Wednesday, June 30, 2010

Capstone Presentation

Hello All,
Here are the slides that I presented today to the MSU capstone committee on the work we did during the 3rd quarter of our calculus class. I hope that it honestly depicts the time and effort we all put into our online adventure. Thank you again for your commitment to the project. I hope that it benefited you as much as it did me.


Cheers and Thanx
Bru

Friday, May 28, 2010

Final Review Slides: May 31, 2010

Hello All,
Here is an overview of what we covered this year in Calculus. It can serve as an initial review for the final exam.
Cheers, Bru

Monday, May 24, 2010

Today's Slides: May 21, 2010

Hello All,
Here are the slides from our introduction into solids of revolution and using a definite integral to calculate their volume.
Cheers, Bru

Monday, May 17, 2010

Today's Slides: May 17, 2010

Hello All,
Here are the slides from our Exploration into 2D apps of the definite integral. (3D apps coming soon!)
Cheers, Bru

Friday, May 14, 2010

Today's Slides: May 14, 2010

Hello All,
Here are today's slides on finding the area between curves.
Cheers, Bru

Thursday, May 13, 2010

Today's Slides: May 12, 2010

Hello All,
Here are the slides from our exploration of some properties of definite integrals.
Cheers, Bru

Thursday, May 6, 2010

Today's Slides: May 5, 2010

Hello All,
Here are today's slides from our discovery of the Fundamental Theorem of Calculus.
Cheers, Bru

Monday, May 3, 2010

Today's Slides: May 3, 2010

Hello All,
Here are the slides from constructing some very special Riemann sums.
Cheers, Bru

Wednesday, April 21, 2010

Today's slides: April 21, 2010

Hello All,
Here are today's slides of our "road trip" to discover the Mean Value Theorem.
Cheers, Bru

Monday, April 19, 2010

Today's Slides: April 19, 2010

Hello All,
We have two sets of slides today. The first one is our review of the entire year of Calculus (to date) in just 7 minutes, all on a single slide!
The second set of slides is our recreation of Rolle's Theorem.
Cheers, Bru

Tuesday, April 13, 2010

Today's Slides: April 13, 2010

Hello All,
Here are today's slides on the definition of the definite integral.
Cheers, Bru

Monday, April 12, 2010

Today's Slides: April 12, 2010

Hello All,
Here are the slides from today's class which introduced you to Riemann sums.
Cheers, Bru

Thursday, April 8, 2010

Forum: A Tale of Two Integrals

We have been working with Auntie Derivative and her Family of Functions, also known as the indefinite integral. We have also worked with the definite integral. Which image below illustrates which type of integral?


Did you pick the correct one? The indefinite integral is a family of functions with a given derivative and the definite integral is the area under a curve. Incredibly, they are related to each other, as we will soon discover!

What method have we used to approximate the definite integral (starts with a "t")? This method uses a strategy developed by Archimedes, considered by many to have been the greatest applied mathematician of antiquity. His method for finding areas under curves laid the groundwork for the invention of calculus by Newton and Leibniz two thousand years later. Read this recent New York Times article by Steven Strogatz,  a professor of applied mathematics at Cornell University. Professor Strogatz discusses Archimedes method of exhaustion and many of the ideas we have covered this year: Zeno's Paradox of Motion, infinity, linear approximations, and the underlying basis for calculus - the concept of a limit. Post a short comment on one "take-away" from the article.

Monday, April 5, 2010

Today's Slides: April 5, 2010

Hello All,
Here are the slides from today's introduction to slope fields.
Cheers, Bru

Wednesday, March 31, 2010

Today's Slides: March 31, 2010

Hello All,
Here are the slides from today's class on the rules of integration.

Cheers, Bru

Tuesday, March 30, 2010

Today's Slides: March 30, 2010

Hello All,
Here are the slides from Exploration 5.1 and our introduction to integrals and integration.

Cheers, Bru

Friday, March 5, 2010

Math Final Group 2

Math Final Project Group 2
Group Member:
YDplusSB, Hyunhwa, J-tron foteen
Materials:

A measuring cylinder
A right circular cone
A plastic bag
A glass
A timer
3 people….

Purpose:

The purpose of our final project is to help us understand calculus espeically the related rate problems better by applying the math into a real world situation. Throughout the process of solving the problem, we could also learn how to edit a video, how to distribute work, and how to work together as a group.

Scenario:
There is a right circular cone with a height of 11.3cm, a radius of 4cm. Initially, there is 15ml amount of water in the cone with a height of 4.85cm. As we unlock the bottom of the cone, the water in the cone will drip with a flow rate of 1.875ml/sec. At the same time, some water is poured into the cone at a flow rate of 0.275ml/sec.

Question:
What’s the rate of change of the radius after 3sec with the volume of 10.45cm3 and the height of 4.226cm?

