**Linear Algebra I & Tutorial 1b **

(G30 Program, Nagoya University, Fall 2020)

This course will be done online. It will be a mix of Zoom lectures and recorded videos.

The grade for Linear Algebra I and the Tutorial 1b will be based on Homework submissions (25%), small Quizzes (10%) and a Midterm (25%) and Final exam (40%). More detailed information are contained in the Course information.

(You can hand in your homework by creating a pdf of out handwritten notes. If some of you want to try to create a computer created version in LaTeX, you can use the following Homework solution template. I use TexStudio as a Latex Editor and can recommend it. Please contact me if you have any questions.)

We will meet for the

For the

The following gives a tentative overview of the topics we will cover each week.

Week 01 (10/05-10/11):

Week 02 (10/12-10/18): Matrices and vectors (Video: Lecture 2, Notes: Lecture 2, HW: HW2)

Week 03 (10/19-10/25): Sets and maps (Video: Lecture 3, Notes: Lecture 3, HW: stay healthy)

Week 04 (10/26-11/01): Linear maps (Video: Lecture 4, Notes: Lecture 4, HW: HW3)

Week 05 (11/02-11/08): Linear maps in geometry

Week 06 (11/09-11/15): Matrix multiplication

Week 07 (11/16-11/22):

Week 08 (11/23-11/29): The inverse of a linear map

Week 09 (11/30-12/06): Subspaces of R^n

Week 10 (12/07-12/13): The image and kernel of a linear map

Week 11 (12/14-12/20): Bases and linear independence

Week 12 (12/21-12/27): Dimension and Christmas

Week 13 (01/11-01/17): Coordinates

Week 14 (01/18-01/24): Orthogonal bases, The Gram-Schmidt algorithm

Week 15 (01/25-01/31): Least square approximation

Week 16 (02/01-02/07):

Last update: 24th October 2020

- Please make sure that you register for "Linear Algebra 1" and "Mathematics Tutorial 1b" in the NU Portal.
- Please feel free to join the
**Facebook group**of this course. (You do not need to join ANY NUCT course page for this course if you are in the Facebook group). - Here is the
**NUCT course page**for this course. (You do not need to join any NUCT course for the Tutorial 1b) - If you are in Nagoya and want to ask questions face-to-face, please always feel free to contact me! We can meet in my office for office hours. For this you can also come in small groups of students.

**Materials**- Course information
- Overview notes (version 4)
- Lecture notes: Lecture 1, Lecture 2, Lecture 3, Lecture 4
- Lecture videos: Lecture 1, Lecture 2 , Lecture 3, Lecture 4
- Homework: HW1 (Sol), HW2 (Deadline: 25th October), HW3 (Deadline: 8th November)
- Tutorial: Tutorial 1, Tutorial 2, Tutorial 3
- Quiz: Quiz 1 (Sol: Tutorial 3)
- Some Japanese Linear Algebra words

**Grading & Homework submission****:**The grade for Linear Algebra I and the Tutorial 1b will be based on Homework submissions (25%), small Quizzes (10%) and a Midterm (25%) and Final exam (40%). More detailed information are contained in the Course information.

(You can hand in your homework by creating a pdf of out handwritten notes. If some of you want to try to create a computer created version in LaTeX, you can use the following Homework solution template. I use TexStudio as a Latex Editor and can recommend it. Please contact me if you have any questions.)

**Course schedule:**We will meet for the

**first Lecture**on**Monday 5th October 10:30 in Zoom**where I will explain how the course will be done. The information for the Zoom meeting will be available in the NUCT page and in the Facebook group. After the first week, the Lectures will usually be recorded and uploaded to YouTube. But if there is demand, I will also offer questions sessions in Zoom during the Lecture time (Monday, 10:30).For the

**Tutorial****1b**we will meet**each Tuesday at 14:45～15:30****in Zoom**(From 15:30 there will be the Tutorial 1a for Calculus 1). The detailed information will be available on the NUCT page or in the Facebook group.The following gives a tentative overview of the topics we will cover each week.

Week 01 (10/05-10/11):

****Linear systems (Video: Lecture 1, Notes: Lecture 1, HW: HW1)Week 02 (10/12-10/18): Matrices and vectors (Video: Lecture 2, Notes: Lecture 2, HW: HW2)

Week 03 (10/19-10/25): Sets and maps (Video: Lecture 3, Notes: Lecture 3, HW: stay healthy)

Week 04 (10/26-11/01): Linear maps (Video: Lecture 4, Notes: Lecture 4, HW: HW3)

Week 05 (11/02-11/08): Linear maps in geometry

Week 06 (11/09-11/15): Matrix multiplication

Week 07 (11/16-11/22):

**Midterm Exam (16th November, 10:30)**Week 08 (11/23-11/29): The inverse of a linear map

Week 09 (11/30-12/06): Subspaces of R^n

Week 10 (12/07-12/13): The image and kernel of a linear map

Week 11 (12/14-12/20): Bases and linear independence

Week 12 (12/21-12/27): Dimension and Christmas

**Winter Vacation (12/27-01/07)**🎅🎄☃️Week 13 (01/11-01/17): Coordinates

Week 14 (01/18-01/24): Orthogonal bases, The Gram-Schmidt algorithm

Week 15 (01/25-01/31): Least square approximation

Week 16 (02/01-02/07):

**Final Exam (1st February, 10:30)**Last update: 24th October 2020