Sagetex Basics: Factoring Quadratics

I've added another worksheet to the Sagetex Basics page on factoring quadratics. This worksheet creates 10 random quadratics on the first two pages. The line

while r1 == -r2:
r2 = Integer(randint(-10,10))

prevents any quadratic from being factorable by the difference of squares formula. If you want to allow quadratics of the form x^2-a^2 then comment those 2 lines out.

The variables outputP and outputA are the strings that contain the text for the Problems and for the output, respectively. This avoids having multiple sagesilent environments and allows a loop to take care of the repetition. The answers are printed out on the third page:

Here are some stories that caught my eye:

  • Oregon man fined $500 for using math to challenge red light cameras: "Mats Järlström learned this first-hand last year when the state of Oregon fined him $500 for publicly suggesting that yellow lights should last for slightly longer to accommodate cars making right turns....."
  • ZeroHedge with a post "Intellectual Intolerance - Stunning Speech From Stanford University Provost Exposes "The Threat From Within"" which says, "...But I’m actually more worried about the threat from within. Over the years, I have watched a growing intolerance at universities in this country – not intolerance along racial or ethnic or gender lines – there, we have made laudable progress. Rather, a kind of intellectual intolerance, a political one-sidedness, that is the antithesis of what universities should stand for. It manifests itself in many ways: in the intellectual monocultures that have taken over certain disciplines; in the demands to disinvite speakers and outlaw groups whose views we find offensive; in constant calls for the university itself to take political stands. We decry certain news outlets as echo chambers, while we fail to notice the echo chamber we’ve built around ourselves.""
  • Listverse has "10 Strange Facts About Pythagoras: Mathematician and Cult Leader"
  • Orrazz with a piece "There Are 5,000 Janitors in the U.S. with PhDs"
  • Shame on the AMS for hosting a racist piece on their website. The post "Get Out of the Way" drew enough comments to get the comments section closed. I suspect that had the comments been praise they'd have kept it open. The criticism isn't too surprising with an opening like this: "Not to alarm you, but I probably want you to quit your job, or at least take a demotion. Statistically speaking, you are probably taking up room that should go to someone else. If you are a white cis man (meaning you identify as male and you were assigned male at birth) you almost certainly should resign from your position of power. That’s right, please quit. Too difficult? Well, as a first step, at least get off your hiring committee, your curriculum committee, and make sure you’re replaced by a woman of color or trans person. Don’t have any in your department?  HOW SHOCKING....What can universities do? Well, that’s easier. Stop hiring white cis men (except as needed to get/retain people who are not white cis men) until the problem goes away. If you think this is a bad or un-serious idea, your sexism/racism/transphobia is showing. It is worth considering your complaints. Are you worried it’s unfair to men? Are you concerned the quality if your institution would plummet? Are you worried about all the brilliant minds you’d be missing? List your reasons and ask yourself which ones you’d value over your own freedom. Women are not free, and even our allies tend to only want us equal-ish. As long as we get there on their terms, as long as they lose nothing.If you are on a hiring committee, and you are looking at applicants and you see a stellar white male applicant, think long and hard about whether your department needs another white man. You are not hiring a researching robot who will output papers from a dark closet. You are hiring an educator, a role model, a spokesperson, an advisor, a committee person. When you hire a non-marginalized person, you are not just supporting this one applicant whom you like, you are rewarding a person who has been rewarded his whole life. You are justifying the system that makes his application look so good. You are not innocent. You are perpetuating a system that requires your participation if not your consent. When your female students of color have no role models in your department, that’s not “meritocracy”; that’s on you. Again, if you think the “great mathematicians” are disproportionately male because of meritocracy, then your sexism is showing...Not to alarm you, but statistically speaking you are the problem. Your very presence. I can’t tell you what is the best strategy for you to stop blocking my path. I can just ask that you please get out of my way." Absolutely disgusting. Could you imagine the furor and screams of