Little Video:


The actually video quality is low. We use a white backgroup to highlight the actual experiment which consists of a right circular cone, a plastic bag, one glass, and a measuring cylinder.

Check out our solution in WIKI

http://crmscalc2010.pbworks.com/Final-Project#

Ski Movie Final Project

The purpose of this final project is to help us understand related rates through teaching them ourselves. We are also hoping that we can help to teach others and challenge them to a new Related Rates problem. About all everyday scenarios, such as skiing, contain some bit of calculus. We are proposing a scenario, in which two skiers are skiing away from each other. We are going to calculate the rate at which the distance between them is changing. This problem was created by skirdude, secret and Flying Slug.

Two skiers are having an extreme day on Snowmass Mountain. They have been skiing together all day, dropping fatty cliffs and schralping mad gnar. Its the end of the day, and they are getting tired, so they now decide they both want to go down different runs. They are total math buffs and decide to turn this into an awesome Related Rates problem!


You can find our solution here!

And a big shout out to the crew at Aspen for being very patient with us and giving us tons of help!

Thursday, March 4, 2010

Real World Related Rates

Final Project Group 1
Related Rates
Co-Authors: Blitzen, Dammitimmad, and mc Casper.

Materials:
Bowling Ball

Marble Video
Camera
Smooth floor (with minimal friction)
Paper and pen to do the work
Black Box (calculator)
Grey Box (brain)

Purpose: For our final project we were asked to create a related rates problem within the real world using a program to draw the actual data from our experiment. Using the video analysis with a program called logger pro we had all of the data needed to solve the problem at hand.

The Problem: Our experiment consisted of rolling a b
owling ball and a marble away from each other at a 90 degree angle. We executed this experiment on a smooth and level concrete floor indoors. We can assume that both balls were rolling at approximately the same speed (see next paragraph below). Our goal is to find the rate of change of that the distance between the two balls is increasing with respect to time.

The great lengths of assuring a constant velocity:
Time frame of experiment was roughly 2 seconds
Very smooth concrete floor used in experiment
No interference after the initial push off
Air resistance is negligible due to being indoors and
no wind

Figure 1:
Video of actual experiment!



Data:

Graph of our data:
You can see from our graph above that the velocity of the two objects is within minor human error, constant. The only part of the lines that are not constant is the beginning portion of the graph due to the ball's being stationary at the beginning of the video. The slight curve that is also apparent before the constant velocity is reached is due to the initial push from us accelerating the balls and bringing them up to speed.

Using the linear regression on our program (called logger pro), we got the equations for the velocity and displacement of each object individually.

Graphs with the linear regression equations.
(Because the linear equations are difficult to read, you can go to our WikiWork Problem to see the equations of these lines more clearly.)
http://crmscalc2010.pbworks.com/WikiWork-Problem-2

General Overview How To Solve:
After obtaining the data and the linear regressions in loggerpro, we found the velocities using the data begotten from loggerpro. We used the X and Y components of object's velocity to find their total velocity.
Next we chose a random point somewhere from the middle of the graph.
To find the rate of change of the distance between the two objects we used the derivative of Pythagorean formula (see wiki). We substituted in the displacements for both objects into the formula and their velocities to find dz/dt (the related rate of the distance between the two objects with respect to time).

We choose to repeat this process for three separate points to see how accurate and consistent our answers were.

After completeing our project we determined that there was very little human error in our experiment because all three final answers were only one tenth different from one another.
***See WikiWork problem for full explination of calculations.***

Final Problem (one last time):
What is the rate at which the distance between the two objects is increasing? The velocity of the bowling ball is 37.957 inches per second. The velocity of the marble is 43.52 inches per second.

***Please see our WikiWork page to see the calculations and solution to this problem***
http://crmscalc2010.pbworks.com/WikiWork-Problem-2

Final Project: The Related Rates Time Machine

Group 4
Nom de plumes: babar, WinnPlot, Tubby.

The purpose of this Final Project was to create a unique related rates problem from a real world situation and then solve this problem, thus expanding our knowledge of related rates, and their application in the real world.




image source:http://www.friedpost.com/wp-content/uploads/2008/10/time-machine.jpg


Young Freddy Newton was trying to make it big in the stock market, and decided to build a time machine (see image) so he would be sure to buy the right Stock. Unfortunately the time machine malfunctioned sending Freddy into a ripple of time and space and landing him in the land of dinosaurs with only a bendy straw in his possession. Freddy was so thirsty upon arrival but could not find any clean water. Finally after three weeks of wandering the land aimlessly Freddy came upon a bowl, that we assume is a half-sphere filled with prehistoric sludge. It had a volume of 355cubic centimeters and a radius at the top of 6.75centimeters. It takes him 22.65 seconds to consume the sludge. Freddy uses his handy dandy bendy straw to drink the sludge for sustenance. We are going to assume that he drinks at a constant rate. Below is a video of this event:




So, the related rates question is:
If a semi-sphere with a volume of 355 cubic centimeters filled with prehistoric sludge takes 22.64 seconds to consume what is the rate, in minutes, at which the height of sludge in the bowl is changing at the moment when the sludge is at 2 centimeters?


