Linear Algebra I & Math. Tutorial 1b
G30 Program, Nagoya University, Fall 2025
Materials
Grading:
The grading will be based on Homework/Quizzes (30%), Midterm exam (30%) and Final exam (40%).
Course schedule:
Lecture:
Course Overview:
The following gives an overview of the topics we will cover each week.
Week 01 (09/29-10/05): Introduction & Linear systems
Week 02 (10/06-10/18): Matrices and vectors
Week 03 (10/13-10/19): Sets and functions
Week 04 (10/20-10/26): Linear maps
Week 05 (10/27-11/02): Linear maps in geometry
Week 06 (11/03-11/09): Matrix multiplication
Week 07 (11/10-11/16): The inverse of a linear map
Week 08 (11/17-11/23): Midterm Exam (21st November 2025, 13:00)
Week 09 (11/24-11/30): Subspaces, Kernel & Image
Week 10 (12/01-12/07): Subspaces, Kernel & Image II, Linear independence I
Week 11 (12/08-12/14): Linear independence II & Bases I
Week 12 (12/15-12/21): Bases II & Dimension, 🎄 19th December: Christmath challenge 2025 in the lecture 🎄
Week 13 (12/22-12/29): 🎅 Tutorial on 23rd but no lecture on Friday 26th 🎅
☃️ Winter Vacation (12/28-01/07) ☃️
Week 14 (01/05-01/11): Coordinates
Week 15 (01/12-01/18): Orthonormal bases & The Gram-Schmidt algorithm
Week 16 (01/19-01/25): Orthogonal projection, Least square approximation
Week 17 (01/26-02/06): Final Exam (30th January 2026, 13:00)
Last update: 7th November 2025
- Lecture notes (V22, 3rd October 2025)
- Course information
- Handwritten lecture notes: Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6
- Tutorial notes: Tutorial 1 (Solution), Tutorial 2, Tutorial 3, Tutorial 4 (Solution), Tutorial 5 (Solution)
- Quizzes: Quiz 1, Quiz 2
- Homework: Homework 1, Homework 2, Homework 3
- Short videos: Image of a non-linear map (notes), When is a linear map surjective/injective (notes)
- 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
- Latex Homework Template (use this if you want to submit homework done in latex)
- Some Japanese Linear Algebra words
Grading:
The grading will be based on Homework/Quizzes (30%), Midterm exam (30%) and Final exam (40%).
Course schedule:
Lecture:
- Time: Friday 3rd period (13:00 - 14:30).
- Place: C13 (Liberal Arts and Sciences Main Building)
- Time: Tuesday first half of 3rd period (13:00 -13:45). First meeting: 7th October
From 13:45 - 14:30, there will be Tutorial 1a (Calculus I). - Room: A407 (Science Building A)
Course Overview:
The following gives an overview of the topics we will cover each week.
Week 01 (09/29-10/05): Introduction & Linear systems
Week 02 (10/06-10/18): Matrices and vectors
Week 03 (10/13-10/19): Sets and functions
Week 04 (10/20-10/26): Linear maps
Week 05 (10/27-11/02): Linear maps in geometry
Week 06 (11/03-11/09): Matrix multiplication
Week 07 (11/10-11/16): The inverse of a linear map
Week 08 (11/17-11/23): Midterm Exam (21st November 2025, 13:00)
Week 09 (11/24-11/30): Subspaces, Kernel & Image
Week 10 (12/01-12/07): Subspaces, Kernel & Image II, Linear independence I
Week 11 (12/08-12/14): Linear independence II & Bases I
Week 12 (12/15-12/21): Bases II & Dimension, 🎄 19th December: Christmath challenge 2025 in the lecture 🎄
Week 13 (12/22-12/29): 🎅 Tutorial on 23rd but no lecture on Friday 26th 🎅
☃️ Winter Vacation (12/28-01/07) ☃️
Week 14 (01/05-01/11): Coordinates
Week 15 (01/12-01/18): Orthonormal bases & The Gram-Schmidt algorithm
Week 16 (01/19-01/25): Orthogonal projection, Least square approximation
Week 17 (01/26-02/06): Final Exam (30th January 2026, 13:00)
Last update: 7th November 2025