Math is rocking the world!!!

Truly, this article is boring. It talks about things that everyone knows. 21st century, for sure is a century of math, of numbers, of data.

Basically, this article is telling us how important it is for people to understand math in this century. Our society now is filled up with data. People who could read and understand these data are appealing to all the big companies. By analyzing the data, math geeks could find out tons of information beyond these numbers. These new information they investigated provides the company a better view to the market and gives the big company a big step ahead of others.

However, there is a big flaw in this new system. As the article says “The power of mathematicians to make sense of personal data and to model the behavior of individuals will inevitably continue to erode privacy”, I think we have lost our privacy for decades. There are cameras everywhere. Government could simply monitor or track someone’s phone with the title of “National Security”. Thing cannot get any worse now, since we are already at the bottom of the abyss.

The title of the article says “Math will rock your world”. I think that is incorrect. I say math is rocking our world and has been rocking our world for at least 20 years.

Think about it, if you will. There are math everywhere in our world. Since the First industrial revolution, science walked into the stage, math also became an irreplaceable part of our society. A huge part of science is actually math. Physics obviously has to do with math. Chemistry involves math. Environment science needs data. Statistics are also math. All the industries, mechanicals, company finance involve what? Math. They need math to sustain the system.

So learning math will be the tendency for the future. For sure, there are other ways to survive in this society, but math will be, and must be the most important thing to know to survive.

Let’s rock…..

I see math

A coordinate system in our school!!



What's at the back of our solor panels? maths!!



School property...



Sweet moon up there



coffee is good

Choice

Derivative of the Inverse of a Function property in words: For any point (a, b) on an invertible function, the derivative of the inverse of this function evaluated at b is equal to the reciprocal of the derivative of the function evaluated at a.
Derivative of the Inverse of a Fucntion property in symbols:
Yes, volume is an invertible function, since it passes the horizontal line test.
The inverse function of volume:
Graph:
Proof: Equations
V(r)=(4/3)3.14r^3
y1=12.566(x-1)+4.1888
R(v)=(v/(4/3(3.14)))^(1/3)
y2=(1/12.566)(x-4.1888)+1

I took the derivative at the point (1, 4pi/3) and (4pi/3, 1).
Y1 and Y2 are the tangent lines.
As it shows, their slopes are reciprocals.

I chose to come to class that day. Firstly, I totally forgot we had the option to come to class or not to. Second, I think I learn better in classroom. So for my own benefit, I chose to come to the class.

anyone can learn from Internet?

I agree that anyone can learn anything, from anyone, anywhere, at anytime. However, “anyone can” doesn’t mean “anyone will”. Internet is a great source for learning, but it is also a source for spreading harmful information, listening to music, watching movies, playing games, and so on. Only a small group of people usually use internet as a source for learning. Most of people use internet as an entertainment. We can learn from Internet, but mostly we won’t. Internet as an entertainment is so distractive that students could barely focus on learning while they are online. Even though internet is a great source for learning, it is also filled with false and harmful information. Sometimes internet doesn’t teach you the right thing. So this requires people to be educated enough to use internet as a source of learning. That’s why a formal school is very necessary. Formal schools provide student a well organized and scientific system to learn knowledge. Schools teach students not only information, but also how to convert the information to their own knowledge. Schools teach students not only how to be successful, but also how to be a good human. Schools teach students not only how to talk, write and read, but also how to communicate with people. There are teachers and good students in school to be other kids’ goal. There are competitions going on in schools to help kids learn better. There are activities in schools to help kids learn for practices. School provides opportunities which internet can never provide. School is a real life experience whereas internet is just a tool. If you want to use internet as a source of learning, firstly, you need to know how to manipulate a computer, how to read, how write, and how to listen. School can teach you these, but internet cannot.

For people who could control themselves and well educated, internet is a great source for further education. For these who are not really self-restrained, a formal school is very necessary, because it helps them focus on learning and teaches you how to be a good human.

Short Post for Friday's Class

Hopefully, everyone had a great skiing day yesterday. Since BlueElephant was absent on Friday, I am the Scribe for Friday’s class.
We finished the exploration 4-2 on Friday. So basically we just checked our answers with Bru.
Firstly, let’s review the Quotient Rule!!!

I think this image just concludes the Quotient Rule. It is pretty straightforward.
Secondly, let’s take a look at the “Your Understanding” part of the package of the Quotient Rule. We went over this part of the package smoothly. The only issue we had was about question 3. In the “In words” part of part e, “As x gets arbitrarily close to 1, the function h(x) gets arbitrarily far from 0”, some people thought that instead of “far from 0” it should be far from 1, since (1,1) is the midpoint of the whole graph. Bru said both 0 and 1 works.
So now let’s turn the page over to Exercises. The 4 questions we talked about in the class are question 2, 4, 5 and 6. You can check the details in the slide show which Bru had posted two days ago. One reminder: Be aware of the composite functions. Don't forget the Chain Rule. Here I will just provide you the answers for the other 2 questions.
1. f '(x) = {(4x^3) * cosx - (x^4) *(- sinx)}/(cosx)^2
= x^3 (cosx + xsinx)/(cosx)^2
3. f '(x) = {(5cos5x)(8x-3) - 8sin5x}/(8x-3)^2
= {(40xcos5x-15cos5x-8sin5x}/(8x-3)^2


If you guys have any questions about my answers, please leave a comment.
Finally, I ask you guys to check out this YouTube clip.

http://www.youtube.com/watch?v=K3MxofAF-9o
This guy is left handed. I believe this YouTube clip will teach you the Quotient Rule again.

By the way, there are some extra credits. Check this link. You will see the problems.
https://docs.google.com/a/crms.org/viewer?a=v&pid=sites&srcid=Y3Jtcy5vcmd8Y2FsY3VsdXN8Z3g6NDMwNzcwYmY2ZTQ2MjE4Mg

There is a quiz on Monday about both Product Rule and Quotient Rule. Be Ready for that.

I feel there is nothing more to say.
So BlueElephant, you are up again.
Feel Free to live any comments!!

About Product Rule

I think the both of them help me understand the product rule. There is a lot of information online. There are some different proofs of product rule online. However, there is a lot of extra information online which I don’t really need. Sometimes we probably just want what we exactly need. Extra information would just make us confused. And a lot of the websites I found don’t provide me the right information. Internet is a really public place. Everyone can put up his or her own ideas online. So wrong information and fake information is inevitable. I think Wikipedia is a good place to find what we want. Even though everyone can edit the content of Wikipedia, most of the information appearing in Wikipedia is very useful and organized. We can simply find exactly what we need at the first sentence, and if we need more details, there is always extra information for us to look at. Textbook is also a useful source, and I feel better to read something that I am actually holding. It is also very simple to find the most important part of product rule in the textbook. The textbook highlights the definition and property of product rule and it is very easy to understand. Example questions and solutions help understand, too. I don’t really have a preference. I think both of the learning sources work for me really well.
Product rule:
Property from the textbook
If y = uv, where u and v are differentiable functions of x, then y' = u'v + uv'
Verbally: Derivative of first times second, plus first times derivative of second.

Simply, take the derivative of the first function times the second function, add this to the product of the derivative of the second fucntion and the first function.

Example:
y = (x^2)*(ln x)
y' = 2xln x + (x^2)*(1/ x) = x + 2xln x

http://en.wikipedia.org/wiki/Product_rule
Check out this.
The product rule is proved by the area of rectangles.
This is very neat.

Concept of calculus Mind map