The rapid progress of computers has made it possible to analyze various social and natural phenomena using mathematical methods, and the importance of these methods is increasing.
This course is designed to provide liberal arts students with basic knowledge of linear algebra as a basis for learning such mathematical methods.
The Linear Algebra B [For non-science majors] is the consecutive course of Linear Algebra A [For non-science majors]. Linear Algebra B [For non-science majors] offers, the students the concepts and techniques that play a central role in linear algebra, based on the basic content of vectors and matrices learned in Linear Algebra A [For non-science majors].

In Linear Algebra B [For non-science majors], students will understand essential ideas and techniques that play a central role in linear algebra, such as determinants, the basis of vector space, inner product, eigenvalues and eigenvectors, and diagonalization of matrices and become proficient in more advanced treatment of vectors and matrices.

The following subjects will be covered.
The number of lessons is 15, including feedback.
The order of the subjects is not fixed; the lecturer will decide according to the lecturer's lecture policy and the student's background and understanding of the subject. Real vectors and matrices will be covered mainly.

1. Determinants (Definition and characteristics of determinant (elementary transformation, product, relation with transpose, substitution, and sign), expansion of determinant, Cramer's rule) [4〜5 weeks]
2. Numerical vector space (linear independence, subspaces, basis and dimension, inner product, orthonormal basis, *direct sum, *orthogonal complementary space, *orthogonal matrix, *QR decomposition) [4-5 weeks]
3. Eigenvalues, eigenvectors, and diagonalization (eigenvalues and eigenvectors, matrix diagonalization, *matrix upper triangulation, *Cayley-Hamilton theorem, *diagonalization of a symmetric matrix by an orthogonal matrix, *positive definiteness of symmetric matrix, *square root of a positive symmetric matrix) [4-5 weeks]
4. Feedback [1 week].

Items marked with an asterisk (*) will be covered if time permits.
In addition to lectures on the above topics, there will be exercises (in-class exercises or homework) related to the topics.

Students are assumed to have a good understanding of high school mathematics except calculus.

Students will be evaluated primarily on their performance in the final examination. The student's performance in exercises and homework may also be taken into account. The details of the evaluation system will be explained by the lecturer in the first lecture.

In order to learn mathematics, it is necessary to try to solve the exercises on your own, in addition to preparing and reviewing the lectures.

Probability theory is indispensable for understanding and describing phenomena influenced by randomness, as arise across the natural and social sciences. Furthermore, it is one of the foundations of mathematical statistics. This lecture course will provide a fundamental introduction to the modern theory of probability.

1.To understand fundamental notions in probability theory such as events, random variables, independence, conditional probability, expectation, variance and correlation.
2. To understand when and how typical distributions, such as the normal distribution and Poisson distribution, appear, and mathematical treatments of those distributions.
3. To understand limit theorems, such as law of large numbers and central limit theorem. In particular, to understand when and how those theorems can be applied.

1. Introduction to the mathematical theory of probability (2 to 3 weeks): probability spaces, events, independence and conditional probability.
2. Introduction to the notion of random variables and related properties (4 weeks): random variable, distribution, expectation, variance, covariance, correlation, independence of random variables and Chebyshev's inequality
3. Important examples of distributions (3 weeks); Bernoulli distribution, binomial distribution, Poisson distribution, geometric distribution, uniform distribution, normal distribution, exponential distribution.
4. Limit theorems (3 to 4 weeks): law of large numbers, central limit theorem.
5. Random walks and Markov chains (supplementary).

A total of 14 lectures and one feedback class will be given.

(Eligible students) mainly the sciences of the second grade. Students are required good understanding of both calculus and linear algebra.

The evaluation of the course will mainly take into account of the result of final examination, but will also include homework and presentation elements.
The details of the evaluation system will be given by the lecturer at the first lecture.

Strongly recommend to solve exercises given in class to have a deeper understanding of contents of lectures.

Office hours are by appointment.

「微分積分学（講義・演義）A, B」および「線形代数学（講義・演義）A, B」，または「微分積分学A, B」および「線形代数学A, B」を前提として，様々な自然科学の学習において基礎知識として必要となる，常微分方程式の数学的基礎について講義をする．主に，定数係数線形常微分方程式をはじめとする初等的に解くことのできる微分方程式についての解法，一般の線形微分方程式の解空間構造などの基本的性質，常微分方程式の数学的理論の基盤となる解の存在と一意性とそれに関連する事項について講ずる.

・定数係数線形常微分方程式をはじめとする初等的に解くことのできる微分方程式についての代表的な解法を修得する
・一般の線形常微分方程式の解空間の構造などの基本的性質について理解する
・常微分方程式の数学的理論の基盤となる解の存在と一意性とそれに関連する事項を理解する

以下の各項目について講述する．各項目には，受講者の理解の程度を確認しながら，【 】で指示した週数を充てる．各項目・小項目の講義の順序は固定したものではなく，担当者の講義方針と受講者の背景や理解の状況に応じて，講義担当者が適切に決める．講義の進め方については適宜，指示をして，受講者が予習をできるように十分に配慮する．
以下の内容を，フィードバック回を含め（試験週を除く）全15回にて行う．

１．導入【１週】
微分方程式とは何か，物理現象などに現れる微分方程式の具体例
２．初等解法【３週】
変数分離，一階線形微分方程式，定数変化法，全微分形，積分因子，級数解法の例
３．線形微分方程式【６〜７週】
線形微分方程式（変数係数を含む）の解の空間，基本解と基本行列，ロンスキー行列，定数変化法，線形微分方程式の解法，行列の指数関数とその計算（射影行列を含む），2次元定数係数線形微分方程式の相平面図
４．常微分方程式の基本定理【３〜４週】
連続関数全体の空間とその性質（ノルム空間，完備性），逐次近似法，常微分方程式の解の存在と一意性（コーシー・リプシッツの定理），初期値に対する連続性，解の延長

特になし

主として定期試験による（詳しくは担当教員毎に授業中に指示する）．

予習・復習とともに，演習問題を積極的に解いてみることが必要である．