Chun Pong--Derek--Chow>>i still don't clearly know what is linear transformation
TA Bong_Lee>>i think the schedule is slow down now
TA Bong_Lee>>how about your quiz?
Chun Pong--Derek--Chow>>failed
TA Bong_Lee>>what? the quiz haven't been graded yet.
Chun Pong--Derek--Chow>>on saturday there is a small quiz...
Chun Pong--Derek--Chow>>and i know i must fail
TA Bong_Lee>>never mind la work hard next time lor
TA Bong_Lee>>as there r many quiz
Siu Him--Lau>>why there is two of me?
Chun Pong--Derek--Chow>>it is because you have logged out
Siu Him--Lau>>hi everyone
Chun Pong--Derek--Chow>>still holapians
Ka Wai--Chan>>hello
TA Bong_Lee>>so i want to know that do u have time to reviw the notes?
Siu Him--Lau>>some execise in chapter 1 are complicated. very long caclulation
Chun Pong--Derek--Chow>>i also want to, but the school work is heavy, luckily tomorrow is a holiday
TA Bong_Lee>>I think the most important and first thing u need to do is that
TA Bong_Lee>>try to understand the notes first!
TA Bong_Lee>>if have more time than do exercise
Chun Pong--Derek--Chow>>but usually i use exercise to know the things!
TA Bong_Lee>> sometimes is helpful
TA Bong_Lee>>but complete all exercise is too time consuming!
Ka Wai--Chan>>I think I don't understand the previous concept well after doing the quiz
TA Bong_Lee>>good at least u know what thing u don't know!
TA Bong_Lee>>tell me!
Chun Pong--Derek--Chow>>i thing doing exercise is to clear my wrong concept
TA Bong_Lee>>if so than do.
Ka Wai--Chan>>so it is important to have review, not just galancing the notes several times
Chun Pong--Derek--Chow>>btw, can you suggest any reference books to us?
TA Bong_Lee>>in fact if u learn linear algebra through the approach of vector
TA Bong_Lee>>u can understand more easily
TA Bong_Lee>>as u can alway have a picture of vector in mind
TA Bong_Lee>>I think the lecture note is very good since many example and analogy is used!
TA Bong_Lee>>For example today's topic is vector and it's linear transformation
TA Bong_Lee>>such geometry thing can be represented by matrix!
TA Bong_Lee>>anyone know that if rotation is represented by matrix, what is it's characteristic?
Chun Pong--Derek--Chow>>what's that?
Siu Him--Lau>>have an angle ^o^
TA Bong_Lee>>that is transformation which keep the length of vector unchanged!
TA Bong_Lee>>but the angle may not change!
Ka Wai--Chan>>Can you give an example?
TA Bong_Lee>>good
Siu Him--Lau>>but reflection to x-axis also doesn't change the length and angle
Ka Wai--Chan>>Iwould like to ask what is 'reflection to x-angle'?
TA Bong_Lee>>u mean reflection about x- axis?
Ka Wai--Chan>>yes
Siu Him--Lau>>yes
Ka Wai--Chan>>what's that
TA Bong_Lee>>y not cahange the angle?
TA Bong_Lee>>the angle change to opposite value!
TA Bong_Lee>>angle count in counterclockwise is positive!
TA Bong_Lee>>clockwise is negative!
Siu Him--Lau>>oh yes from + to - . then y the angle after rotation may not change?
TA Bong_Lee>>since we can think that identity matrix is rotation 360deg
TA Bong_Lee>>y so few student here!
Siu Him--Lau>>i have a Q to ask. what is linear transformation different from transformation? or can u give an example that is not linear?
TA Bong_Lee>>first linear transformation need 2 requirement
TA Bong_Lee>>f(X+Y)=f(X)+f(Y)
TA Bong_Lee>>and
TA Bong_Lee>>f(cX)=cf(X)
TA Bong_Lee>>X,Y are vector
TA Bong_Lee>>c is scalar
TA Bong_Lee>>let me think the example!
TA Bong_Lee>>yeah
TA Bong_Lee>>for example
TA Bong_Lee>>[ln 3]
TA Bong_Lee>>[2 ln]
TA Bong_Lee>>ho sorry this example may wrong!
Chun Pong--Derek--Chow>>what is 2 In?
