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."

SageTex: Relabeling the Vertices

If you use Sage to generate graphs you'll find there are times when the vertices aren't labelled the way you expect them or want them to be:

In this case the graph is the line graph of a complete graph on 5 vertices, so labelling the vertices with 2-tuples makes sense--the vertex (0,2) would correspond to the edge (in K_5) from vertex 0 to vertex 2. but the "None" part of each label is annoying, to say the least. And that has created an additional problem of vertices which are too big. Luckily Sage has the ability to relabel vertices. In this case, I'm going to relabel using the vertices as just 2-tuples corresponding to vertices in K_5 of {1,2,3,4,5} to get:

The relevant part of the code is

g = graphs.CompleteGraph(m)
H= g.line_graph().complement()
H.relabel([(i,j) for i in range(1,m+1) for j in range(i+1,m+1)])

The first line creates the complete graph on m, equal to 5, vertices. The second line uses Sage's knowledge of graphs to create the line graph of K_5. The line

H.relabel([(i,j) for i in range(1,m+1) for j in range(i+1,m+1)])

generates the desired labels and as a result the vertices are not so huge. The code for the figure above can be found on the Graph Theory, Sage, LaTeX page.

Here are some stories that caught my eye.

  • A new math series has launched on PBS: NOVA calls it Inifinte Secrets. And yes, the woman waves her hands a lot.
  • President elect Donald Trump has picked Betsy DeVos as Education Secretary. She is anti Common Core. KHOU has 5 things you should know about her.
  • Gallup pats themselves on the back for accurately predicting the results of the presidential election. They've also given some excuses to explain the failure at the local level: "State polls typically have smaller sample sizes, have more variable quality depending on what organization conducts the poll, are estimating an outcome that can shift more readily because the population is smaller, are often conducted further away from Election Day and are more dependent on precision in estimates of turnout by geography...To the degree that organizations want to predict the Electoral College, they are going to have to find ways to finance or encourage larger-sample, higher-quality state polls, rather than relying on the haphazard polls that happen to be conducted in the various states..". So an "F" performance by most everyone's count but their's. And notice the certainty of the predictions were based on "haphazard polls"---never heard that mentioned before they made themselves look like fools.
  • CNBC reports that a partner of ETS, the company that provides security for the SAT, has helped to compromise the SAT: "When the new SAT was given for the first time in March, the owner of the test took unprecedented steps to stop "bad actors" from collecting and circulating material from the all-important college entrance exam. But in the months since, China's largest private education company has been subverting efforts to prevent cheating, Reuters found. The company, New Oriental Education & Technology Group Inc, has regularly provided items from the tests to clients shortly after the exams are administered. Because material from past SATs is typically reused on later exams, the items New Oriental is distributing could provide test-takers with an unfair advantage....Hundreds of thousands of students enroll in New Oriental's test-prep classes. It has a stock market capitalization of $6.6 billion and a listing on the New York Stock Exchange. New Oriental's founder and executive chairman, Michael Minhong Yu, is a business celebrity in China. Yu's company is also a business partner of Educational Testing Service, or ETS - the New Jersey non-profit that both owns the TOEFL and provides security for the SAT.
  • Reuters on New Oriental hooking up with colleges, too: "Eight former and current New Oriental employees and 17 former Dipont employees told Reuters the firms have engaged in college application fraud, including writing application essays and teacher recommendations, and falsifying high school transcripts. The New Oriental employees said most clients lacked the language skills to write their own essays or personal statements, so counselors wrote them; only the top students did original work. New Oriental and Dipont deny condoning or wittingly engaging in application fraud.".
  • Teachers this generation have a different set of challenges. has a piece on "Police believe students may have hatched an "elaborate plot" to frame their teacher for viewing pornography on his computer at school. Investigators cleared a teacher at Longfellow Middle and High School of wrongdoing after students accused him in November of watching a porn video on his school computer in class, Fox 59 reports. "Investigators believe the teacher left a laptop sitting out, and students were able to breach the (Indianapolis Public Schools') firewall and load a porn website onto the computer," according to the news site. "Police say they discovered inconsistencies in the allegation against the teacher," WTHR reports. "They say the students 'may have been involved in an elaborate plot to frame the teacher.'" "
