**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 (Video: Lecture 5, Notes: Lecture 5, HW: HW4)

Week 06 (11/09-11/15): Matrix multiplication (Video: Lecture 6, Notes: Lecture 6, HW: Prepare for & relax from Midterm exam)

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

Week 08 (11/23-11/29): The inverse of a linear map (Video: Lecture 7, Notes: Lecture 7,HW: HW5)

Week 09 (11/30-12/06): Subspaces, Kernel & Image (Video: Lecture 8, Notes: Lecture 8, HW: 😴)

Week 10 (12/07-12/13): Linear indepedence (Video: Lecture 9, Notes: Lecture 9, HW: HW6)

Week 11 (12/14-12/20): Linear indepedence & Bases (Video: Lecture 10, Notes: Lecture 10, HW: HW7)

Week 12 (12/21-12/27): Dimensions and Christmas (Christmath challenge in the Tutorial on 22nd December!) HW: Build a snowman

Week 13 (01/11-01/17): Coordinates (Video: Lecture 11, Notes: Lecture 11, HW: HW8)

Week 14 (01/18-01/24): Orthogonal bases, The Gram-Schmidt algorithm (Video: Lecture 12, Notes: Lecture 12, HW: Start thinking about Final Exam & HW8)

Week 15 (01/25-01/31): Least square approximation (Video: Lecture 13, Notes: Lecture 13,HW: Learn for the Final Exam)

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

Last update: 1st February 2021

- 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 14)
- Lecture notes: Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9, Lecture 10, Lecture 11, Lecture 12, Lecture 13
- Lecture videos: Lecture 1, Lecture 2 , Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9, Lecture 10, Lecture 11, Lecture 12, Lecture 13
- Homework: HW1, HW2, HW3, HW4, HW5, HW6, HW7, HW8
- Tutorial: Tutorial 1, Tutorial 2, Tutorial 3, Tutorial 4, Tutorial 5, Tutorial 5 Extra, Tutorial 6, Tutorial 7, Tutorial 8, Tutorial 9, Tutorial 10, Tutorial 11, Tutorial 13, Tutorial 14, Tutorial 15
- Quiz: Quiz 1 (Sol: Tutorial 3), Quiz 2 (Sol: Tutorial 5), Quiz 3 (Sol: Tutorial 9), Quiz 4 (Sol: Tutorial 14)
- Midterm preparation: Midterm 2019 (Sol), Tutorial 6 2019 (Sol), Lunch session 12th November, Question session 14th November
- Final exam preparation: Final exam 2019 (Sol), Tutorial 9 2019 (Sol), Prep. session I (25. Jan) , Prep. session II (30th Jan.)
- Exam:
- 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) or at Lunch time on Thursday.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 (Video: Lecture 5, Notes: Lecture 5, HW: HW4)

Week 06 (11/09-11/15): Matrix multiplication (Video: Lecture 6, Notes: Lecture 6, HW: Prepare for & relax from Midterm exam)

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

**Midterm Exam (16th November, 10:30)**Week 08 (11/23-11/29): The inverse of a linear map (Video: Lecture 7, Notes: Lecture 7,HW: HW5)

Week 09 (11/30-12/06): Subspaces, Kernel & Image (Video: Lecture 8, Notes: Lecture 8, HW: 😴)

Week 10 (12/07-12/13): Linear indepedence (Video: Lecture 9, Notes: Lecture 9, HW: HW6)

Week 11 (12/14-12/20): Linear indepedence & Bases (Video: Lecture 10, Notes: Lecture 10, HW: HW7)

Week 12 (12/21-12/27): Dimensions and Christmas (Christmath challenge in the Tutorial on 22nd December!) HW: Build a snowman

**Winter Vacation (12/27-01/07)**🎅🎄☃️Week 13 (01/11-01/17): Coordinates (Video: Lecture 11, Notes: Lecture 11, HW: HW8)

Week 14 (01/18-01/24): Orthogonal bases, The Gram-Schmidt algorithm (Video: Lecture 12, Notes: Lecture 12, HW: Start thinking about Final Exam & HW8)

Week 15 (01/25-01/31): Least square approximation (Video: Lecture 13, Notes: Lecture 13,HW: Learn for the Final Exam)

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

**Final Exam (1st February, 10:30)**Last update: 1st February 2021