Linear Algebra I & Math. Tutorial 1b - Fall 2023
Course information•Homepage for this course: https://www.henrikbachmann.com/la1_2023.html. Please check this page
regularly for updates on the schedule and/or to get information on the course and the Homework.

Preliminary schedule
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5
6
7
7
8
910
11
12
13
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Tutorial (1b)
3rd Oct (Tu)10th Oct (Tu)
17th Oct (Tu)24th Oct (Tu)
31th Oct (Tu)
7th Nov (Tu)
14th Nov (Tu)
21st Nov (Tu)28th Nov (Tu)
5th Dec (Tu)
12th Dec (Tu)
19th Dec (Tu)
16th Jan (Tu)
23rd Jan (Tu)
30th Jan (Tu)

Lecture6th Oct (Fr)13th Oct (Fr)20th Oct (Fr)27th Oct (Fr)- culture day 10th Nov (Fr)17th Nov (Fr)18th Nov (Sa)24th Nov (Fr)
1st Dec (Fr)
8th Dec (Fr)15th Dec (Fr)22nd Dec (Fr)10th Jan (We)19th Jan (Fr)26th Jan (Fr)
2nd Feb (Fr)

Preliminary lecture topic
Introduction & Linear systems
Matrices and vectors
Sets and functions
Linear maps
Linear maps
Linear maps in geometry
Midterm exam (in the lecture)
Matrix multiplication
The inverse of a linear map
Subspaces, Kernel & Image
Linear indepedence & Bases I
Bases II & Dimension
Coordinates, + Christmath challenge +Coordinates & Orthogonal bases
Orthogonal projection
ReviewFinal exam (in the lecture)

Section
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1-5
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9,10
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Times and venues• All lectures take place in the room C15 in the Liberal Arts and Sciences building, between 13:00
and 14:30. All tutorials take place in the room A407 in Science building A, between 13:00 and13:45. (From 13:45 there will be the Calculus tutorial in the same room)• Before the midterm and final exams, I offer question sessions in Zoom. We will decide together on
the day and time for this.

Contact
Henrik Bachmann, Office: Graduate School of Mathematics Building, Room: 457(http://en.nagoya-u.ac.jp/map/index.html, Building D3-4)
E-mail: henrik.bachmann@math.nagoya-u.ac.jp
Homepage: http://www.henrikbachmann.com
Please feel free to contact me at any time via email or come directly to my office. There are no ”stupid
questions,” and asking a lot of questions will not influence your grade in any way.

Textbook & Notes
Every student is encouraged to take his/her personal notes during the lecture and tutorial. We will provide lecture notes and update it after each lecture. There also exists a reference book: Otto Bretscher:Linear Algebra with Applications, 4th edition, Pearson 2009. (available at the Central and Science libraries). You will not need to get this book, but it contains a lot of practice Exercises.

Version: October 3, 2023

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Examination
The examination consists of a midterm exam and a final exam, together with homework.
• The midterm exam is held on the 17th of November, 2023, and the final exam is on the 2nd ofFebruary, 2024. Both will take place in the lecture room C15 during the usual lecture time.
• Homework : There will be a number of homework assignments during the course. Collaborationis encouraged, but solutions must be written and handed in individually. You can write down yoursolutions by hand (paper, tablet) or by computer (Latex only. No word!). Write your name, thehomework number and the course name on the first page of your solution. Create one pdf-file (forexample, by using a scanner app on your phone) and submit it before the deadline ends in TACTat the corresponding Assignment. Use exactly the following format as a filename:”Familyname Givenname LA1 HWX.pdf”,
where X stands for the number of the Homework. We will remove points if you do not follow these
simple rules.
• Repeat exam: There will be a repeat exam during the winter vacation for those who failed theordinary examination. This will take place somewhere in March 2023.

Grading
A total score T (0–100 %) is calculated as the weighted average of the percentages obtained from thehomework H (0–100 %), midterm exam M (0–100 %) and final exam F (0–100 %) as follows
T = αH H + αM M + αF F .
Here the weights αH , αM , αF can be determined from the following information:
A student who ..
1. .. got 70% in the Homework, 70% in the midterm, and 75% in the final, gets a total score of 72%.
2. .. got 80% in the Homework, 80% in the midterm, and 85% in the final, gets a total score of 82%.
3. .. got 100% in the Homework, 80% in the midterm, and 95% in the final, gets a total score of 92%.
What are the weights αH , αM , αF ?
The total score will be used to determine a grade A+, A, B, C, C-, or F. (The exact grading scheme will
be determined after the final exam). This grade will be the final grade for both ”Linear Algebra I” and”Math. Tutorial 1b”. If you plan to just take one of these courses, please contact me (This is possible.).

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