Here is a hyperlink to the solution:
http://crmscalc2010.pbworks.com/Final-Project-Group-4#view=page

Wednesday, March 3, 2010

Group 5's Final Project Presentation

MMMhmmm....Ice Cream....


Beston, Marley, and BlueElephants's Final Project Presentation


The purpose of this final project is for us to watch, learn, and teach a real world application of calculus. Our problem involves a conical container and a volume of liquid that is flowing out of the bottom. The purpose is to find what the rate of change of the volume with respect to time is as the liquid flows out at a certain height.
In our problem we measured the rate of change of the ice cream flowing out of an ice cream cone with respect to time.

RELATED RATES
PROBLEM:
An ice cream cone has a radius of 2.5 cm at the top and has a height of 10.2 cm. If the height of the melted ice cream is decreasing at a rate of 0.35228 cm/s, how fast is the volume of the melted ice cream decreasing when the height is 8.271cm?

Materials:

-ice cream cone
-ice cream
-microwave
-knife

Instructions:

Take the ice cream cone and cut off the very tip so that there is a small hole. Measure radius and height of cone. Melt ice cream in microwave. Fill the ice cream cone up with melted ice cream. Film using loggerpro. Move knife down as level of ice cream decreases. Using loggerpro, plot data points based off of level of knife in relation to the base of the cone.




Here is a delightful video of us, showing you, our data collection...





To see our solution please go to the Wiki.


MMMhmmm....Ice cream...But don't let it all melt away...



Photo Credits:

Lady eating ice cream:http://repossibility.com/wp-content/uploads/2009/08/Melting-Ice-Cream-Lady-300x300.jpg
Earth melting:http://collegian.csufresno.edu/a/wp-content/uploads/2008/02/f_icecream.jpg

Thursday, February 25, 2010

Future Math

It seems to me that every year there is new, incredibly ground breaking technology. Math included. This technology always is portrayed as the "future." Its gonna change the world around us! Well, I believe that we do that by ourselves. We already have the technologies to change our world, how we use should be the most pressing issue.

Currently, everything we create is built in order to streamline the process. As shown in the article, shopping is included. The fact that a company has the rights to what music I'll be buying next, or my favorite author may, in fact, be quite frightening. I am a believer in the fact that the more this technology piles on, the more cautious we need to be about how we use it. Computers already have capabilities far beyond that of any human. As a race, we need to hold true to our roots. We must embrace technology in a way that we do not inhibit our natural tendencies.

I don't mean to be all superficial and such, but is this really that far from possible?...

Alright, maybe thats a little far fetched. But, I would say that we are likely on our way there.

I think that all this technology is definitely beneficial and could greatly change the world we live in. It has the opportunity to benefit all of us. However, I would stress that we should keep in mind where we would like to be, and where we are going.

Tuesday, February 23, 2010

Related Rates 2.0

What are Related Rates?
http://www.donself.com/images/confused-baby.bmp

A related rate problem has a few qualities:

a. 2 changing quantities
b. Hopefully enough information about those quantities

c. And (as with most Calculus problems) asks you to figure out the rate at which on is changing


There are a few tricks to helping you solve these most complex problems:

1. DRAW A PICTURE!
You might think your too cool for school... but guess what? Your not.
Drawing a picture gives you time to organize and think, which could help with a breakthrough.

2. Identify the quantities
Determine and label, which quantities can change (variables) and which are constants?
Again, keeping these organized is your road to success.

3. Algebra, Algebra, Algebra...
Write your equation... remember what you learned in Algebra? You should!

4. Calculus... your new friend
Use your newly sharpened Calculus skills to differentiate the equation. This should be easy as pie... right?

5. Find the rates of change
Dissect the problem. Find out what quantities could be rates of change (I'm talking about units here!)

6. Substitute!
Here comes the fun. Now you can work with your sweet equation to answer the problem.

Wait! Don't forget... this was a word problem if I remember correctly. Which means......?

Answer in a complete sentence, with units of course.

This is a good site to practice... in case you feel you need to work on your skills.

I know that this is the kind of problems we were doing last week, but just a little play by play to help anyone who is still confused out.



Don't forget the take home quiz assigned in class... all about Related Rates.

And we have a new final project about Related Rates coming up, so start brainstorming and coming up with fun creative ideas.

The next scribe will be Blitzen.

http://www.timtim.com/public/images/drawings/large/Skier.gif
-Skirdude-

Final Project: Learning in Motion

 

We’ve discussed the learning paradigm of “Watch it, Do it, Teach it”. It is one thing to watch someone do something; still another to do it yourself; but quite another to teach it to someone else. Real learning comes from teaching. Learning also does not occur in a vacuum. We learn through our interactions with others and with our environment. Collaboration is an important life-skill for the 21st century global citizen.

