EE 2030 Linear Algebra

Spring 2025

Course Staff

Instructor:

Jay Cheng (鄭傑), Delta 811 (台達館 811), ext. 62207.

Lectures: W3W4F3F4, Delta 216 (台達館 216).

Office Hours: W2F2, after classes, or by appointment.

Teaching Assistants:

黃信翔 (whu910116hung1009@gmail.com)
李亞宸 (niki5060948@gmail.com)

EECS 805 (資電館805), ext. 34154

TAs' Office Hours: W9

Announcements

The following schedule is subject to change as the course progresses, and you should come back frequently for the most recent update.

Homework solutions and your grades are constantly updated at https://elearn.nthu.edu.tw/
It is your responsibility to keep us informed as soon as possible if there is any mistake regarding your grades.
We do not allow any change of the grades two weeks after they are posted.
W3W4F3F4
這門課授課時數為3小時，另有1小時為彈性運用時間。
本學期時間應用如下：W3W4F3F4授課時間為10:10~11:30 am，若授課進度落後則延長至12 pm。
Presentation
想要加簽的同學請不用另外寄信來詢問，直接從學校系統進行選課作業就可以，老師一定會同意。

2月19號上完第一堂課之後，決定要修這門課的同學可以跟助教登記影印上課筆記 (要付助教影印記費用)，
從2月26號開始一直到學期末同學們就要開始上台報告
(每次上課前先閱讀完上課筆記與課本內容，基本上每個星期至少會輪到一次)。

這門課適合肯努力想提升水平的同學，想輕鬆過關或者沒有足夠動機努力的同學建議千萬不要修。
同學們很喜歡問何謂努力認真，我覺得每個星期最起碼花20到30個小時在這門課應該就可以。
之前第一堂課大概有130多位同學，第三個星期之後剩下大概20位左右，學期末剩下大概10左右，
從這幾年的經驗來看學校裡每年應該只有10位左右的同學勉強可以修這門課。
Schedule (subject to minor changes)

2/26: pp. 0-1~0-6 (it will do you good to first read pp. 171~182 of the classnotes)
3/5: pp. 0-7~0-13
3/7: pp. 1-1~1-8
3/12: pp. 1-9~1-16
3/14: pp. 1-17-1~1-24
3/19: pp. 1-25-1~1-31 + HW#1
3/21: Exam #1

3/26: pp. 2-1~2-7
3/28: pp. 2-8~2-14
4/9: pp. 2-15~2-21
4/11: pp. 2-22~2-28
4/16: pp. 2-29~2-35
4/18: HW #2 + Exam #2

4/23: pp. 3-1~3-9
4/25: pp. 3-7~3-13
4/30: pp. 4-1~4-6
5/2: pp. 4-7~4-12 + HW #3
5/4 Exam #3

5/7: pp. 5-1~5-9
5/9: pp. 5-10~5-18
5/14: pp. 5-19~5-27
5/16: pp. 5-28~5-36
5/21: HW #4 + Exam #4

5/23: pp. 6-1~6-7
5/28: pp. 6-8~6-14
6/4: pp. 6-15~6-22
6/6; HW #5 + Exam #5.
HW #0 (due 2/26)
HW #0: Read Appendices A~C.
(i) Wiki: Mathematical logic; Set theory; Number systems; Constructions of the real number system.
Describe what you have known/learned from the Internet about these three subjects (there is no standard answer for this question).
(ii) What is your opinion on the following paradoxes.
Russel's paradox (logic paradox): Let A={x: x does not belong to x}. Does A belong to A?
Berry's paradox (semantic paradox): Let A be the set of all the natural numbers that can be described in fewer than twenty words of the English language.
Then A contains only a finite number of natural numbers (why?) and hence there is a "least natural number that cannot be described in fewer than twenty words
of the English language" (but we have just described this least natural number in sixteen words of the English language).
HW #1 (due 3/19)
HW #1: Exercises 1.1.7, 1.2.17, 1.3.12, 1.3.29, 1.4.3(a)(c), 1.5.8, 1.5.20, 1.6.7, 1.6.23, 1.7.3
Exam #1 (held on 3/21: 10:10 am~12 pm)
Exam #1: Chapter 1. (Before the exam starts, you will have 5 minutes to write down your personal note on the first page of the exam booklet.)
HW #2 (due 4/18)
HW #2: Exercises 2.1.5, 2.1.18, 2.1.25 (this is 2.1.26 in 5e), 2.2.3, 2.3.3, 2.3.22 (this is 2.3.23 in 5e), 2.4.19, 2.4.22, 2.5.6(c), 2.6.3, 2.6.7, 2.7.3(a)(c),
Exam #2 (held on 4/18)
Exam #2: Chapter 2.
HW #3 (due 5/2)
HW #3: Exercises 3.1.9, 3.2.6(f), 3.2.19, 3.2.20, 3.3.8, 3.3.12, 3.3.14, 3.4.4(b), 3.4.9, 3.4.10, 4.3.6, 4.3.22, 4.3.28,
Exam #3 (held on 5/2)
Exam #3: Chapters 3~4. (Before the exam starts, you will have 5 minutes to write down your personal note on the first page of the exam booklet.)
HW #4 (due 5/21)
HW #4: Exercises 5.1.4(g) (this is 5.1.5(g) in 5e), 5.1.10 (this 5.1.11 in 5e), 5.1.11 (this is 5.1.12 in 5e), 5.1.18 (this is 5.1.19 in 5e), 5.1.23,
5.2.3(f), 5.2.14(a) (this is 5.2.15(a) in 5e), 5.3.2(h), 5.3.10(b), 5.3.11, 5.4.2, 5.4.6(b)
Exam #4 (held on 5/21)
Exam #4: Chapter 5. (Before the exam starts, you will have 5 minutes to write down your personal note on the first page of the exam booklet.)
HW #5 (due 6/6)
HW #5: Exercises 6.1.5, 6.1.8, 6.1.24(b)(c) (this is 6.1.26(b)(c) in 5e), 6.2.2(i)(l), 6.2.19, 6.2.20,
6.3.2(b), 6.3.3(b), 6.3.20(c), 6.3.22(c), 6.4.2(b)(d), 6.5.2(e), 6.5.27(b)
Exam #5 (held on 6/6)
Exam #5: Sections 6.1~6.5. (Before the exam starts, you will have 5 minutes to write down your personal note on the first page of the exam booklet.)

Textbook

S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra, 4th ed., Prentice Hall, 2003. (Website for the 5th edition: http:/goo.gl/y1jz4Y/)

References

1. G. Strang, Introduction to Linear Algebra, 3rd ed., Wellesley Cambridge, 2016.

2. S. J. Leon, Linear Algebra with Applications, 10th ed., Prentice Hall, 2021.

Course Descriptions

This is an introductory course to linear algebra and is the key to the success of many subjects that you will encounter in the future.

Syllabus

1. Vector Spaces

2. Linear Transformations and Matrices

3. Elementary Matrix Operations and Systems of Linear Equations

4. Determinants

5. Diagonalization

6. Inner Product Spaces

7. Canonical Forms

Homework

Homework assignments will be due at the start of classes one week after they are announced (unless otherwise specified) and no late submissions will be accepted.
If you are using brand new paper for your homework reports, please write down your answers on both sides of the paper so that we won't waste too much of our natural resources (we reserve the right not to grade such homework reports).

You may discuss the homework problems with your classmates, but should write down every piece of the homework yourself instead of copying others' works.
You should note on each submission the names of everyone you have worked with regardless of whether you have given help, received help, or both
(failing to do so will lead to a failing grade for this course).