(https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html)
計算機を活用して数学の問題を解く方法を学ぶ．そのためのソフトェアとしてMATLAB・Octaveを用いて行うが，その使い方よりも，数学的な技術を身に付けることに重きを置く．
最初にOctave（あるいはMATLAB）の基本的な使い方と簡単なプログラム作成方法を学んだ後，様々な問題を対象に，簡単なプログラミングによって数理的問題を解決する方法を学ぶ．講義時間は前半を問題およびその解法の説明に費やし，残り時間で，各自でレポート課題に取り組んでもらう．微積分，微分方程式，線形代数などの既習の数学だけでなく，数値計算，信号処理，数理統計や機械学習など未習の数学も対象とする．
本演習の目標は，Octave（あるいはMATLAB）を用いて，各演習で扱った各問題を解く能力を習得し，さらに，新しい問題に対してもどのように計算機を活用し得るかの心構えを得ることにある．
Google Classroom class code: aaicjmk
The class code for Google Classroom can be found on the Web site of
the School of Engineering:
https://www.eng.tohoku.ac.jp/edu/syllabus-ug.html (JP Only)
Students will learn how a computer can be used to solve mathematical problems. Although the course will use MATLAB or Octave for this purpose, its focus is more on mastering mathematical skills rather than learning how to use it.
Starting with the basic usage of Octave (or MATLAB) and how to write a program on it, students will learn how they can solve various mathematical problems by writing and executing simple programs. The first half of each class day will be spent for explaining problems and their solutions. Students will try to solve exercise problems the rest of the time. The course will cover not only mathematics that students have already learned, such as calculus, differential equation, linear algebra, etc., but also those that they have not learned, such as numerical computation, signal processing, statistics, machine learning, etc.
The goal of this course is to have students master skills of solving the specific problems considered in this course using Octave (or MATLAB) and futher obtain a concept of how they can utilize a computer to deal with novel problems.
本授業ではルベーグ積分論(解析学概論B1)の演習を行う。
ルベーグ積分論の理解を深化させるために、基本的な演習問題を解く。
さらに、重要な定理の具体的な適用例を学ぶ。
This course deals with exercises in Lebesgue Integration Theory (Analysis B1).
The students will solve basic exercises to understand the Lebesgue integration theory deeply.
Moreover, the students will study various applications of important theorems.
線形代数学AおよびBでは、行列の基本的な演算や行列式から概ね行列の対角化まで、主として数ベクトルのなす空間の基底や次元などの基本的事項とともに学んだ。この代数学序論Bでは、これらに引き続いて、一般のベクトル空間と線型写像について学ぶ。
特に、ジョルダン標準形と呼ばれる、対角化が必ずしもできない場合の標準形が一つの目標となるが、そのためにもベクトル空間の直和、商空間、テンソル積といわれるベクトル空間の間に定義される演算や、群・環・体という代数学における基本概念についても、体系的に述べるための言葉として慣れることがもう1つの目標となる。
In linear algebra A and B, we treat basics in matrix algebras such as determinants or diagonalization, together with basic notion for vector spaces such as basis or dimension. Following these knowledge we will treat general vector spaces as well as linear maps.
In particular we will learn so called Jordan canonical form for a linear transform in case of diagonalization is not possible, which will be one of the goal of the course. To describe things systematically we will need operations for vector spaces, namely direct sums, quotients and tensor products, together with basic notion in algebra such as groups, rings and fields. To become familiar with these will be another goal of the course.