Applied Math 40S

Here it is: The Flip Site. Click on the guy in the striped shirt to see him flip the coin. He's been filping it once every five seconds since midnight, January 1, 2006. (He starts over again every new year.) It may also be interesting to explore the streaks link and watch the changing probabilities.






And, in the Theatre of Mathematics ...

• Probability Definitions and Finding Sample Spaces


• Solve Problems Using Sample Spaces

And in the Tutorial Room ...

• Sample Spaces and Events


• Experimental Probability
  (In this tutorial they call it Estimated Probablity)


• Theoretical Probability
  (In this tutorial they call it Empirical Probablity)

This week's game is called Grow.



Draw each item to the center of the ball to Grow it. If you drag them in the right order you will reach the maximum growth level for each object -- that's the challenge and it's not easy. ;-) Lots of trial and error. The number of different ways to play this game is 479 001 600. Can you find the winning strategy?

The Applied Math class will learn how to figure this out this week. Pre-Cal will learn it in about two more months and the AP Calculus students should remember from the Pre-Cal class. Do you?

Have Fun!

First of all cool...our blog is multiligual.....anyways...

What I've learn about matrices is pretty a lot, first it was confusing why learning all this stuff when i actually can't get money from it....hahahaha..but everything changed...matrices is actually a significant topic in math...it really applies math in it....In transition matrix first i was struggling to learn it...because i wasn't in class by the time they were learning it....I'm actually a lazy type of student satisfied with a 50 percent grade....but since i was in this class.. i think applied is easy to learn...trust mee i hated applied eversince grade 10....because of our introduction topic of matrices i was interested...and chose to go to class everyday...i just think matrices is a fun topic.it..twist your mind..but you need to twist it back to get it.... i think i'm writting a story now... butt anywayss.. that'ss ittttttttttttt. Hopefully I'm able to get all the questions this friday for the test.

You'll notice that all posts on our blog now have a series of flags automatically added to the bottom. Click on a contry flag to have the blog translated into that country's language. You can choose from:

French, German, Italian, Portugese, Spanish, Japanese, Korean, Chinese and Filipino

If you speak any of these languages, let me know if they work well enough to be understood. And tell your parents all about it! ;-) Encourage them to leave comments on the blog as well.

Chinese Checkers it is called in England. Kinasjakk (Chinese Chess) in Norway. The truth is that it has nothing to do with neither checkers, chess, nor China.

'The Chinese Checkers game board is in the shape of a six pointed star and is playable with two up to six people at the same time. Each player uses pegs or markers of a different color placed within one of the points of the star. The object is to move all your ten pegs across the board (move one step at the time or jump over adjacent pegs) to occupy the star point directly opposite. The player getting all pegs across first wins.' - More.

You can play it here.

(Thanks again to Think Again!)

This is an introduction to matricies.

You can review the basic operations (addition, subtration, scalar multiplication) on matricies here.

Learn about matrix multiplication there.

You can also watch two movies about Transition Matricies. (You might need to download the Quicktime Player; you can get it (free) here.) The first one explains the mechanics of what they are and how they work. The second movie takes you through two different examples, slowly and carefully, showing how to solve transition matrix problems. Something I haven't yet mentioned in class; transition matrix problems are also called Markov Chains. "Markov" is the name of a person.

Each Sunday, just for fun, I will post an online game or puzzle. This week it's a logic puzzle ... we look in on a prisoner with a problem ....

---

For the last trial, the king used not two, nor three, but nine rooms! The prisoner was told that one room contained a Lady and the other eight were either empty or filled with a tiger. The sign on the Lady's door was true, the signs on room with tigers were false, and empty rooms had signs that were either true or false.

These were the signs:

1. The lady is in an odd-numbered room.


2. This room is empty.


3. Either sign 5 is right or sign 7 is wrong.


4. Sign 1 is wrong.


5. Either sign 2 or sign 4 is right.


6. Sign 3 is wrong.


7. 7. The lady is not in room 1.


8. This room contains a tiger and room 9 is empty.


9. This room contains a tiger and 6 is wrong.

The prisoner studied the nine signs for a while and came to the conclusion that the problem was unsolvable. The king admitted his mistake and told the poor prisoner if room eight was empty or not.

The prisoner needed no more help. He deduced where the Lady was. What about you?

Problem source: The Lady or the Tiger and other Logic Puzzles by Raymond Smullyan. (With thanks to Think Again!)

Eyy...everyone.....Ivy would like to tell all the 40s Applied Math student... what happened or what she've learned today....

We only have one class...but sure do my brain almost explode in what we have for the group problem...but anywaysss...