TA Bong_Lee>>[ln ln]
TA Bong_Lee>>[ln ln]
TA Bong_Lee>> is not linear!
TA Bong_Lee>>ln is natural log
Chun Pong--Derek--Chow>>you mean Inx?
TA Bong_Lee>>the entry in this matrix is not number but a function instead!
TA Bong_Lee>>for example
Chun Pong--Derek--Chow>>ar yes!
TA Bong_Lee>>[ln ln] 2
TA Bong_Lee>>[ln ln] 3
TA Bong_Lee>>we have
TA Bong_Lee>>[ln2+ln3]
TA Bong_Lee>>[ln2+ln3]
TA Bong_Lee>>[ln6]
TA Bong_Lee>>[ln6]
TA Bong_Lee>>call the matrix
TA Bong_Lee>>[ln ln]
TA Bong_Lee>>[ln ln]
TA Bong_Lee>>f
TA Bong_Lee>>than u can easily check that
TA Bong_Lee>>f((2,3)+(4,5)) =f((6,8)) not equal f((2,3))+f(4,5))
TA Bong_Lee>>so f is not linearly transformation
Prof Yan--Min-->>hello everybody
TA Bong_Lee>>hi
Siu Him--Lau>>hi
Chun Pong--Derek--Chow>>hello prof!
Ka Wai--Chan>>hello
Shuk Fan--Chau>>hi
TA Bong_Lee>>maybe due to holiday effect
Prof Yan--Min-->>I saw you were talking about linear transformation
TA Bong_Lee>>a few people here
TA Bong_Lee>>yes ar
Prof Yan--Min-->>any difficulty?
Chun Pong--Derek--Chow>>but usually there is just these people
Prof Yan--Min-->>Perhaps I should send e-mail to everybody, encouraging them to participate
TA Bong_Lee>>yes
TA Bong_Lee>>i found that the pace is slow down already!
Prof Yan--Min-->>They do not have to talk. I think watching the other people talk is also beneficial
Chun Pong--Derek--Chow>>just like me!
Prof Yan--Min-->>The pace is slowed down just this time. We cannot afford further slow down
TA Bong_Lee>>i see
Prof Yan--Min-->>Any difficulty about the two sections?
Chun Pong--Derek--Chow>>when i read the notes, it seems easy. but when i do the exercise, it's difficult!
Prof Yan--Min-->>OK. Any difficulty about verifying linear transformations?
Prof Yan--Min-->>I mean concrete problems
Chun Pong--Derek--Chow>>i would like to know what is the use of linear transformations?
Prof Yan--Min-->>I thought I explained in the description pages. At the moment, it is the language that makes it possible to visualize systems of equations
Prof Yan--Min-->>In the bigger context, it is the simplest mathematical model -- description of the world
Chun Pong--Derek--Chow>>for example?
Prof Yan--Min-->>Are you asking small or big?
Chun Pong--Derek--Chow>>big
Prof Yan--Min-->>The derivative is the linear approximation of functions.
Prof Yan--Min-->>Remember the tangent line is very much like a linear function
Prof Yan--Min-->>Linear questions are easy because we have a systematic way of solving systems of linear equations
Prof Yan--Min-->>For general non-linear problems, we approximate them by similar linear problems (i.e., taking derivative of the problem) and solve the linear one. The answer to the linear problem is very close to the answer to the original probolem
Chun Pong--Derek--Chow>>can you give us an example?
Prof Yan--Min-->>OK. Consider the Q: Is f(x) increasing near x =a?
Prof Yan--Min-->>We approximate f near x = a by g(x) = f(a) + f'(a)(x-a).
Chun Pong--Derek--Chow>>that's differentiation?
Prof Yan--Min-->>Note that h(t) = f'(a)t is a linear function of t, and the increasing/decreasing of g is the same as the inc/dec of h
Prof Yan--Min-->>Because h and g essentially differ by only a constant f(a)
Prof Yan--Min-->>The answer for the inc/dec of h(t) = At, A=f'(a) is very easy: A > 0 => inc; A < 0 => dec
Prof Yan--Min-->>So f'(a) > 0 => g inc; f'(a) < 0 => g dec
Prof Yan--Min-->>So far so good?
Prof Yan--Min-->>Understand my argument so far?