The goal of this final project is to work together to teach a calculus concept
and by doing so learn at the same time.

Nowhere is it more evident that calculus is the mathematics of change than in related rates problems. When two quantities change over time, the rates of their change are often related to each other. That’s one of the differences between algebra and calculus. In algebra we study the relationship between quantities. In calculus we study the rates of change of those quantities. In this respect, an algebraic equation is a static snapshot of two quantities frozen in time, while a differential equation of calculus represents a dynamic video of those quantities set in motion.

Within each group, the final project consists of three tasks:

PRESENT a related rates problem. Select a scenario from the pool of classic related rates problems or create an original situation with similar parameters. Act out the scenario either by video or by stitching together a storyline of still photos. Be creative! Use toys, props, or other inventive ways to illustrate your scenario (puppets, claymation, etc.). Here are some examples to spark your imagination.
Filling a cylinder
Baseball runner
Moving sea creatures
Stone thrown in lake
Flying pig
Reeling in the big fish
Your related rates problem should be presented clearly and concisely; i.e. in a way that it could be used as a homework or test problem. Make sure that it is fully-specified, but not redundant (that is, there can’t be too little or too much information to solve the problem). Your problem should not be ridiculously difficult, nor should it be so simple that it is practically trivial. It must require calculus to solve.

SOLVE your related rates problem. The solution will include a written description of the problem. All variables used to model the scenario will be clearly defined. The solution will contain a graphic to illustrate a “snapshot” of the scenario; and each step of the solution will be properly annotated.

REFLECT on your work on this project.
Each member of the group will describe his/her contribution to the project.
Each member of the group will write a reflection on what he/she learned from working on the final project. This may include the use of a new Web 2.0 tool or computer skill, thoughts on collaborative group work, or insight into related rates problems.

The presentation of your problem will be posted to our blog. It will begin with an introduction which includes a statement of purpose, the nom de plume of each group member, and a brief description of the project scenario. After the presentation, provide a hyperlink to our wiki where you will post the solution and reflection portions of the project. Here is the rubric for the project.

The finished project is due by 3:00 pm on Friday, March 5. This final project will be a reflection of your learning, group effort, and commitment to excellence. I hope that you have fun teaching the concept of related rates to others who will benefit from your knowledge.

Cheers, Bru

Sunday, February 21, 2010

Math in our everyday life!!

“There has never been a good time to be a mathematician.”

In today’s society, everything falls on math. All the careers have some math concept involved in somehow. This has been the case for several years, but nowadays, as evolutions keeps on going farther, the need of math increases. Statistics is used in the medical field to determinate the improvement of health conditions, in business to improve the quality of work done, in security agencies to insure the safety of the citizens.

First, this article explains the pros of math and its development. The world is now dominated by Web2.0. Education, entertainment, shopping, careers, etc. everything can be done online, and this won’t be possible without the contributions of mathematicians. Since they are much needed in today’s society, the article suggests that students, especially in America, should be encouraged to pursue their careers in math or math related major fields. The example is given in the case of the NSA which employs only US citizens. From here, it can be concluded that the security of Americans is limited, since it is less than what it could be.

The other side of the article explains how these ongoing improvements in the math’s world are quite disturbing. Since people are concerned about the privacy problem, it’s hard to make improvement in medicine for example. Since much of these math based programs use people’s private information, there have been some complaints about this, and they are refusing to give up their information to the public. This pushed mathematicians, doctors and other concerned people to look for other alternatives in their problem solving strategies

Overall, this article made me think about all the connections that can be made between the world of math, which is always perfect (with exact answers), and the real world, which is always a cumulative result of more or less estimations and probabilities. There have been some times when, in the middle of class or while doing a math problem, I said to myself “when am I ever going to use this?” This article reminded me that’s always a rhetorical question I have in mind, that somewhere in the back of my conscious mind I know that I will use it. It also reminded me the saying that says “Math is related to Physics, Physics related to Chemistry, Chemistry related to Biology, and Biology related to Life.” So, in the end, math is related to our lives, either directly or indirectly.

Ahhh Math!!

This article mainly focuses on the fact that we live in a predominantly technology focused world which means math is becoming more apparent in our everyday lives. Whether we know it or not, every time we check our email, or watch tv, math played a big part in getting that type of information into our homes. Since computers became popular around the world, it is much easier for companies to track their products and to see what their customers really think. This type of media, I think, makes the world a more communal place since everyone gets to express their views and show them to the whole world.
I think that the math the article talks about is more behind the scenes more most of the population. Many people don't know how much math goes into their daily activities, and they will never need to know or be exposed to it in any way. I think you would only really realize how big of a role math plays in our technological society if you had a job as a computer programmer, or your job entailed a lot of statistics. To use computers the average person doesn't need to know much about math, in fact it seems like each new version of various operating systems make it so there is less and less calculations and knowledge involved. Now almost anyone can use a computer. I think the world is moving towards simplicity. Only a select few will know all the math involved in shaping our society. Computer programming knowledge will be the new skilled craftsmen. Instead of needing painters and woodworkers, in the future we will need more computer programmers.

