Lego Grad Student

The biggest coffee break/procrastination craze sweeping the grad student world since phdcomics or xkcdhttp://legogradstudent.tumblr.com/

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The Winners Write the Textbook

 Guest Author: Dan Walls

It is said that the winners write history. While usually this is reserved for the perspectives in history textbooks and other writings, it also finds true in the evolution of mathematical history as well. Beg to differ? Ask Recorde. He has Leibniz and his winning calculus notation to thank.

Daniel Walls_925508_assignsubmission_file_Sh to ch to x DW

From “sh” to “chi” to X Images from TED.com

Find x. Well, we have found it several times as mathematicians, used it several times in problems, and assumed it as the universal unknown. The unknowns span from just a mathematics variable and into popular culture, spanning the X-files, the X-factor, and Project X. But where did we get x? In a TEDx (again, why x?) talk, Terry Moore presents a brief explanation of what he has found is the reason we use x, and the reason is perhaps more comical than expected.

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The Role of Generalization in Advanced Mathematical Thinking

Generalization and abstraction both play an important role in the minds of mathematics students as they study higher-level concepts. In the second chapter of the Springer book Advanced Mathematical Thinking, Tommy Dreyfus defines generalization as the derivation or induction from something particular to something general by looking at the common things and expanding their domains of validity. As we teach our own math courses, we can look out for opportunities to introduce generalization and abstraction in order to help our students better understand the pattern behind what they are learning. Continue reading

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False Positive vs. False Negative

A guest post by Long Nguyen:

Not all results of medical tests are absolutely correct. Scientists can make mistakes when they conclude that something is true when it is actually false or that something is false when it is actually true. False-Positive2When something is concluded true and it is actually false, we have a false positive or type I error. On the other hand, when something is false and it is actually true, we have a false negative or type II error.

Should we really be worried about a positive medical test for a rare disease?

Mammography is one way to detect breast cancer at its early stage, which helps patients to increase their survivalBN-HB837_HJourn_F_20150223124818 rates. In 2009, John Allen Paulos, a mathematics professor at Temple University, wrote an article, Manmogram Math, to discuss how frequent women should have their mammograms. If mammograms could help diagnose breast cancer, why wouldn’t we have them more frequently? According to Paulos, it is controversial whether women should have mammograms monthly since the tests could cause harmful effects resulting from radiation. Also, suppose you have a positive test, is this absolutely true that you have cancer? The answer is no. Continue reading

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Creating a Successful Learning Environment

Welcome to graduate school. Here, we will find ourselves immersed in a subject that inspires us. Here, we will become engaged in conversation with masters of the field. Here, we will be mentored into a community to which we will dedicate ourselves. Of course, there is a learning curve along the way. In most respects, we expect this. There will be an increase in work time and confusion. There will be difficult times in which we feel like there are not enough hours in the day. It will feel a lot like running a marathon with shoelaces tied together. We will feel inadequate, helpless, and isolated, but hey, it’s worth it. This is what graduate school is all about, right?

Having come to graduate school after teaching at a progressive secondary school, I questioned if it really had to feel this way. I moved out of the position of teacher—helping my students to feel positive about their progress and empowering them to actively participate in their education—and into the position of struggling student looking for assistance. It was during my reflection on the first semester that I began to give myself the same advice that I would give my students and take a more active stance in my education through self-advocacy. Continue reading

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