User:JasonYerardiMath

About Me
I love math!

Five Things I Learned About Wikipedia and Wikiversity
I've learned multitudes of various aspects of Wikipedia and Wikiversity over the past couple weeks. This short list highlights some of the more interesting things I've discovered. I've included topics that are technically oriented as well as general topics, such as the staggering amount of legal paperwork that exists in order for all of this material to be "free and open" in a legal manner.

 
 * 1) I learned that Wikiversity, even while still in its youth, can be a very valuable resource for organizing a full course comprising scholarly material. This is especially true as more and more academics/scholars add new sections, extend existing sections, and so on. Wikiversity is a very powerful easy-to-use tool that facilitates collaboration and has great potential to become a widely used tool in academia.
 * 2) I learned that there is an incredible base of knowledge on Wikipedia covering every imaginable topic one might conceive. Through reading the Wikipedia pages for this week's classes, though, I found that some material is accurate and presented very well, while other pages are either stubs with little information or a page that lacks citations, references, etc., thereby causing its academic merit to be questioned.
 * 3) I was surprised and glad to learn that these sites use LaTeX (or variants thereof) to formulate material, such as math formulas, which can't be displayed using the regular Wiki grammar constructs. I especially like the abstraction of the complicated LaTeX from the relatively simple Wiki grammar.
 * 4) I learned that there is a huge volume of legal material that defines entities and the allowable actions they can legally perform with digital media. By entities, I mean the groups of people who maintain organizations such as GNU (GPL), Creative Commons, and other public domain sources. I have worked with GPL-based systems (e.g., Linux) for many years and never realized the complexity of the legal issues behind this "free software" and "public domain" content.
 * 5) I learned the differences between Wikipedia and Wikiversity, and why it's important to maintain educational-oriented material separately in Wikiversity and not merge it with pure reference material provided by Wikipedia. A publicly available central resource of free editable scholarly material, as well as the ability to easily create and manage courses through the system, was a marvelous idea. I am glad that I am now aware of Wikiversity.

A Complicated Mathematical Formula: Polar Coordinate Form of Complex Numbers
The formula below is from my Modern Algebra I course. It is a formula that defines the multiplication of two complex numbers in terms of polar coordinates. The equation was retrieved from the Wikipedia page "Polar coordinate system," which I found during reading that page for help understanding the formula. The reference is given at the bottom of this page.

Given two complex numbers z1 = r1(cos φ1 + isin φ1) and z2 =r2(cos φ2 + isin φ2) the formula for multiplication is
 * $$z_1 z_2 = r_1 r_2 (\cos(\varphi_1 + \varphi_2) + i \sin(\varphi_1 + \varphi_2)).\,$$

My Proposed Edit on the Talk Page for the Rate of Convergence Page
Here is the link to my proposed edit: http://en.wikipedia.org/wiki/Talk:Rate_of_convergence#Correction_of_Citation_for_Convergence_of_Secant_Method.3B

As mentioned in my professor's review to me, the error was relatively small and not of high significance given its context. I was also incorrect in stating that there should be a link to Wikipedia's "golden ratio" article -- in fact, such a link did exist. In the future, I will consider posting proposed edits on a Talk page only after thorough review. I still think this article can be improved, and so I propose a revised and more detailed edit below. (I will await my professor's suggestions before posting on the Talk page for discussion.)

In my original proposal, I stated that the golden ratio should be mentioned more explicitly, but I did not fully articulate my concern. While there is a link to its Wikipedia article, the problem is that the link is plain text and only one letter, making it difficult to detect. The citation's small text further contributes to this problem. But most important is that even such minor issues today can become much more significant given the rapid rise in use of mobile devices (smart phones, tablets, etc.) to access the internet.

I therefore propose the following two changes to this article: (1) explicitly state "golden ratio" and make it part of the link so as to increase its visibility and (2) reference this number both in its exact form (an inline formula) and an approximation. These changes would significantly increase the visibility of the citation's link to the golden ratio page while emphasizing the importance of this number.