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?

Choices

Derivative of the Inverse of a Function:

1. If f(x) is an invertible function, then for any point on an invertible function, the derivative of the inverse of the function evaluated at b is equal to the reciprocal of the derivative of the function evaluated at a.

2. If f(x) is an invertible function, then for any point (a,b) of f(x):

3. The volume of a sphere is a function of its radius:

Is volume an invertible function?

”Why yes indeed it is”

4. Inverse Function

5. Graph of:

(2) Choose any point (1,4.188) on V(r) and graph the tangent line through this point (Blue)(1) The volume function, V(r) (black)

(3) The inverse function r(V) (red)

(4) The tangent line through the “mirror” point on the graph of the inverse function. (Green)

6. OH MY! The tangents are reciprocals!

Function of the tangent line for V(r) at point (1,4.188)

Function of the tangent line for r(V) at point (4.188,1)

7. I am a strong believer in attending Calculus. I like having the opportunity to ask questions an see what specifically I have trouble understanding as well as listening to a variety of explanations from Bru and other students. I also seem to struggle with the Internet and technology in general so good old-fashioned pencil and paper helps me take in the material much better. Lastly, I am a procrastinator/ minimalist, so having the time to sit down in class provides a much more productive learning experience for me.

I See Functions!

Invertible

LINK: http://www.flickr.com/photos/47183167@N03/4325838211/

Continuous & Differentiable

LINK:http://www.flickr.com/photos/47183167@N03/4326566468/in/photostream/

Non One-to-One

LINK:http://www.flickr.com/photos/47183167@N03/4326552974/

Continuous, Non Differentiable

LINK:http://www.flickr.com/photos/47183167@N03/4325766571/in/photostream/

Not Continuous or Differentiable

LINK:http://www.flickr.com/photos/47183167@N03/4326444560/in/photostream/

Preparing for Jobs that Don't Exist!

“… schools are preparing students for jobs that don’t yet exist…with technologies that haven’t been invented … in order to solve problems we don’t even know are problems yet …” using technology that quickly becomes obsolete. If all this is true, then what should schools be teaching?

I think that it is very true that we are all preparing ourselves for a world that we know nothing about, however, I think it is very easy for us to prepare for this unknown. I think the best things that teachers can teach students are problems solving skills. Though we may not know what awaits us in the future, we can prepare for how we adapt to it by simply practicing adapting. Our blog for example, contains the same math that has been taught in the world for decades, while also teaching us how master new skills in the up and coming electronic world. The world's way of connecting and working is shifting into an electronic era and by adapting to the current technological changes we will be more prepared for whatever changes lie ahead. Teachers teach us to learn, from that we can learn to do anything!!!

Product Rule for visual Learners

When searching the internet for the product rule i stumbled upon a Youtube video. As a visual learner, i found it very helpful because the man gave an easy (non mathy) way to understand the procedure of the power rule. Also it allowed me to watch and listen to someone solving equations. However, the textbook gave a much more in depth explanation of what the Product Rule is. I found that the textbook was better for understanding the concept, but the video was much more helpful for explanations.

Product rule:

If f and g are differentiable functions, then the derivative of the product fg is:

(fg) '(x) = f(x) g '(x) + g(x) f '(x)

Example:f(x)=g(x)(h(x))f(x)=5x^3sin4xf'(x)=(15x^2 (sin4x))+(4cos(4x)(5x^3))

link:http://www.youtube.com/watch?v=uPCjqfT0Ixg

Magnificent Mind Map