  • RT has the most gripping video footage, courtesy BBC’s ‘Planet Earth 2’ of a lizard being chased by snakes---lots and lots and lots of snakes. This is a video you must see!!
  • RT on teachers getting in trouble for anti-Trump comments. Meanwhile, has a piece on all the hate crimes inspired by Trump that turned out to be hoaxes. And college snowflakes are melting down again because of Donald Trump winning the election "The University of Michigan’s distressed students were provided with Play-Doh and coloring books, as they sought comfort and distraction. A University of Michigan professor postponed an exam after many students complained about their “serious stress” over the election results. Cornell University held a campuswide “cry-in,” with officials handing out tissues and hot chocolate. One Cornell student said, “I’m looking into flights back to Bangladesh right now so I can remove myself before Trump repatriates me.” The College Fix reported that “a dorm at the University of Pennsylvania … hosted a post-election ‘Breathing Space’ for students stressed out by election results that included cuddling with cats and a puppy, coloring and crafting, and snacks such as tea and chocolate. The University of Kansas reminded its stressed-out students that therapy dogs, a regular campus feature, were available. An economics professor at Yale University made his midterm exam “optional” in response to “many heartfelt notes from students who are in shock over the election returns.” At Columbia University and its sister college, Barnard, students petitioned their professors to cancel classes and postpone exams because they were fearful for their lives and they couldn’t take an exam while crying....Does a person even belong in college if he cannot handle or tolerate differing opinions? My answer is no.” Unfortunately, that's the coming generation. Wonder how they'll handle the inauguration?!? (spoiler alert: badly)
  • on "Students at the University of Pennsylvania have decided that William Shakespeare “doesn’t represent a diverse range of writers,” so they ripped his portrait off the wall in the English department. The triggered students replaced the famous playwrights portrait with that of author Audre Lorde, a black lesbian feminist and civil rights activist who is best known for her poetry. While she is absolutely deserving of honor and respect, there are likely plenty of walls for both. The school, instead of punishing the students for vandalism, are rewarding them and caving to their petulant demands.....Campus Reform noted that the school’s code of conduct expressly prohibits students from  “stealing, damaging, defacing, or misusing the property or facilities of the university or of others.” Yet, universities across the nation continue to teach their students, who are primarily adults, that tantrums work. Sadly, they will likely be ill-prepared to deal with the real world where everything isn’t sunshine, rainbows, and getting their way."
  • The challenges of teaching today's darlings: RT has a headline which says it all. "Master bakers: Omaha high-school pranksters trick teacher into swallowing semen frosting". From the article, "Three freshmen thought it would be funny to masturbate into a container and add the fluid to the frosting ingredients, the Omaha World Herald reports.The students’ 59-year-old female teacher then suffered the misfortune of tasting the boys’ finished product. She noticed the turnovers tasted a little funky.Another student later told the teacher that he had heard the culprits talking about their plans to add something salty to the ingredients.The three boys, ages 14 and 15, were questioned by school authorities. Two admitted to their deed, and a third said he had chickened out of the act.Police were called and the boys’ frosting containers seized.“The students will face consequences,” said Brandi Petersen, a spokesperson for Westside High. “We do not tolerate anything of this nature.Sadly, there is no law against adding bodily fluids to food. While the frosting was no doubt an assault on the senses, it doesn’t count as an actual assault as there was no bodily injury."
  • 21st Century Wire hosts a piece asserting "disturbing development at the University of Oregon, whose administration made clear to its faculty last week that if you say things about race, sexual orientation, sex, religion and so on that enough people find offensive, you could get suspended and possibly even fired. This can happen even to tenured faculty members or to anyone else."

SageTex: Polynomial Interpolation 1


Vacation! But before it's time to go I've added a problem to the SageTex: Matrices page. It's not enough to have a lesson on polynomial interpolation like was mentioned earlier so I've put together a problem. Given what starts out as the Fibonacci sequence, students will have to find a polynomial to justify the sequence continuing with a term which breaks the pattern that people think is there.