I found this video that shows some of the math involved in computer programming:

Math is Super

This article really made me think about my future. It seems as though, if you want to be someone with influence in the world, your best bet is to become a math major. Baker talks of how math greatly influences the world we live in. Although i did not fully understand the relationship, I understood that it math is very critical in the world today. Most everything in our daily lives can be analyzed in number because of patterns that exist. Words, movements and emotions can all be described in numbers. Its all quite amazing. Businesses use these patterns to predict what we people want in order to sell products and such. Internet, for example, is monitored by computers that gather data from keywords that we type to build a sort of profile of each person in order to see what we want. These companies use the data to advertise their products. Though this analyzation of the internet, companies can find out what is popular among people fairly easily. This is a concern to many because it is in some way an invasion of our privacy.  There are debates regarding the monitoring of the internet and phones in congress. On the hand, these computers can pick up suspicious behavior that could help with the war on terrorism. Companies are working to protect privacy as well as get enough info to build good data. All these companies are at the frontier of the technological movement of mathematics playing a huge part in our daily lives. And the workers at these companies are kids straight out of college who are good at math. And they make a good amount of money if they score a big idea that another company wants to buy. Its a good place to be, which make me consider taking that route. Plus, the US needs more locals to be these math geniuses because so many of the people working at these companies are foreign born. Its also kind of scary how much math can do. How it can predict what people want and how it can pick up conversations through computers that were intended for few people. Our whole way of life is being converted into numbers. Although computers have the capability to cure illnesses and stuff in is important to note that eventually they may turn on us like they did in terminator, just a thought. In conclusion, like Baker states, it is a good time to know math because it is what is moving the world forward. 

Math is Everywhere

The article was about how math is used; it is used in everything now. It is used to track the way people buy products, where they buy products, and the way they react to ads. Google uses it to see which sites people are clicking on, and what sites they are buying things from. All of this monitoring, does have it’s downsides though, even though companies will be saving money what about people’s personal privacy, do they still deserve that?

I think that the main problem with this whole thing is that idea of lost privacy. I don’t necessarily want people watching all of the things that I buy, and all of the things that I click on the Internet even if it isn’t inappropriate. So as the article pointed out I would probably take measures to see that the companies couldn’t track what I said, bought and clicked on. The article also pointed out that the government is using the same data to find terrorists, and track diseases. So it is a mixed bag whether we should trust this whole database of information about us. What is interesting and more concrete though is that people who are going into college right now should probably major in something math related if they are at all into it because that is where the market is. At least that is what the article said. I disagree. I think that it would be sad if all these bright people decided to go into math simply because that is where the jobs lie. People should follow their passion. This was an interesting article but I disagree with it in some aspects, I don’t think that our lives should be so closely monitored even if it does help homeland security or our health, it isn’t natural, or healthy in my opinion. And I don’t want my life to be run by either a government or by industries.

Math Changes The World Once Agian

The article directly handles the effects of a rapidly changing world and how Calculus and other even more advances areas in the field of mathematics can be used to not only describe, but predict and change our future. They quite clearly state that the need for advanced mathematics is growing nad the those who will be the most successful in the job world will be those who have atleast some portion of advanced mathematics.

How Math Transforms Industries discusses many different fields ranging from business to media and explains how each has and will be effected by further advances in technology and mathematics. How Much Math Do We Need to Know discusses just that, how much is going to be enough? Touching on Calculus, statiscs, advanced algebra and Geometry. Pointing out that in extremely advanced Geometry, techniques were used from that field to create search engines such as Google, and Yahoo. How? I don't know, but it says thats how they did it.

For me this article to me wass incredibly fasinating. The fact that we are moving into an age where quite simply understanding and being able to apply multiple types of advanced math to pieces of data,collections of information, to quite simply predict the future. Adjust plans, marketing schemes, business models, all based off of data. This following paragraph clearly illustrates a prime example of what has been done and what is still to come form this field of advanced mathematics in business.