racism if "white cis males" was replaced with some other ethnic group? Some of comments are interesting, in particular Math Colleague who notes "We are all painfully aware of the inequalities in faculty composition and trying hard to fix it. *Every* math department I know of is trying really hard to hire every qualified minority and female applicant out there (and by qualified I mean: a *very* generous ballpark within the hiring range of each department). The real problem is that there are not enough such candidates, and most departments end up making offers to the same few that are available in the market each year.". Math Colleague's explanation jibes with everything I saw in graduate school as well as out in the world where a woman and/or minority is highly sought after even when they are the weaker candidate. I know some minorities who were given a chance and were grateful for it.. Math Colleague sums up with "And all I can say is that if you did not get a tenure-track offer already, it is because you didn’t apply to enough places. If you what you want is a job at a top research institution, then you’ll need to prove that you are in the ‘generous ballpark’ of the research level you aspire to. I’ll be blunt: you have no grants, one publication, and the one paper is co-authored with your advisor. Write more papers, and we will hire you.You have great potential to make a difference for minorities and women in mathematics. Come up with a reasonable plan to help minorities, and NSF will fund it. But this post is unnecessarily destructive, discriminatory, inflammatory, and counterproductive to our inclusion efforts.". With a little more digging you'll find Piper on another blog where she says "They asked how many years spent on coursework (3), how many years spent on dissertation (10).  TEN YEARS?! WHAT KIND OF PERSON SPENDS TEN YEARS ON ONE DOCUMENT AND STILL HAS TO BUILD UP COURAGE TO DISCUSS IT OPENLY?... Oh, am I here because of Affirmative Action? Oh, am I here because I’m a woman? Oh, am I here because of a mistake? Okay, haha, I get it. Oh, do my friends think I took the spot of someone who deserved it more? That’s okay. It’s okay if my friends think that. Then there was the actual math. Funny story, I was exceptionally behind my peers when I got to Princeton. I’m tired of talking about it. I should have made myself a Tshirt that said “I only took 7 math classes before coming here, and my peers took 20 – 30, so that’s great.”". These comments appear to demonstrate she understands, at least to some degree, that she didn't get into Princeton for purely academic measurements-- she was "exceptionally behind" her peers. Princeton gets geniuses like Terry Tao if they want so there is lots of reason to suspect affirmative action has given her a chance. This, combined with 10 years work on a thesis which has led to one paper isn't awe inspiring. So Piper has gotten a chance to go to a prestigious university but that isn't enough. Remember the quote: "Stop hiring white cis men (except as needed to get/retain people who are not white cis men) until the problem goes away. If you think this is a bad or un-serious idea, your sexism/racism/transphobia is showing". Again, substitute any minority in for white cis male and ask yourself how that sounds. That would be grounds for someone losing their job; do you think it will happen to her? I don't. Or how about, "You are not hiring a researching robot who will output papers from a dark closet. You are hiring an educator, a role model, a spokesperson, an advisor, a committee person." Actually, the schools are trying to hire people qualified in math and producing research is part of the job description but regardless, white cis males are not incapable of being  a role models, spokespersons, advisors, and all the rest, are they? Contrast this Piper's situation with the piece above at Orazz with 5,000 PhDs working as janitors--I suspect they would be jealous of the chances she is getting. Piper's been given a chance that many lots of people haven't gotten and, invariably that means some have been the victims of reverse discrimination. Again, shame on the AMS post for hosting a piece that dismisses other people on the basis of being white males and white females, because "Remember having white cis women run the world is no kind of solution.". You can read a little more about Piper and her thesis by going to her blog.
  • The College Fix reports "After black student activists issued a demand list to American University in response to the racist-banana incident two weeks ago, the administration agreed to three demands.One of them is a ban on whites using a new “student lounge” for the rest of the spring semester."

Leave a Reply

Your email address will not be published. Required fields are marked *

AlphaOmega Captcha Classica  –  Enter Security Code