Mr. K gave us some matricies question.. about connectivity matrix at the first part of our class....yesterday i was pretty confused about it.. but i finally got it when Shane actually explain it to me...Second part is about our text book assignment...Mr. K asked us about any problems we encounter by doing the textbook questions...and so he explained some problems that we didn't get.


The Group Problem
WE did this problem about 6 guys doing the activity of ski jump. It has the number of points that those guys got and the difficulties. The question is....how can we explain by multiplying the points and the difficulties by making a matrix model; also to find who got the greatest points and the least. How can we do that?

Guy 1 - 24.3 27.5 27.1 21.4
Guy 2 - 21.2 24.2 18.3 15.2
Guy 3 - 21.3 21.8 15.9 21.5
Guy 4 - 18.7 27.2 21 18.6
Guy 5 - 24.4 24.2 21.4 24.5
Guy 6 - 27.6 18.3 21.6 21.5

^ What you See on top is the ski-jumpers points.^

I 1.4 1.5 1.3 1.6 1.5 1.2
II 1.6 1.4 1.7 1.4 1.6 1.5
III 1.5 1.9 1.9 2.0 1.9 1.7
IV 1.7 2.1 1.4 1.8 2.0 1.9

^ What you See on top is the Ski-jumpers difficulties.^

It's also asking us which way is the better idea to multiply the points and difficulties. Lets give a names to this two data of the ski-jumpers.in matricies.. Let be Points = A and Difficulties = B. So which way is better?


[A] is (6x4)
[B] is (4x6)
THEY CAN BE SOLVE IN BOTH WAYS. butttttttt........which is the right one????


SOLUTION
Lets put it this way [a] x [b] = THE PRODUCT. So if [A] got rows and columns by 6x4 and [B] got 4x6 it can be solve...and our product should have 6x6 in rows and columns. We are solving it this way because we need to find all the total points for each ski-jumpers and it's possible to do this way, yes they do have different types of difficulties in each jumpers but in order to be fair we need to multiply them with the different numbers of the other ski-jumpers. NOW if we got all the product by multiplying [A] x [B] in matrix..thenn...to add up all the total points of the ski-jumpers we need to multiply the product with "1" that has 6x1 rows and columns...

We don't add the following individualy because it's going to take time, by multiplying with "1" in 6x1 we should have the ski-jumpers total...and see who got the most points and least.

<<------------------------->>


[A] x [B] = THE PRODUCT
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]
[ PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT PRODUCT] [ 1 ]


<<-------------------------->>


AND THAT'S THE CASE!!! HOPE I DIDN"T CONFUSE YOU........

Monday's Scribe (Feb. 13, 2006) is going to be : Corrie.
I'm sorry for the person that i chose... i barely know everyone in this class...

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post is can be quickly accesed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.

Cycle 4

Cait Shane Allan Ivy Nikki Steph

Nik # 1/2 Corrie jessica jason Dominator mohamed

khan Andrew Pa3k reign Hesy muuxi Rubie

So far in class we've learned how to add and subtract matricies, how to multiply maticies by a scalar quantity and how to multiply matricies.

Matricies are usually used to solve "systems of equations" like you did in Applied Math 30S. We wont really be using them in that way in this course but you can read about it here. It may be worth your time to review that link if you'd like to go over the definition of what a matrix is. You may also want to look it up in the Math Dictionary or Encyclopedia you'll find in the Links list over there --> in the right hand sidebar.

You'll find a review of our lesson on Matrix Addidition here and Matrix Multiplication there. (There's a cool animation -- you'll see what I meant about "using your fingers." ;-))

Find a little addtional Matrix Addition practice here, and Matrix Multiplication practice there.

Finally, test your knowledge with these online interactive quizzes (refresh the page if you want to try five new ones):

• An Introduction to Matrices (5 questions)


• Adding and Subtracting Matrices (5 questions)


• Multiplying Matrices (5 questions)

Remember, those quizzes are tonight's homework.

Cheers!
Mr. K.

We had a good couple of classes today. I was very happy with how well you seem to be, as a class, learning and applying the material but there's one thing that concerns me. Do you remember my "zoned out minute?" Well, at that point I was feeling as though you were all there in body but not in spirit. What I mean by that is there is a BIG difference between learning and just being there. Learning is an interactive sport; not a spectator sport. There has to be a conversation between us, back and forth, as we work through the material. Learning doesn't happen when I talk and you listen; learning happens when you have a conversation -- with me and with each other. I'm looking forward to participating in more conversations in our future classes, then, maybe, I wont zone out. ;-)

We were talking about exactly what sort of post you're supposed to make to get that mark on your test. The kind of post I'd like you to make should have one or more of these characteristics:

• A reflection on a particular class (like the first paragraph above).


