Siu Him--Lau>>pair of derek
Shuk Fan--Chau>>gd evening!
Chun Pong--Derek--Chow>>when is your app maths test?
Siu Him--Lau>>on fri
Ka Wai--Chan>>hi
Siu Him--Lau>>15% of half year
Ka Wai--Chan>>Why TA Bong not here
Siu Him--Lau>>doesnt matter
Chun Pong--Derek--Chow>>we learn set theory again in here...
Chun Pong--Derek--Chow>>actually, does today have a chatting session?
Prof Yan--Min-->>hello everyone, again holapians only
Prof Yan--Min-->>any Qs?
Prof Yan--Min-->>I am waiting...
Chun Pong--Derek--Chow>>why do you introduce the 3 examples at the beginning
Chun Pong--Derek--Chow>>?:
Prof Yan--Min-->>Would you understand the definition of vector space if I give no examples?
Prof Yan--Min-->>Moreover, we only make definitions when we feel a compeling reason. The examples suggest us something we should do.
Chun Pong--Derek--Chow>>i know more what you are saying...
Prof Yan--Min-->>which means ?
Prof Yan--Min-->>Do you feel you understand the concept of vector space?
Chun Pong--Derek--Chow>>uptil now, i feel i still understand, but not the subspace
Prof Yan--Min-->>The best way is through the comparison with subnumber system.
Chun Pong--Derek--Chow>>i still not get used to familiar with the set notations
Prof Yan--Min-->>It is the basic math language. The sooner you get fluent with it, the better.
Chun Pong--Derek--Chow>>yes i know
Chun Pong--Derek--Chow>>what dows C and F means in C(R) and F(R)?
Prof Yan--Min-->>My canotonese is not very good. This limits my circle of activity in Hong Kong.
Prof Yan--Min-->>C means continuous. F means funcitons.
Prof Yan--Min-->>Do you learn sets in high school?
Shuk Fan--Chau>>yes
Ka Wai--Chan>>yes
Prof Yan--Min-->>But you still have difficulty using it effectively?
Shuk Fan--Chau>>yes,
Prof Yan--Min-->>I guess themore fundamental the concept, the more experience it takes to master it.
Shuk Fan--Chau>>may be that's why i still not understand what subspace is,
Prof Yan--Min-->>The only way is probably trying to use it and observe how others use it.
Shuk Fan--Chau>>would you mind........
Shuk Fan--Chau>>explain?
Prof Yan--Min-->>Again learn through examples. Try to understand why C(R) is a subspace of F(R), for example
Prof Yan--Min-->>C(R) is continuous funcitons, F(R) is ALL functions. of course C(R) is part of F(R), i.e., a subset.
Prof Yan--Min-->>You use the subset language when you see one set is part of another. Right?
Prof Yan--Min-->>Do you understand what I said about C(RE) and F(R) so far?
Shuk Fan--Chau>>yes
Prof Yan--Min-->>So C(R) is a subset of F(R). Right?
Prof Yan--Min-->>But C(R) is more than just a subset. It also has some nice properties.
Prof Yan--Min-->>f and g continuous => f + g and cf continuous
Prof Yan--Min-->>Translation: f anf g in C(R) => f + g and cf in C(R)
Prof Yan--Min-->>So far so good?
Shuk Fan--Chau>>just ok
Chun Pong--Derek--Chow>>i want to ask some technical problems in the answers to ex of subspaces
Prof Yan--Min-->>OK go ahead
Chun Pong--Derek--Chow>>http://algebra.math.ust.hk/vector_space/02_subspace/exercise1_answer.shtml
Chun Pong--Derek--Chow>>Q7
Chun Pong--Derek--Chow>>and (2, 0) + (-1, -1) = (1, -1) H
Chun Pong--Derek--Chow>>i saw a SQUARE between (1, -1) and H, is that a symbol or my computer's problem?
Chun Pong--Derek--Chow>>does it means 'not belongs to'?
Prof Yan--Min-->>The square should be the symbol for "not in"
Prof Yan--Min-->>Do you have the same problem for the answer to Q6? we have (1 1 2 ) not in H.
Chun Pong--Derek--Chow>>is that the opposite of the E-like symbol?
Prof Yan--Min-->>Yes
Chun Pong--Derek--Chow>>thx
Prof Yan--Min-->>What about answer to Q6?
Prof Yan--Min-->>I also use the same symbol there.
Chun Pong--Derek--Chow>>i know what it says. at first i just thought that's it's my computer's problem, because my teacher does't use that symbol
Prof Yan--Min-->>What symbol does he use?
Chun Pong--Derek--Chow>>the combination of E-like and '/', just like = and =/=
Chun Pong--Derek--Chow>>or is that symbol really exist?
Prof Yan--Min-->>This IS the symbol I tried to use. So it is probably still your computer problem.
Prof Yan--Min-->>So what is your computer set-up?
Chun Pong--Derek--Chow>>my IE doesn't support that code? that fun
Prof Yan--Min-->>Could be. I use the Mac version of IE 5.2
Chun Pong--Derek--Chow>>mine is 5.5
Prof Yan--Min-->>I am testing on Netscape 6.2 now.
Prof Yan--Min-->>The netscape displays the symbol correctly.
Chun Pong--Derek--Chow>>it doesn't matter, i know what the symbol says is more important
Prof Yan--Min-->>Since Netscape 6+ is platform independent, I think you should get more satisfactory result with netscape. The current verision is probably 7
Prof Yan--Min-->>I have 6 or 7 browsers installed in my machine and constantly have about 3 running. When I am not satisfied with one, I switch to another.
Chun Pong--Derek--Chow>>i have never installed netscape at home
Prof Yan--Min-->>It might be difficult if you have a slow connection. The download takes time.