Here are some stories that caught my eye this past week:

  • The Daily Caller has noted "The University of North Carolina at Chapel Hill issued a guide this week which instructs students that Christmas vacations and telling a woman “I love your shoes!” are “microagressions.” The taxpayer-funded guide — entitled “Career corner: Understanding microaggressions” — also identifies golf outings and the words “boyfriend” and “girlfriend” as microagressions...Christmas vacations are a microagression, the public university pontificates, because “academic calendars and encouraged vacations” which “are organized around major religious observances” centralize “the Christian faith” and diminish “non-Christian spiritual rituals and observances.”"
  • NJ1015 with a tragic story, "The 17-year old Robbinsville High School student who fatally ran over this district’s beloved schools superintendent in April was talking on her cell phone at the time of the crash, prosecutors said Thursday.The student, who is now 18 but is not being named by authorities because she was a juvenile at the time of the crash, has been charged with second-degree death by auto and leaving the scene of a motor vehicle accident resulting in death.She also was ticketed for reckless driving, improper use of a cell phone while driving and leaving the scene of an accident, the Mercer County Prosecutor’s Office said."
  • ZeroHedge with a piece on Randi Weingarten and teacher unions, "Weingarten instructed investment advisers at the federation's Washington headquarters to sift through financial reports and examine the personal charitable donations of hedge fund managers, focusing on those who want to end defined benefit pensions, and entities backing charter schools and the overhauling of public schools. In early 2013, the union federation published a list of roughly three dozen Wall Street asset managers it says donated to organizations that support causes opposed by the union, and the federation wanted union pension funds to use the list as a reference guide when deciding where to invest (or not invest) their money. Said otherwise, if asset managers don't support unions, the unions won't invest with the funds." You'll have to go to the link to see what happened next.
  • with a story that's gotten a lot of coverage, "On June 16, police were called to an unlikely scene: an end-of-the-year class party at the William P. Tatem Elementary School in Collingswood. A third grader had made a comment about the brownies being served to the class. After another student exclaimed that the remark was "racist," the school called the Collingswood Police Department, according to the mother of the boy who made the comment....The boy's father was contacted by Collingswood police later in the day. Police said the incident had been referred to the New Jersey Division of Child Protection and Permanency. The student stayed home for his last day of third grade."
  • Campus Reform has a story on "Donald Trump’s campaign slogan is a “racialized, targeted attack” according to Skidmore College’s Bias Response Group (BRG). Three white board messages with the phrase “Make America Great Again” were included in the BRG’s annual report and classified as “written slur[s] or graffiti” because they had been written on the white boards of female faculty of color." These Bias Repsonse Groups provide flimsy cover to assault free speech.
  • WGBH news reports on the Harvey Silvergate's Muzzle Awards for 2016. First place went to Yale over "...a string of events that started with an email about Halloween costumes, Nicholas and Erika Christakis, two well-respected professors at Yale University, resigned their administrative posts as faculty of Silliman College (a dormitory) amid student protests."

Sage: Polynomial Interpolation


In an earlier post I mentioned that it's not that uncommon for math teachers and even education professionals making up academic resources to mess up badly on sequences. For example, the IXL site, which is, in general, an excellent resource for teachers and students makes a common error with sequences both here and here. Experiment with the problems that are randomly created at those 2 links. Try entering a "wrong" answer and you'll get an explanation of what the "right" answer is. But the "logic" they're using is that here's a formula that describes the sequence, therefore the next term is... The problem is that if you follow the same logic you can justify the missing terms of the sequence to be whatever you want. Therefore those problems have no correct answer and should not be given. Moreover, they shouldn't mark other answers as wrong.

Whenever teachers and math professionals are wrong on the math, you've got a teachable moment. This lesson would be for someone teaching about matrices who has gotten through reduced row echelon form. I'll suggest that you start a class by working through the material on the IXL website and have them figure out what the terms of the sequence are. Write the various sequences on the board to refer to later. When they've gotten comfortable ask them what will happen if you put in a term that doesn't seem to fit the pattern. They'll predict that you will be marked wrong. After showing them that you are indeed marked wrong by IXL figure out a formula to justify your answer and have students confirm that it works. You now have a formula that justifies a sequence that IXL was marking you wrong for. Get the class to discuss what it must mean for an answer to be correct (you can find a formula) and for what it means to be incorrect (it's impossible for anyone to find a formula).

