2020 Advanced Linear Algebra I

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Academic unit or major
Undergraduate major in Mathematics
Mizumoto Shin-Ichiro 
Class Format
Lecture    (ZOOM)
Media-enhanced courses
Day/Period(Room No.)
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Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

This course covers the concept and examples of vector space in linear algebra. Exercise problems will be presented within the lectures to cement understanding. This course is followed by "Advanced Linear Algebra II".

Prior experience with linear algebra using specific matrices is assumed, and this course discusses in detail the basics of vector space and linear mapping. These activities are important, also serving as practical exercises for students to acquire basic methods in learning other fields of advanced mathematics.

Student learning outcomes

The important notions are as follows:
vector space, linear span, linear map, isomorphism.


linear space, linear map, linear span, isomorphism

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Standard lecture course accompanied by discussion sessions

Course schedule/Required learning

  Course schedule Required learning
Class 1 vector space Details will be provided during class session
Class 2 linearly independency Details will be provided during class session
Class 3 subspace Details will be provided during class session
Class 4 linear span Details will be provided during class session
Class 5 basis Details will be provided during class session
Class 6 properties of dimension Details will be provided during class session
Class 7 sum and direct sum of linear spaces, linear map Details will be provided during class session

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


None required

Reference books, course materials, etc.

Saito, Masahiko: Introduction to Linear Algebra, University of Tokyo Press

Assessment criteria and methods

To be evaluated based on exercises in discussion sessions and the final exam as a whole. Details will be announced during the course.

Related courses

  • LAS.M102 : Linear Algebra I / Recitation
  • LAS.M106 : Linear Algebra II
  • MTH.A212 : Advanced Linear Algebra II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are expected to have passed Linear Algebra I / Recitation and Linear Algebra II.

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