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授業の目的 【英語】
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【Standardized across all programs】 "Linearity" is the most basic concept of quantitative treatment in modern science and is used in all fields. Linear algebra is a method of mathematically dealing with the linearity. The goal of this course is to familiarize yourself with the mathematical treatment of matrices and vectors and to understand various concepts as the first half of the year-round lecture. In particular, we emphasize geometric understanding by coordinate geometry (plane / solid), familiarity with solving simultaneous linear equations, and understanding of the concept of determinants.
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授業の達成目標 【英語】
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The first half of the course will deal with solving linear systems in a systematic way. We will view linear system from several different points of views and see how this will lead to a lot of powerful tools for real life applications.
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授業の内容や構成
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Linear systems, Gaussian elimination, matrices, vectors, linear maps, matrix multiplication, the inverse of a linear map, subspaces of Rn, image and kernel, linear independence, bases, dimension, coordinates, orthogonal bases, the Gram–Schmidt algorithm, QR factorization, orthogonal complement, orthogonal maps, least square approximations.
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履修条件・関連する科目
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No formal prerequisites. Some ability to manipulate systems of linear equations and understanding of elementary geometry will be useful for the understanding of the course material. It is strongly recommended to also follow the course Mathematics Tutorial I b. Highly motivated students can also attend the lecture “Mathematics for machine learning”, where some concepts of Linear Algebra 1 are applied.
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成績評価の方法と基準
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There will be two main, written exams: midterm and final. Additionally, there will be homework assignments and quizzes. The grading scale will be A+, A, B, C, C-, F. Students need to notify the course withdrawal to the instructor when they have no intention of finishing the course during the semester.
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教科書
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We will provide lecture notes for this course.
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参考書
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Otto Bretscher: Linear Algebra with Applications, fourth edition, Pearson 2009.
ISBN: 978-0-13-600926-9
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課外学修等
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Students are expected to review the previous lecture of Linear Algebra I before attending the next lecture.
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注意事項
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Everything you need to know will be on the regularly updated homepage below. Please check this homepage regularly for updates.
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本授業に関するWebページ
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担当教員からのメッセージ
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Please feel free to contact me in advance if you have any questions on the course. If you are wondering if you should take this course, then the answer is always yes!
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実務経験のある教員等による授業科目（大学等における修学の支援に関する法律施行規則に基づくもの）
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授業開講形態等
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A-1）Face-to-face course （Only face-to-face classes)
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