Now it's time for math! Elicit that a sequence is a function from the positive integers into the real numbers (or integers, depending on how you teach it). Remind them that this means the sequence -5, 3, 11, 19, 27, ... corresponds to the function where f(1)=-5, f(2)=3, f(3)=11, f(4)=19, f(5)=27. Give them the mathematics known as polynomial interpolation or Lagrangian interpolation, and using one of the IXL sequences written on your board, set up a Vandermonde matrix. Work through the mathematics to create the polynomial. Get those calculators out to solve the matrix equation. And at the end you'll have a polynomial which they'll need to confirm works to generate the sequence. By the end of class your students will have learned about Vandermonde matrices, seen the math behind polynomial interpolation, used the calculator to power through some of the calculations and construct a polynomial that shows that even the "experts" get things wrong. That's a lesson the class will remember long after they've forgotten how to do the math.

But it's easy to make mistake with calculations so I've constructed a Sage program to go through the steps to create an interpolating polynomial using Vandermode matrices. It's posted on the Python/Sage page. A little warning is necessary, however. Usually you just go to a SageCellServer (or SageSandbox on this site) and copy/paste the code and press "Evaluate" to get the code to run. For reasons I don't understand, sometimes you get some sort of I/O Error such as the one below.


That error can pop up at various stages in compilation. The code runs, sometime it's just a matter of pressing "Evaluate" several times.

In order to set the code for your sequence, you need to alter xvalues and yvalues in the code. For example, if your sequence is 3,2,_,0,-1,-2, _,... and someone says that the pattern is to subtract 1 from the previous terms so the missing numbers are 1 and -3 then you'll need to pick the values you want in your sequence. If you choose to complete the sequence as 3,2,5,0,-1,-2,11,... then you'll need to set xvalues = [1,2,3,4,5,6,7] because you have 7 terms in your sequence and yvalues = [3,2,5,0,-1,-2,11] because those are the terms of your sequence. Press "Evaluate" and you'll get a polynomial that goes through those points. So there is a formula for your sequence--it's just not obvious to most people.

Here are some stories that caught my eye this past week:

  • The74million notes that Common Core lowers standards and that's a good thing. HUH? "Implementation of the Common Core has run headlong into high school exit exams, which many states require students to pass in order to graduate. But now states that have adopted the Common Core are grappling with whether raising academic standards should also mean making it harder to graduate.To supporters, tough graduation requirements are necessary to encourage student effort and ensure a diploma “means something.” Some have even pushed for requiring students to demonstrate “college and career readiness” in order to graduate.But decades of research now show that exit exams have not really raised standards, and have actually harmed disadvantaged students....In other words, the unintended consequence of the Common Core may have been to lower the bar to graduate — and research suggests that this was a good thing."
  • Decades ago, a high school degree was normal and few people had college degrees. Yet people could get jobs that allowed them to provide for a family. Now the quality of high school education has been watered down, graduation rates are higher and a college degree is "necessary" to get a job. And that means people are some $30,000 in debt after college (which is more likely to be 5 years now) and too many students have taken courses in topics that lack rigor and meaning. And while I've taught algebra to many young students outside the US, somehow in the US algebra is too complicated for 18-22 year old students to master--it's actually standing in the way of people graduating. How can you get horribly educated students through college with a pesky math course in the way? Simple--water down standards at the college level. Now Wayne State University leads the charge in dumbing down education, "Up until now, students had to take one of three different math classes before they could earn their degree. Now, depending on their major, students may be able to squeak through college without taking math. The university is leaving it up to the individual departments to decide whether math will be a required part of a degree's curriculum." So in the future, students can graduate high school and college and still not have the math skills of someone who only graduated from high school 50 years ago...and pick up a lot of student loan debt along the way. But at least more people are graduating from college! Progress?
  • Now compare the American drive to banish math with this clip from NextShark called "Watch Korean Students Take the American SAT Math Section For the First Time". You'll hear some people talk about Americans as "exceptional"--that probably shouldn't be taken as a compliment. Even the weak Korean students are feeling better about their math now....
  • The Columbus Dispatch reports "The State Board of Education is expected to lower minimum proficiency standards on two new high school math tests after results came in lower than expected.The move raises questions about whether benchmarks for new assessments will accurately gauge a student’s readiness for college or a career" Somehow I doubt they care about college readiness...
  • with an article on "deep learning" that underpins AlphaGo and other computer programs.
  • Mental Floss with "15 Observational Facts About Isaac Newton"
  • The bit-player blog has a fascinating post on the non randomness of the prime numbers. "These remarkably strong correlations in pairs of consecutive primes were discovered by Robert J. Lemke Oliver and Kannan Soundararajan of Stanford University, who discuss them in a preprint posted to the arXiv in March. What I find most surprising about the discovery is that no one noticed these patterns long ago. They are certainly conspicuous enough once you know how to look for them...For the past few weeks I’ve been noodling away at lots of code to analyze primes mod m. What follows is an account of my attempts to understand where the patterns come from. My methods are computational and visual more than mathematical; I can’t prove a thing. Lemke Oliver and Soundararajan take a more rigorous and analytical approach; I’ll say a little more about their results at the end of this article."
  • A May 18th, 2016 interview with graph theorist Maria Chudnovsky on Looking for a female mathematician to inspire the girls in your classes.  Look no further; she's even been in 2 commercials.

