Linear algebra (Spring 2008)


Time: M,W,F 13:00-14:00


Exams: Wednesday 13:00-15:00 (2 hours)

Lecture assistant:
(1) Jaesoon Ha: Building E6-1 No. 4423
hjs83 at kaist dot ac dot kr Phone: 2772
(2) Dhrubajit Choudhury: Building E6-1 No. 4423
druba.choudhury at kaist do ac do kr Phone 2772



Grade distributions: A:30%, B:40%, C or below 30%. (I will include the people who drop the course.)

Lecturer: Suhyoung Choi at Room E6-4403

schoi at math dot kaist dot ac dot kr

This course begins abstract mathematics and is a good introduction to all the methods of
modern abstract mathematics. This course is your finest initiation into abstract thinking which you won’t find
in any other course in the universities today. So take this opportunity to develop this mode of
thinking. I wrote and linked some help at  http://math.kaist.ac.kr/~schoi/teaching.html


This course concentrates on justifying the linear algebra theorems and procedures with
proofs, definitions and so on. You will learn to prove some theorems here.
(A part of the purpose of this course is to introduce you to proving theorems, lemmas,
and corollaries.)

You are expected to have prepared for the lecture by reading ahead and solving
some of the problems.

Course Book:  Linear algebra 2nd Edition by Hoffman and Kunz Prentice Hall

 

Helpful references:

Paul R. Halmos, Finite dimensional vector spaces, UTM, Springer (mostly theoretical)
B. Hartley, Rings, Modules, and Linear Algebra, Chapman and Hall
Larry Smith, Linear Algebra, 2nd Edition, Springer (Similar to our book, But fields are either the real field or
the complex field.)
Seldon, Axler, Linear algebra done right, Springer (Similar, Same field restriction as above)
S. Friedberg et al., Linear algebra 4th Edition, Prentice Hall (Most similar to our book. More
concrete. weak in theoretical side.)
Gilbert Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press, MA, USA
Two Korean books of almost the same content as Hoffman-Kunz:
선형대수학, 3 김응태,박승안공저, 청문각 2000
선형대수학,개정3,임근빈,임동만공저, 형실출판사2006

 

Grades: Midterm(150pts) Final(150pts) Quiz (100pts) Class participation (50pts)
Total 450pts

Exams will be given according to the KAIST schedule. There are old exams at math.kaist.ac.kr/~schoi/teaching.html.

Quizzes: There will be a quiz almost every week. There will be one or two problems to solve
given 20 minutes. The quiz problems are very similar or identical with the homework problems.
One should prepare for them by groups of students working on homework problems together.
The homework problems are not to be turned in.

Points will be given to the questions pertinent to the materials that we are learning.
30 points will be given to answering teacher questions which will be evenly distributed to the students
and 20 points will be given to asking question. If you don’t ask questions, then you will be given 0 points here.

 

Introduction to formal mathematical proofs

Chapter 1: Linear equations

Chapter 2: Vector spaces

Chapter 3: Linear transformations

Chapter 4: Polynomials

Midterm

Chapter 5: Determinants

Chapter 6: Elementary canonical forms

Chapter 7: The rational and Jordan forms

Final

 

The teaching homepage:

http://math.kaist.ac.kr/~schoi/teaching.html

Course homepage: mathsci.kaist.ac.kr, math.kaist.ac.kr/~schoi/linearalg2008I.htm

 

Monday

 

Wednesday

 

Friday

 

2/11

Introduction to linear algebra

2/13

1.1,1.2.

2/15

1.3,1.4.

2/18

1.5,1.6.

2/20

1.6.

2/21

2.1

2/25

2.2

2/27

2.3

2/29

2.3.

3/3

2.4., 2.5.

3/5

2.5, 2.6.

3/7

3.1.

3/10

3.2.

3/12

3.3.

3/14

3.4.,3.5

3/17

3.6.

3/19

4.1,4.2.

3/21

4.3.

3/24

4.4.

3/26

4.4.

3/28

4.5.

3/31

midterm

4/2

midterm

4/4

midterm

4/7

5.1

4/9

5.2

4/11

5.3.

4/14

5.4.

4/16

6.1,6.2.

4/18

6.3.

4/21

6.4.

4/23

6.4.

4/25

6.6.

4/28

6.7.

4/30

6.8.

5/2

6.8, 7.1.

5/5

holiday

5/7

7.2.

5/9

7.2.

5/12

holiday

5/14

7.2.

5/16

7.3

5/19

7.3.

5/21

7.4.

5/23

7.4. Q&A session

5/26

final

5/28

final

5/30

final

 

 

 

 

 

 

 

 

 

 

 

 

 Old lecture note for mathematical logic odd pages and even pages

I will be attempting to write new lectures notes in ppt files and post them here.

MIT Linear algebra class (with recorded lectures)
           There are many Java applets to play around here. See demos. Lectures are given by Gilbert Strang, the author
           of one of the textbooks above. This is more for engineers but has many worthy advanced applied
           mathematics in it. This course corresponds to the introduction to linear algebra course, one level below this one

MIT Linear algebra class (This correspond to our course exactly.)

Harvard Linear algebra class (correspond to our course)

Homework sets: Do not turn in your works but you should know how to solve these problems.
For quizzes, the teaching assistants will make problems similar to these. The best way is
to study the problems that were taught on that day.

S.1.2:p.5:1,4,5, S.1.3:p.10:2,p.11:4,8, S.1.4: p.16:4,6,

S.1.5: p.21:1,6, S.1.6: p.26:3,6,7, S.2.1:p.33:1, p.34:4,6, S.2.2: p.39:1,2, p.40:6,8,

S.2.3:p.48:2,3,6, p.49:11, S.2.4:p.55:3,4,6.

S.2.6:p.66:1,3,5, S. 3.1:p.73:1,3,7,9, S.3.2:p.83:1,3,5, p.84:7.

S.3.3:p.86:2,3,S.3.4:p.95:2,5,7, S.3.5:p.105:1,2,4,7, p.106:9,11,12.

S.3.6: p.111: 1,2, S.4.2: p.123:2,4,7,9, S.4.3:p.126:1,2,3.

S.4.4:p.134:1,2,4, S.4.5:p.139:2,3

S.5.2:p.148:1, p.149:8,9,10, S.5.3:p.155:2,4,7, p.156:11.

S.5.4:p.162:1,3, p.163:7,9,12, S.6.2:p.189:1,3,5, p.190:6,10,11, S.6.3:p.198:3,4,6,8.

S.6.4:p.205:1,3,4,5,9, p.206:11,12, S.6.6:p.213: 1,2,3,8.

S.6.7:p.218:1,2, p.219: 4,5,9, S.6.8:p.225:1,2, p.226:5,9

S.7.1:p.230:1,2,3, p.231:6,7, S.7.2:p.241:1,2,3, p.242: 4,8,9,p.243:11,12. (13th and 14th week together)

S.7.3:p.250:3,6,7,8, S.7.4:p.261:4.