"The clearest example of math's disruptive power is in advertising. There Google and other searchcompanies built on math are turning an industry that grew on ideas, hunches, and personalrelationships into a series of calculations. They can pull it off because, quite simply, they know wheretheir prospective customers are browsing, what they click on, and often, what they buy. Internetcompanies use this data not only to profile customers but also to pitch for more contracts. Some 18months ago, 3blue-chip companies, from Procter & Gamble Co. () to Walt Disney Co. (), underwent a series of tests promoted by the Interactive Advertising Bureau, an industry group. These studiescrunched consumer data to measure the effectiveness of advertising in a host of media. The resultscame back in hard numbers. They indicated, for example, that Ford Motor Co. () could have sold anadditional $625 million worth of trucks if it had lifted its online ad budget from 2.5% to 6% of the total. Ford responded vigorously: Last August it announced plans to move up to 30% of its billion adbudget into media targeted to individual customers, half of it through online advertising. Such movesare sure to generate even more data, giving greater clout to the numbers people."

http://www.businessweek.com/print/magazine/content/06_04/b3968001.htm?chan=gl (2 of 6)1/17/2006 2:47:50 AM

While clearly beyond my understanding of how they can make these predictions, i find it amazing that as math has become more and more complicated it has, due to advances in technology only become more and more applicable in the modern work force.

As time progresses mathematic literacy is going to become more and more relavant and I believe more and more a part of our daily lives. So while at times maths and science appear to be largely irrelavant to our futures and what we may possibly want to do with our lives, they may prove to be by far the most important pieces of information we learn in our time in school.

Math is ruling the world

I'm not sure if I'm being sarcastic right now, but this article was truly interesting to me. It explained the close relationships between mathematics, numbers and our daily life containing internet.

Cover story starts with the giant title saying that math will rock the world which is totally true. It starts the article with the system that organize, and structures any written information published by its context, concept, and theme. By doing so, it says that it needs numbers and math to accomplish it. In one sense this sounds totally new to someone, but in other side, this is just a basic common sense that already has been known to the public.

Since the beginning of the construction of computer, math always has always been in people's life style. Like it stated in the article, math is essential to everyday life. Everything is organized with math equations, and everything is programed with algorithms online, and companies have been dealing with their costumers and products based on mathematical models.

Issue of privacy has to come right after that. In the several articles in the cover story it stated about how individual's privacy is becoming public by the development of technology based on math. People's lives have been monitored and gathered as a data for the bigger companies. This is one of the greatest fear that people might have. For the company they have to do this research in order to gain biggest possible profit that could be happen.

Mathematician will be the largest group of people who are ruling the world. It is true that most of the job will provide math skills. Highest rates of mathematics elites will gain the most profit. Math will rock the world; it has been and it will.

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…..

How Far Can Math Take Us?

In the first portion of the cover story Math Will Rock Your World, Steven Baker discussed the different applications of math in our world today. The first section discussed the conversion of words into math in order to classify and organize them. He gave the example of Neal Goldman, a math entrepreneur who takes press articles and blog posts and groups them together with related pieces based on their content. The article also discussed mathematical models and their ability to predict a variety of different things such as how to become more productive, make a profit, etc. Through collecting data, they use their findings to establish trends. One potential problem with this system lies with the population and their ability to breech the system. Although this system appears very dependable it also brings its challenges for the United States and the world. As a nation we must work towards creating more mathematicians at home and prevent outsourcing by preparing our students for the business world. Another challenge math entrepreneurs face is individual privacy. They must discover a means of invading privacy to the least extent possible by trying to share group information without sacrificing that of the individual . It surprised me how much math manifests itself in our daily lives. "Some models predict what music we'll buy, others figure out which worker is best equipped for a particular job." I never realized the full potential of math in everything we do. I was also astounded by the extent to which math can invade our privacy and how frequently numbers have begun to replace the individual.
The second portion of the cover story Online Extra: The NSA: Security in Numbers discussed the usage of numbers in terms of security. Baker discussed the NSA's role and how they use math to help figure out terrorist plots and other issues of security. One of the challenges the NSA faces manifests itself in recruiting its mathematicians. They are faced with competition from Google, Yahoo and other organizations. How are they managing? They offer a more quiet, stable lifestyle, which is especially more appealing to women. I thought it was interesting that they were looking for younger employees who did not know the company as well. I assumed they would want older, more experienced workers. I found the selection process quite interesting in that it is a contest which acts as somewhat of an advisory for their decisions.
The third portion Online Extra: Search Advertising by the Numbers discussed bidding on keywords. Baker specifically discussed Imran Khan and his involvement in E-Loan. Kahn makes sure those who are looking for his product will surely find it. Parts of this passage made it seem like math can often get a little bit too invasive, "It (numbers) enables marketers to track customer behavior, and replaces hunches with science." It may have just been the way I read into the article, but that sounds as though it could be problematic in terms of individual privacy issues. I also found the discussion of bidding on keywords and the science behind it a bit confusing.
How Much Math Do We Need to Know? summed up the different uses of Calculus, Algebra and Geometry, Statistics and Probablility, and Math Tools in different careers. Some of the associations are not as obvious as they seem, for example, advanced geometry is used not only in floor tiling but also in designing search engines. With the growing demand for mathematics based, or even just related professions, knowing your math might prove to be helpful. I guess calculus really will pay off in the long run!
How Math Transforms Industries discussed the specific uses of mathematics in many different fields, such as consulting, police and marketing and the media. Who knew a company could "turn written articles into bits of geometry and organize them in a virtual library?" and eventually these automatic systems could make editors obsolete. I found it amazing how much of a difference math has a potential of making on our society. We always talk about technology taking over life as we know it, but what about math?