Prof Yan--Min-->>Assuming you understand. Since g and f are close (that is what approximation means)
Prof Yan--Min-->>we conclude f'(a) > 0 => f inc, etc
Prof Yan--Min-->>A key point to remember: If Q and Q' are very close problems, then solution to Q is very loikely the solution to Q'
Prof Yan--Min-->>Remember our conclusion about inc/dec for g? We simply replaced g in the statement by f.
Prof Yan--Min-->>We can do this because f is close to g
Prof Yan--Min-->>I guess it might take some time to digest what I said. Let us move to a new problem
Siu Him--Lau>>I want to ask sth small. What do the graph of system of eq of 4 variables look like? I can't imagine that.
Prof Yan--Min-->>You are supposed to draw pictures for the 2 or 3 variable case and imaagine that more variable case is similar
Prof Yan--Min-->>Imagine is different and is beyond concrete picture
Prof Yan--Min-->>For example, you cannot draw the picture of the sequence 1, 1/2, 1/3, 1/4, ..., 1/n, ...
Prof Yan--Min-->>I means the whole sequence.
Prof Yan--Min-->>However, you may draw the dots 1, 1/2, 1/3, ..., 1/10 on the papar. This is good enough for you to IMAGINE that the limit is zero.
Chun Pong--Derek--Chow>> for 1, 1/2, 1/3, 1/4, ..., 1/n , is it because we cannot find the general solution?
Prof Yan--Min-->>I do not means solution, I mean the limit of 1/n when n -> infinity
Prof Yan--Min-->>You need a little bit imagination beyond actually drawing pictures, in order to see the limit is zero
Prof Yan--Min-->>Why so quiet?
Chun Pong--Derek--Chow>>ar yes, do prof you know our maths teaher?
Prof Yan--Min-->>I do not know your teacher. Why?
Chun Pong--Derek--Chow>>he said he knows you
Prof Yan--Min-->>Did he tell you how he knew me?
Prof Yan--Min-->>I am rather courious
Chun Pong--Derek--Chow>>yes
Prof Yan--Min-->>More details please
Chun Pong--Derek--Chow>>last saturday, on the open day, he ask us about this course, and we talks about our prof
Prof Yan--Min-->>Then?
Chun Pong--Derek--Chow>>we said you teach us, and then he said he knows you
Prof Yan--Min-->>Was he a ust student?
Siu Him--Lau>>and you knows him.
Chun Pong--Derek--Chow>>don't know
Prof Yan--Min-->>Can you tell me where I may have met him?
Siu Him--Lau>>he said nth about this
Prof Yan--Min-->>Well. Would you please find out?
Chun Pong--Derek--Chow>>PRI MESSAGE
Prof Yan--Min-->>What does PRI MESSAGE mean?
Chun Pong--Derek--Chow>>SOR wrong message
Siu Him--Lau>>i want to know the detial also.
Chun Pong--Derek--Chow>>me too
Siu Him--Lau>>but he just say nth
Prof Yan--Min-->>Then please ask him. I reaally have no idea
Siu Him--Lau>>His name is Leung Tak. Do you remember him?
Prof Yan--Min-->>I see. He was a UST student.
Ka Wai--Chan>>really?
Chun Pong--Derek--Chow>>oh god
Prof Yan--Min-->>His math was quite good. Unfortunately, he had no time because he was busy with high school teaching.
Siu Him--Lau>>It is good to study in UST. Why do he keep it as a secrect?
Chun Pong--Derek--Chow>>only quite good...
Ka Wai--Chan>>Prof, are you his teacher in UST
Prof Yan--Min-->>I think he is mathematically well qualified to be a high school teacher. Perhaps much more qualified than most of math teachers.
Prof Yan--Min-->>Yes I taught him something. He was a part time student. He was so busy with high school teaching and had little time left.
Chun Pong--Derek--Chow>>he didn't said to us
TA Bong_Lee>>he is part time MSc student?
Prof Yan--Min-->>Well I guess he tried his best but did not quite achieve what he intended. Being a part time student is very tough on him
Chun Pong--Derek--Chow>>what is MSc?
Prof Yan--Min-->>Master of Science.
Prof Yan--Min-->>His goal was higher than MSc
Chun Pong--Derek--Chow>>isn't he a doctor?
