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.

Derivative of Inverse Trig Functions

Calculus… Episode 2/9/10: The Scribe Post Strikes Back.

Monday we discussed the topic of Derivatives of Inverse Trigonometric Functions
Let’s begin. We started out with a quick refresher on the different trigonometric functions and their individual inverse. Since none of the trig functions pass the horizontal line test because they are periodic, none of them are actually invertible functions or one-to-one functions. So in actuality they are inverse trig relations. Therefore in order to actually create an inverse of the functions you must restrict the domain of each so that they do become one-to-one functions.
This is simply done by taking only half of their corresponding unit circles.

This chart shows all of the inverse trig functions and their derivatives. Illustrating how they are to be used is shown above in those few example equations from class. Below I provided a few links that hopefully will be helpful. Lastly the next scribe post is dammitimmad.


http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/invtrigderivdirectory/InvTrigDeriv.html

See Math

Continuous and Differnetiable



Not a one to one function



Continuous but not Differentiable



Invertible Function



Not Continuous and not Differentiable



Now I see math

Forum Post: Choices

1. For any function that is invertible, the derivative of the inverse of a function at a point is equal to one over the derivative of inverse of the original function.

2.




3.





Is volume an invertible function?
Yes Volume is an invertible function.

4.





5. Using the online graphing tool (right sidebar) or another graphing tool, plot the following four graphs:

(1)





(2)




(3)





(4)





















6. I found the derivative of (1,4/3pi) and then (4/3pi,1), yielding slopes of 12.566 and 1/12.566. The slopes of the two tangents are recipricols of one another.


7. I decided to come to class due in large part to the fact that I felt that I would benefit the most from being able to participate in my education in person and would be able to activitly pursue and ask questions of what we were doing and how to do them. As well I felt if necessary the web material, the virtual classroom would be avialable to me after class to furhter expand upon my knowledge.

Edu Cusp

2. Mark Twain said, “Never let formal education get in the way of your learning.” What did he mean by that? Is technology blurring the boundary between formal and informal learning?


Mark Twain puts it quite eliquently. Education should never stop, inside or outside the class, the pursuit of knowledge is a life long quest. So for many formal class room education gets in the way of their actual success as a person outside the class room. Once you leave a classroom the learning doesn't stop it only changes and becomes a more expansive basis to learn from. At CRMS we participate in the concept of education inside and out. Meaning that our trips our active program and interim are all extremely involve learning processes, not just trips for fun. They provide opportunities to learn about one's self and the world around them, while also encouraging independence and self sufficiency.

This quote also explains that the traditional workings of a classroom should not hinder your learning and should not be the only source for it. You must look beyond the classroom even for your traditional classroom education. For example with the progression of technology there are now many new sources for information that may provide information not found in text books. I have found a number of youtube videos and written examples that have helped in further expanding my knowledge base for the bast two rules that we studied in calculus. Technology has been progressively blurring the line between the classroom, the rest of the world and ultimately the idea of informal versus formal learning.

Education never stops and that has become no more evident than in the current modern era that we live in. With the expansion of technology we will more and more sources of media that provide an education and a smaller and smaller divide between when formal education stops and starts.

Product Rule

While both explanations where helpful in explaining the Product Rule the internet site I found would not have been enough with the book. The book was extremely clear in its definition while also providing a straight forward expample to begin creating further understanding with. As well as the verbal definition, the derivative of the first times the second, plus the first times the derivative of the second. However the site provide a number of more complex examples which could prove to be more useful in the future and more applicable during further practice. Unfortunately the site was limited in the number of examples and was more focused on why this rule makes sense and how to prove that it actually works and is accurate. Ultimately both are moderately useful and work well together but would require more information for a successful watch it, do it, teach it, learning process.

http://en.wikipedia.org/wiki/Product_rule

y'=u'v+uv'
y=x^4cos6x
y'=4x^3cos6x+x^4(-sin6x)*6
y'=4x^3cos6x-6x^4sin6x

Mind Map