Math Has Rocked My World

In the article "Quantifying Humanity" the author discusses the uses of math in the business and technological worlds. The author specifically references each math genre (calculus, geometry, statistics etc.) and gives examples of how they can improve technology and create jobs for people in any field of study. For example he talks about how statistics is a major contributer in every job market because whether you are dealing with fashion trends, environmental patterns or oil sales you will be analyzing large sets of data and comparing trends. The article also talks about the importance of calculus in technological advancements and how geometry is not just for laying tile floors but is a huge aspect of engineering.

I personally thought this article was very interesting. I already knew that math was a huge part of the future, but had no idea of the relevance it serves in our every day lives. It was very interesting to learn about the enormous variety professions that use math to succeed. I have never really thought about how math is a huge part of the sales industry or how it helps major distributers like Ford and even insurance companies. It was great for me to see all of the practical uses of math, because it reminded me of why I continue to take math classes and work hard to understand every aspect of math. Math is not my strongest subject, but I believe that it will create many opportunities for me, as well as the rest of the world, in the future. Math has definitely rocked my world, has it rocked yours?

Math: The Future!

This article talked about how math is beginning to become more and more a bigger part of our everyday lives. One way it does this for example, is using math to analyze how well advertising is doing for a company, and how changing advertising can effect profits and sales. It is not limited to this though. Essentially what this article was saying is that math can be used to model and analyze just about everything in the world. Machines, productivity, security, sales, even humans. Another thing that I found really interesting was how important this math really is. The top mathematicians in the world, a select few, are becoming some of the highest paid people. I never would of thought that math would be getting you a 6 figure salary right out of college. This just goes to show how important and how helpful these models are for companies. Another thing it talked about is how these models can be an invasion of privacy, but I didn't really see how. For the most part, I see these models as looking at numbers not people. It turns people into numbers and so I don't really see the invasion of privacy, unless people feel invaded being turned into numbers. It is really interesting though, to think that everything can be justified with numbers.
This is one thing the article reminded me of was the movie Pi, an artistic, mind-blowing thriller about a paranoid mathematician who sees math everywhere and is one the verge of discovering the unifying number that explains everything. Here's a trailer:




The three points he makes about math being everywhere and thus it being able to explain the patterns everywhere in our world is pretty interesting, and relates back to this article. When I first saw this movie, I thought it was a little far-fetched, but now... I'm not so sure. The thing that really got me was that they're working on ways to model human behavior, a supposedly random and unpredictable thing. Maybe math is everywhere, maybe eventually we'll be able to see the patterns present in nature, and maybe someday we can use that knowledge of the patterns for the betterment of humanity and our world. We'll just have to wait and see.

Math Geeks Will Rule the World

In the cover story in Business Week, Steven Baker addressed how math is becoming necessary in today's world. Because our world is now filled with oceans of data, math is being used more and more to 'mine', interpret, and use the data. The beginning of the article talked about how mathematical models can be used by companies to increase revenue:

"These studies crunched consumer data to measure the effectiveness of advertising in a host of media. The results came back in hard numbers. They indicated, for example, that Ford Motor Co. () could have sold an additional $625 million worth of trucks if it had lifted its online ad budget from 2.5% to 6% of the total."(3).

This kind of data is hugely valuable and could be potentially used on a federal level to calculate spending in the government. A lot of the article, however, talked about how math can be used with people, "The power of mathematicians to make sense of personal data and to model the behavior of individuals will inevitably continue to erode privacy." (2). Companies can use math to quantify and analyze their consumers and use that to create effective advertising.

I feel that, if taken too far, this could lead to a bad future. If we live in a world where every person is one of several million that fit a certain profile, that will be used for advertising, our society will continue to be controlled by media and consumerism. I once read a book call Fahrenheit 451, and this article reminded me of that book. In the book, books were banned, and nobody ever had independent thoughts or opinions. Everyone was stuffed full of information and data, but never taught to think about it or draw conclusions from it. Of course, this is a huge exaggeration of our world, but I feel that if the world moves more towards machines, and numbers, and data that generalize society into numerical patterns and equations, the opportunity for free thought and imagination will become less.

As for the part about how what we're leaning now is actually going to help us in the future, I think the importance of knowing high level math is overestimated. Really, we only need a few geniuses to write the computer programs and then the computers do all the math. I guess though, when math geeks and computers rule the world, those with calculus level math education have a better chance of survival.

Will Math Rock My World?

"The next Jonas Salk will be a mathematician, not a doctor." (3) The article 'Math Will Rock Your World' in BusinessWeek explains why.