• A reflective comment on your progress in the course.


• A comment on something that you've learned that you thought was "cool".


• A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.


• Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.


• Respond to a Blogging Prompt I posted. (see below)

Your posts do not have to be long. I'm far more interested in the quality of what you write rather than the quantity.

Blogging Prompt
To help us along our blogging journey I've decided that I will also occasionally post a Blogging Prompt. It will be easy to find because I'll always put it under a heading like the one above this paragraph. Feel free to create your own Blogging Prompt for the rest of us if you like. If it's a really good one (i.e. has rich possibilities for blogging) we'll count it as your post. ;-) Here's my first one:

We've learned about two different kinds of mutliplication that can be done with matricies; scalar multiplication and matrix multiplication. There's also ordinary multiplication, such as 2 x 3 = 6. Blog a brief paragraph identifying ways in which these three types of multiplication are similar. Blog a second paragraph outlining the ways in which they are different. Also, give us an example of two 2x2 matricies, A and B, that DO commute. i.e. AB = BA.

This sort of compare and contrast exercise can be made easier to do using Venn Diagrams. Draw two large overlapping circles. List the similarities in the overlapping section and the differences in the appropriate non-overlapping sections. If you like, you can use this web tool to do it online. If you do blog about this prompt and want to post your diagram we'll talk about how to post pictures sometime in class. ;-)

Happy Blogging!

Blogging is a very public activity. Anything that gets posted on the internet stays there. Forever. Deleting a post simply removes it from the blog it was posted to. Copies of the post may exist scattered all over the internet. I have come across posts from my students on blogs as far away as Sweden! That is why we are being so careful to respect your privacy and using first names only. We do not use pictures of ourselves. If you really want a graphic image associated with your posting use an avatar -- a picture of something that represents you but IS NOT of you.

Two teachers in the U.S.A. worked with their classes last year to come up with a list of guidelines for student bloggers.

One of them, Bud The Teacher, has these suggestions, among others:

1. Students using blogs are expected to treat blogspaces as classroom spaces. Speech that is inappropriate for class is not appropriate for our blog. While we encourage you to engage in debate and conversation with other bloggers, we also expect that you will conduct yourself in a manner reflective of a representative of this school.



2. Never EVER EVER give out or record personal information on our blog. Our blog exists as a public space on the Internet. Don’t share anything that you don’t want the world to know. For your safety, be careful what you say, too. Don’t give out your phone number or home address. This is particularly important to remember if you have a personal online journal or blog elsewhere.



3. Again, your blog is a public space. And if you put it on the Internet, odds are really good that it will stay on the Internet. Always. That means ten years from now when you are looking for a job, it might be possible for an employer to discover some really hateful and immature things you said when you were younger and more prone to foolish things. Be sure that anything you write you are proud of. It can come back to haunt you if you don’t.



4. Never link to something you haven’t read. While it isn’t your job to police the Internet, when you link to something, you should make sure it is something that you really want to be associated with. If a link contains material that might be creepy or make some people uncomfortable, you should probably try a different source.

Another teacher, Steve, developed a set of guidelines in consultation with his students. You can read them here.

Look over the guidelines and add the ones you like in the comments section below this post; either from one of Steve's students or one of your own. I think Bud's suggestions are excellent. We'll be using the one's I highlighted above as a basis for how we will use our blog.

Cheers,
Mr. K.

Hi There! You found our blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; to get copies of a handout you didn't get in class (here's the course outline); for parents to find out "How Was School Today;" to share your knowledge with other students;.... Most importantly it's a place to reflect on what we're learning.

Remember what I said about the Forgetting Curve? Well a big part of Learning and Remembering involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, or make your own blog and link it to this one, or....the sky's the limit...let your imagination soar and lets get down to some serious blogging!

Here's your first online assignment:

Do you see the Links list in the side bar over there on the right? Follow the Study Skills Resources link. Browse through the sites until you find one that you think has excellent suggestions on how to study math; then, on a piece of loose leaf paper (or this worksheet) to be handed in on Monday:

1. Write the address and name of the site you most liked.


2. Rate the site out of 100; i.e. give it a grade!


3. Write a brief description (no more than 4 or 5 sentences) of the site.


4. Include a comment on what it was about this site that made it stand out for you (no more than 1 or 2 sentences).

Repeat this exercise for the second link that deals with Test Taking, i.e. how to write a test.

If you take this assignment seriously now and invest some real time and energy into it, you'll probably do real well in my class this semester...who knows, it might even help you in your other classes too! ;-)

Have Fun!

PS Don't forget to email me ASAP and get signed up as a contributor to our blog!! When you get your "invitation" to our blog, follow these directions to get yourself signed up at Blogger.