Prof Yan--Min-->>I am not quite sure because it was some time ago
Prof Yan--Min-->>last time you mentioned he was a good teacher. right?
Chun Pong--Derek--Chow>>so good
Prof Yan--Min-->>That was what I thought. He had quite good understanding of mathematics.
Siu Him--Lau>>He always teach deeply into a Q and use different methods to solve it. But usually we don't understand.
Ka Wai--Chan>>Yes it 's difficult to understand
Prof Yan--Min-->>I see. His math is very good. But he may have some problem with communication skill
Chun Pong--Derek--Chow>>but in the past, we do the Q extensively but not intensively
Prof Yan--Min-->>you mean lots of question but not hard questions?
Chun Pong--Derek--Chow>>first lots of Q, but not go so deeply
Prof Yan--Min-->>I guess the kind of math your teacher trying to show you is closer to the math in the university
Chun Pong--Derek--Chow>>for example, today he is teaching us how to prove arithmetic mean > geometric mean in many methods, but it may not be useful in the exam
Siu Him--Lau>>but i would like to learn them
Prof Yan--Min-->>Well you guys should change the attitude. Doing math is fun for your teacher. Exam is less important
Chun Pong--Derek--Chow>>but HKAL is more important in our life, although i lke maths
Prof Yan--Min-->>How unfortunate
Siu Him--Lau>>it is not more important but more urgent
Prof Yan--Min-->>I do feel quite sorry for what you have to go through
Chun Pong--Derek--Chow>>sigh
Prof Yan--Min-->>I really think the hong kong edu system is rather crule. Everything dictated by exams
Prof Yan--Min-->>Exams kill lots of things, expecially the fun
Chun Pong--Derek--Chow>>never mind, we have get used to it for a long time
Prof Yan--Min-->>Well, I hope you will have more fun after you get into universities
Chun Pong--Derek--Chow>>if we can get into universities
Prof Yan--Min-->>Please do not worry too much. My attitude is always that worrying does not help you perform. Instead of worrying, please try your best
Prof Yan--Min-->>I also went through many exams in China. I never worry during exams because I knew it would only affect my performance
Prof Yan--Min-->>Will you choose math when applying for universities?
Shuk Fan--Chau>>of course, but i am talking on phone
Prof Yan--Min-->>What about the others?
Shuk Fan--Chau>>ha what?
Chun Pong--Derek--Chow>>may be not
Prof Yan--Min-->>Why not math?
Siu Him--Lau>>I am not sure about that.
Ka Wai--Chan>>It's my goal
Prof Yan--Min-->>What are the considerations for not choosing math?
Chun Pong--Derek--Chow>>may be because of the career, and may be because of the interest
Ka Wai--Chan>>Maybe engineering or psycho.
Prof Yan--Min-->>Look at the computer. It was very hot several years ago. Now it is not so good anymore
Prof Yan--Min-->>Talking about the engineering. This year all the engineering departments ggot the worst students
Chun Pong--Derek--Chow>>oh why
Ka Wai--Chan>>mechanical engineering as well?
Prof Yan--Min-->>Perhaps the job market isnot so good, given the bad economy
Prof Yan--Min-->>Certainly electronic engineering in UST got the worst.
Prof Yan--Min-->>I read from Ming Pao several days ago about this year's university students.
Chun Pong--Derek--Chow>>then which department get the best students?
Ka Wai--Chan>>then what about the career for maths
Prof Yan--Min-->>In UST, it is accounting.
Prof Yan--Min-->>In Chinese U, it is translation. Translation? Come on.
Prof Yan--Min-->>Math students are considered smart by the public. This is your advantage
TA Bong_Lee>>it's difficult to find a post of programmer now
Prof Yan--Min-->>This year our department got much better students than last year
TA Bong_Lee>>most of job is financial plannar for insurance comp
Chun Pong--Derek--Chow>>oh really? i am thinking of studying physics
TA Bong_Lee>>bcos of nano carbon tube?
Prof Yan--Min-->>Good idea. Physics also trains your mind and makes you smarter.
Ka Wai--Chan>>Derek, do you want to be a physics teacher?
Chun Pong--Derek--Chow>>i don't want to be another mr. siu
TA Bong_Lee>>but if u want to go deeper u need a lot of math!i think!