SageTeX: First Derivative Test


This week I've added another problem to the SageTeX: Derivatives page. The screenshot is above. Given a polynomial students need to create a table to show when the function is increasing or decreasing. Then they have to determine the local extrema.

Filling out the table makes use of Sage's ability to calculate derivatives. Here's a small snippet of the code. Note the indentation has been lost.

if df(0)>0:
a13 = '+'
a14 = "increasing"
a13 = '-'
a14 = "decreasing"

Depending on whether the derivative is positive or negative we can fill out the chart. And the same logical reasoning that allows you to fill out the chart by hand is the same logical flow that the Python code goes through--but without the errors we humans are prone to make. And of course, recompiling can generate lots and lots of problems with an answer key, faster and more accurately than any human could.

Here are some stories that caught my eye this week:

  • ZeroHedge has the latest on the Chicago Pension Scandal, "Take the example of two union lobbyists who substitute taught for one-day in the public schools and then started collecting over $1 million of lifetime public ‘teacher’ pension payout – despite a state law expressly designed to stop them. And now take all the other 7,499 educators. The retirees in question paid so little into their own retirement (breaking even on their cost basis within the first 20 months of retirement) that taxpayers now face a $900 million bill just to keep the pension payments flowing!...The fraud appears to be focused on the city of Chicago. Some examples:
    • Northern Illinois school districts are driving the majority of $100,000 pensions. In fact, 6,706 pensions for over $800 million in annual payouts were conferred by districts in the Chicago metropolitan suburban area. Only 793 six-figure pensions totaling $95 million in annual payouts were conferred by school districts in the rest of the state. Yet, income-taxpayers across the whole state guarantee the retirement annuities for everyone.
    • The Top 100 All-Time pensions: #1 $302,991 (Lawrence Wyllie at Lincoln-Way CHSD) to #100 $200,812  (Michael Radakovic at Aurora East USD 131). Read the Top 500 All-Time IL teacher pension list.
    • The Top 5 school districts conferring six-figure pensions are Palatine TWP HSD 211, Palatine (449); Township HSD 214, Arlington Heights (419); Consolidated HSD 230, Orland Park (196); Northfield TWP HSD 225, Glenview (188); Maine TWP HSD 207, Park Ridge (180)."
  • You thought hoped her 15 minutes of fame were over. But it isn't--she's baaaack! Melissa Click was interviewed, shamefully enough, by the Chronicle of Higher Education. dissects it all: "More:

    While Ms. Click acknowledges that she was certainly frustrated that day, she says she was simply trying to protect the black student protesters. Everything she has come to stand for since the video came out—intolerance, anger, mouthiness, and dismissiveness—is exactly the opposite of who she says she really is. Focusing on her behavior, she says, is a way to take attention away from the demands of Concerned Student 1950, the group of protesters. 

    "I’m not a superhero," Ms. Click says. "I wasn’t in charge." But she’s taken the fall. "When it got out of control," she says, "I was the one held accountable." 

    And not by accident. Click was held accountable because she committed assault. If her behavior is drawing attention away from the student activists, that's entirely her own fault. 

    The Chronicle story also includes some biographical details that uncritically accept Click's I-am-a-hero narrative....Is this the profile of a woman who has overcome great adversity, or the profile of an intolerant ideologue firmly convinced of her own greatness?.....But she doesn't deserve sainthood, either. She did a very bad thing, and her revisionist attempts to explain away her criminal behavior should be rejected. Assault is wrong, even if the person committing it has a minor in women's studies."

