Linear Algebra I  & Tutorial 1b 
(G30 Program, Nagoya University, Fall 2021) 

• Please make sure that you are in the NUCT group for this course. If you can not enter this group please contact me.
• There exists a Facebook group for this course. If you want please join this group to get more information & updates on this course. Joining the Facebook group is not compulsory. 

​Materials​

• Overview notes (v. 3, 18th January 2022)
• Lecture notes:   Course overview, 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 14​
• Tutorial notes:  Tutorial 1, Tutorial 2, Tutorial 3, Tutorial 4, Tutorial 5, Tutorial 6, Tutorial 7, Tutorial 8, Tutorial 9, Tutorial 10, Tutorial 11, Tutorial 12, Tutorial 13, Tutorial 14
• Homework: HW1, HW2, HW3, HW4, HW5, HW6, HW7
• Midterm preparation: Midterm 2020 (Sol), Midterm 2019 (Sol), Question session notes
• Midterm (Sol)
• Final exam preparation: Final 2020 (Sol), Final 2019 (Sol), Tutorial 9 2019 (Sol), Question session notes (29th January)
• Final + Solution​

​The video recordings of the lectures & tutorials can be found in NUCT and the Facebook group. 

​Additional materials:

• Short videos: Image of a non-linear map (notes), When is a linear map surjective/injective (notes) ?
• Lecture notes (Fall 2020): 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
• Videos (Fall 2020): 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​
• Some Japanese Linear Algebra words​
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Grading & Homework submission:
The grade for Linear Algebra I and the Tutorial 1b will be based on Homework submissions (30%),  a Midterm (25%) and Final exam (45%). More detailed information will be explained at the beginning of the course. 

Course schedule: 
We will meet for the first Lecture on Monday 4th October 10:30 in Zoom where I will explain how the course will be done. The information for the Zoom meeting are available in the NUCT page (at Announcements) and in the Facebook group. 

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 (10/04-10/10): ​Introduction & Linear systems 
Week 02 (10/11-10/17): Matrices and vectors 
Week 03 (10/18-10/24): Sets and functions
Week 04 (10/25-10/31): Linear maps
Week 05 (11/01-11/07): Linear maps in geometry
Week 06 (11/08-11/14): Matrix multiplication 
Week 07 (11/15-11/21): Midterm Exam (15th November 2021, 10:30) 
Week 08 (11/22-11/28): The inverse of a linear map
Week 09 (11/29-12/05): Subspaces, Kernel & Image 
Week 10 (12/05-12/12): Linear indepedence & Bases I
Week 11 (12/12-12/19): Bases II & Dimension
Week 12 (12/20-12/26): Bases & Coordinates 
Winter Vacation (12/27-01/07) 🎅🎄☃️ (There will be no lecture on 27th December 🎅)
Week 13 (01/10-01/16): Coordinates & Orthogonal bases, The Gram-Schmidt algorithm I
Week 14 (01/17-01/23): Orthogonal projection, Least square approximation 
Week 15 (01/24-01/30): Review
Week 16 (01/31-02/06): Final Exam (31st January 2022, 10:30) 

Last update: 1st February 2022