Prof Yan--Min-->>Teacher is not the only career for Physics students. There are many Physics PhDs doing financial work in Wall street
Chun Pong--Derek--Chow>>i think wilde, who is not here, will probably study maths in U
Chun Pong--Derek--Chow>>it's too far away...
TA Bong_Lee>>I just think that HK student have not much time to find out what subject they like
TA Bong_Lee>>as time is dedicated to public exam!
Prof Yan--Min-->>The financial sector in US, for example, think of math and physics students highly. They believe their training make them smarter
Prof Yan--Min-->>If you think you are good at math and likes math, you should give math a try. Math is no doubt the most analytical subject. Math training is good for the analytical skill, the problem solving skill. They also make people more careful and patient. These are the qualities for people to be succeful in the society.
Chun Pong--Derek--Chow>>you should talk to wilde!
Prof Yan--Min-->>Is wilde enrolled in my course?
Chun Pong--Derek--Chow>>yes, he is also a holap student, but he cannot acess to the internet so he can't chat with us
Prof Yan--Min-->>Because he has no computer?
Siu Him--Lau>>He has computer but not internet service.
Prof Yan--Min-->>Does it help if I ask the technician to allow him to use the modem to connect to UST?
TA Bong_Lee>>possible
Prof Yan--Min-->>Wait a minute. If he does not have internet access, How does he study my material?
Chun Pong--Derek--Chow>>in school, and we sometimes print it out for him
Prof Yan--Min-->>Is modem fast enough for reading my web page and joining in chatting?
Ka Wai--Chan>>sometimes he comes to my home and studies with me
Prof Yan--Min-->>Is modem fast enough?
Siu Him--Lau>>yes i think
Chun Pong--Derek--Chow>>yes just text
Prof Yan--Min-->>OK. I will try to make some arrangements.
Ka Wai--Chan>>Yes i oftens do
Prof Yan--Min-->>What kind of internet access do you guys have?
Chun Pong--Derek--Chow>>IMS Broadband
Prof Yan--Min-->>Anybody using modem?
Siu Him--Lau>>It should be ok to modern. Don't worry about that.
Siu Him--Lau>>to use
Prof Yan--Min-->>It is getting quite late. But hey, tomorrow is holiday.
Chun Pong--Derek--Chow>>just sending text is fast enough
Siu Him--Lau>>Holiday is for homeworks.
Prof Yan--Min-->>Sad reply
Chun Pong--Derek--Chow>>heavy schoolwork and heavy ECA wok
Prof Yan--Min-->>ECA?
Chun Pong--Derek--Chow>>extra cirricular activity
Prof Yan--Min-->>I though ECA should be fun. Right?
Chun Pong--Derek--Chow>>yes, but it should go along with careful time management
Ka Wai--Chan>>what is your ECA work
Prof Yan--Min-->>What kind of school is holap? Band 1? Chinese? English?
Siu Him--Lau>>Band 1, Eng
Chun Pong--Derek--Chow>>officially, band 1, eng
Prof Yan--Min-->>Why officially?
Siu Him--Lau>>We don't believe it is band 1.
Prof Yan--Min-->>You look down on your school?
Chun Pong--Derek--Chow>>quite
Prof Yan--Min-->>More details, please.
Chun Pong--Derek--Chow>>student's discipline, acedemic performance, shouldn't be band 1
Siu Him--Lau>>The aveage quality of students is getting worse since long time ago.
Prof Yan--Min-->>Maybe band 1 is not that high standard anyway. I confess I am quite ignorant of HK edu system besides these names.
Chun Pong--Derek--Chow>>just this year, the syllabus of the additional maths cut again
Prof Yan--Min-->>But more material does not necessarily mean better education.
Prof Yan--Min-->>Especially only small number of math teachers understand the material as good as Leung Tak
Prof Yan--Min-->>quiet. Shall we stop here?
Chun Pong--Derek--Chow>>what't the time now?
Prof Yan--Min-->>after nidnight
Siu Him--Lau>>0005
Chun Pong--Derek--Chow>>tonight's chatting session is so meaningful!
Siu Him--Lau>>I am going now. Bye bye everyone.
Chun Pong--Derek--Chow>>i really have to restart my computer, see you!
Ka Wai--Chan>>goodnight!
Siu Him--Lau>>Have a nice dream.
Prof Yan--Min-->>Bye