This article is essentially an overview of one of the directions that math is going in today's world. It focuses on how applied math is becoming increasingly valuable in the world of computer sciences and virtual analysis. Today, those programmers who can write the best algorithms or mine the most crucial data from the internet and its vast quantity of 'unstructured data,' are becoming increasingly valuable. Programs that sift through thousands of blogs, articles, advertisements, etc., and can quantify their results in a way that can create profit are not only becoming more numerous but also more accurate and because of that, more valuable. Because there is such a host of information on the web, the algorithms that are able to pick out useful patterns and tendencies are becoming the new '.com's' of our world. And the people who are math savvy are being increasingly rewarded both monetarily and with power and position.

Beyond that, there was a huge emphasis on humans being transformed into points on a graph. Our behavior, race, achievements, socioeconomic status, and anything else that can be seen as an essential character brick, are being transformed into a statistic on a chart.
“The clearest example of math's disruptive power is in advertising. There Google and other search companies built on math are turning an industry that grew on ideas, hunches, and personal relationships into a series of calculations...Rising flows of data give companies the intelligence to home in on the individual customer. Internet marketers are the natural leaders, but traditional businesses are following suit. Gary W. Loveman, CEO of casino giant Harrah's Entertainment Inc. () and a former Harvard B-school professor, has led the company to build individual profiles of millions of Harrah's customers. The models include gamblers' ages, gender, and Zip codes, as well as the amount of time they spent gambling and how much they won or lost. These data enable Harrah's to study gambling through a host of variables and to target individuals with offers, from getaway weekends to gourmet dining, calculated to maximize returns. In the last five years, Harrah's has averaged 22% annual growth, and its stock has nearly tripled...[Another company scans the web for articles and blogs and] breaks down English messages into the smallest components -- words, phrases, grammar, even emotions -- and turns them into math.” (3-4)

Essentially, that which has been reserved for the qualitative side of analysis is now being analyzed quantitatively.

When I first read this, I was somewhat disturbed. "What right does some algorithm have to turn me into math?! What a gross violation of my humanity!," I thought. But then I realized that if these companies are finding ways to successfully analyze things that have so long been considered subjective, then maybe this isn't a case of the proverbial David getting squashed by Goliath. It's not as if these programmers are making things up about me, they are doing nothing other than analyzing what is already there. And what's so horrible about that? Well, this is where I'm split.

Mystery has always been an essential part of the human experience. Not knowing everything about the present and future has allowed for creativity to flourish and exploration thrive. But, if said mystery is reduced to a margin of triviality, then maybe the exploratory drive that has propelled humanity through the ages will be replaced by a sequential system with the sole goal of profit, eliminating many creative freedoms we now enjoy today. But, on the other hand, maybe they won't be. Maybe computer programs will never be able to map the impetuousness of human nature, and will simply allow us to explore more efficiently, with a more defined direction and with greater success.

But as of now, I'm torn, which will it be?

Quotes cited:

http://www.math.uiuc.edu/MSS/2006-Spring/MathWillRockYourWorld.pdf

Scribe Post Feb 19th

Related Rates!!

Followed by last scribe post, in this post we will talk about the extension of Porky Problem.

This post will follow the exploration done in class: Section 4.9 A: Related Rates Warm Up



Review!
Calculus is the mathematics of change, and everything changes with respect to time.

In algebra we study the relationship between variables.

In calculus we study the relationship between the rate of change of variables.


There are infinite amount of scenarios that can be produced.
- A bathtub is filling at the rate of 2gal/min
- A balloon is deflating at a rate of 3 cubic centimeters/second
- A football is kicked with an initial upward velocity of 30yd/s

Lets translate these scenarios into mathematical models!
all theses scenarios are rates volume changing respect to time.





Now let's play with some real related rates problems!
Make sure you have the exploration in front of you!

Rippling Water Problem

- This problem deals with the radius of the circle, and the area.
Therefore we should write out the equation involving two different variables.

Let A be Area

Now we are using Implicit Differentiation
to express the rate of change of the area of the circle with respect to time t.

Process starts with stating that this equation will be derived with respect to variable.


Use chain rule to implicitly differentiate the equation.


This is the hardest part where everyone is having hard time, or at least some of us!!
It is simple, let's look at again.

- This is our original equation

each of variables, in this case A and r, is a function composed with t.
Since the letter r itself is a function, outside function is squared, and inside function is r

Using chain rule,
derive the outside, leave inside alone

- We get the result.

now we have to multiply the derivative of inside function, which is r'
However, since the function r is the function of t, we can also write out the derivative of r in different form.


It's the change in numerator over change in denominator.
This is why there is additional fraction representing derivative after each implicit differentiations.

This is how to do the implicit differentiation relating two different rates.
Rest of the question and answers are posted in Bru's post of Friday's class.
If there is any additional question, please let me know.

-Hyunhwa-


:0 Our next Scribe Post will be by Skirdude