Prof Yan--Min-->>Actually you should try Modzilla (verion 1.1?) It is better than netscape.
Chun Pong--Derek--Chow>>actually i don't like the font display in netscape, especially chinese
Prof Yan--Min-->>In terms of font display, the best one is OmniWeb. Unfortunately is Mac only.
Chun Pong--Derek--Chow>>ar.....i haven't used mac
Prof Yan--Min-->>The ugliest is iCab, which is also Mac only. I use iCab more often than IE because it is much more faster.
Prof Yan--Min-->>Please give Modzilla a try.
Chun Pong--Derek--Chow>>you are so good at different browsers, i use IE only...
Prof Yan--Min-->>I use whatever is good, not whatever is given. I do not like many things in webct. So I use my own web page.
Chun Pong--Derek--Chow>>actually i browse newsgroups more often then browsing websites
Chun Pong--Derek--Chow>>do i don't care my browser
Prof Yan--Min-->>There is another browser Opera, which claims to be the fastest. Give it a try.
Prof Yan--Min-->>By the way, Opera is quite small. The download does not take much time.
Chun Pong--Derek--Chow>>i think i am so different from you. maybe i am a stubborn person. i use softwares whatever i am familiar and used long
Chun Pong--Derek--Chow>>i seldom test new things
Prof Yan--Min-->>To study math better, you should try new things.
Chun Pong--Derek--Chow>>maths is different from computer!
Prof Yan--Min-->>Some of the old habits and methods in the high school may not be suitable for university level materials.
Chun Pong--Derek--Chow>>for example?
Prof Yan--Min-->>I think I am more of a hands-on guy. I like mechanical things. It is such a fun to take things apart and assemble them together again.
Prof Yan--Min-->>Cramer's rule is no good for solving equations. Row operation is the way to go.
Chun Pong--Derek--Chow>>i want to ask, what is multiple evaluations ? (in linear transformation part 1)
Prof Yan--Min-->>Sorry for the delay. I try to catch a call.
Chun Pong--Derek--Chow>>never mind~
Prof Yan--Min-->>It is given by the formula. The values of the funciton at 0, 1, 2.
Prof Yan--Min-->>So more precise name for the transformation is triple valuation
Chun Pong--Derek--Chow>>thank you
Prof Yan--Min-->>More Q?
Prof Yan--Min-->>Why ShukFan and Ka Wai are so quiet?
Chun Pong--Derek--Chow>>may be they are busy
Prof Yan--Min-->>what is the green house?
Chun Pong--Derek--Chow>>we have 4 houses in our school
Chun Pong--Derek--Chow>>red, blue, yellow, green
Chun Pong--Derek--Chow>>just like Slytherin, Gryffindor in Harry Potter
Prof Yan--Min-->>Sorry I did something stupid and had to launch IE again.
Chun Pong--Derek--Chow>>that's never mind
Prof Yan--Min-->>I had not watched Harry Potter.
Prof Yan--Min-->>Is green house a building paited green in your school?
Chun Pong--Derek--Chow>>no
Chun Pong--Derek--Chow>>it's just an association
Prof Yan--Min-->>Back to math. Any more Q?
Chun Pong--Derek--Chow>>again, what's the use of learning subspaces?
Prof Yan--Min-->>Many constructions needs to be given a suitable name.
Prof Yan--Min-->>What is common for the following constructions:
Prof Yan--Min-->>1. the range of a linear transformation
Prof Yan--Min-->>2. The colleciton of b such that Ax = b has solutions.
Prof Yan--Min-->>3.the soluitons of Ax = b.
Prof Yan--Min-->>4. The kernel of a linear transformation.
Prof Yan--Min-->>5. The plane (x, y, 0) in the (x, y, z) -space. etc.
Chun Pong--Derek--Chow>>that's all subspaces, right?
Prof Yan--Min-->>They are infinite, flat and passing throught the origin.
Prof Yan--Min-->>They share the same property that u, v in H => u + v and cu in H
Prof Yan--Min-->>With so many examples, we have to give a name to the concept.
Chun Pong--Derek--Chow>>i think i always think of applications when i learn maths
Prof Yan--Min-->>Yes. Abstraction makes sense only if there are many concrete examples.
Prof Yan--Min-->>The only way to learn a concept is through applications, examples.
Chun Pong--Derek--Chow>>yes..
Prof Yan--Min-->>This also explains your very first Q. Why examples before the def of vector space.
Prof Yan--Min-->>You see. Math is not a dry subject. The theory arises only when we have enough examples and experience.
Prof Yan--Min-->>Then we feel it necessary to summarize our observations and derive a theory.
Chun Pong--Derek--Chow>>this is so true in this course
Prof Yan--Min-->>I like teahcing linear algebra because its conceptual requirement.
Prof Yan--Min-->>Conputaitonally there is only the row operation. But conceptually it is quite rich.
Chun Pong--Derek--Chow>>YES!
Prof Yan--Min-->>The key point os the course is the concepts
Chun Pong--Derek--Chow>>but concepts needs time to digest
Prof Yan--Min-->>You are quite right. I wish you have more time on good math.
Chun Pong--Derek--Chow>>i hope so...
Prof Yan--Min-->>Unfortunately, the test system takes away lots of time from high school students.
Chun Pong--Derek--Chow>>never mind, we are used to it
Prof Yan--Min-->>But it is such a waste
Prof Yan--Min-->>Any more Q?
Prof Yan--Min-->>I will leave if there is no more Q
Chun Pong--Derek--Chow>>i think no
Prof Yan--Min-->>OK. Let's have a good dream. Bye
Chun Pong--Derek--Chow>>BB