  • An article in the Tennessean says, "Police handcuffed multiple students, ages 6 to 11, at a public elementary school in Murfreesboro on Friday, inspiring public outcry and adding fuel to already heightened tensions between law enforcement and communities of color nationwide.The arrests at Hobgood Elementary School occurred after the students were accused of not stopping a fight that happened several days earlier off campus. ....Murfreesboro police didn't say what state law the kids violated, but parents of several of the arrested children say the kids were charged with "criminal responsibility for conduct of another," which according to Tennessee criminal offense code includes incidents when a "person fails to make a reasonable effort to prevent" an offense."
  • NPR reports on the latest report card of public high schools, "This tiny downtick was statistically significant in mathematics, but not for the reading test....NAEP scores are comparable across decades — back to 2005 for math and all the way back to 1993 for reading....According to research by Ho and others, just under 40 percent of students score at college and career ready levels on NAEP....One is that in 2015 the nationwide high school graduation rate was 82 percent, not 40 percent. That leaves a potentially large group of kids who got diplomas but who weren't ready to succeed in college. Who is right: their high schools or NAEP?
    ...On the other hand, he says, "the less-than-charitable view would be that graduation is just a lower standard than college readiness. If you get right down to it, the reading and math required by NAEP, the ACT, the SAT, colleges and careers is much greater than what high schools are saying is sufficient." High schools with dumbed down standards to increase graduation? Shocking!
  • Most of us aren't particularly excellent at what we do, but imagine if we could compete against high school students. We'd look really good then. Vice News continues "A few weeks ago, Jonathan Nicola was the star player on his high school basketball team, with a coach who believed he had a shot at going pro. But now that it's come out that the 17-year-old is actually a 29-year-old man, his ambitions — whatever they may have been — have been put on hold, and he's begging the Canadian government to send him back home to South Sudan."
  • The Huffington Post looks at standardized testing, "Turns out, academic conformity sells, and business is booming: As of 2011, Gaston Caperton, the president of the College Board,nonprofit owner of SAT, was paid $1.3 million. Richard Ferguson, formerexecutive officer of ACT Inc., made roughly $1.1 million. Meanwhile, The National Board on Educational Testing and Public Policy at Boston College reported that the value of the standardized testing market was anywhere between $400 million and $700 million........Standardized testing isn’t just about every student meeting the same standards. It is about every student, school, and administrator paying for the same product." So, so true. And public education means there companies have less people to persuade. Give an incentive for those at the top and a lot of money flows to the company. A good article which is worth reading very carefully.
  • Chessbase reports on Fabiano Caruana winning the US Chess Championship. The US Women's Chess Championship was won by Nazi Paikizde after the favorite to win, Irina Krush, had an uncharacteristically bad tournament and the tournament leader, Tatev Abrahamyan, lost the final round. Some very ugly chess by the women but fighting chess that kept me riveted as never knew who would make the final mistake to lose. The tournament was followed by the Ultimate Blitz championship which featured Kasparov, Nakamura, So, and Caruana. Nakamura won, Kasparov was only .5 points behind but the highlight was a So-Kasparov brilliancy. The Chessbase report quotes Yasser Seirawan as saying "Wesley's game against Kasparov will go down in history as one of the greatest blitz games ever played. I will remember that game for the rest of my life." and Kasparov said "It reminded me of games Morphy played against amateurs.". It's that brilliant. Make sure you check out the game at the Chessbase link.
  • It looked like Carlsen was going to easily win the Altibox Norway Chess tounament. A loss in the penultimate round kept the issue in doubt but winning the final round gave Carlsen first place. Chessbase has the story here.
  • The Atlantic looks at "Why would a Teacher Cheat?" I can think of some reasons but back to the article, "The prevalence of test-score manipulation in the United States is well-documented. In fact, with the help of the same researchers who authored the Regents Exams study, The Wall Street Journal in 2011 revealed a significant spike in the number of exams in all the main subjects with scores of 65 points out of 100—the minimum passing grade....There’s good evidence that score manipulation does harm kids, particularly when teachers are falsifying their responses outright for the sake of avoiding sanctions. But there’s also good evidence to suggest that score inflation—teachers grading a bit more leniently, often because they think the student underperformed on the exam—may have positive effects as well. While inflating an individual student’s test score doesn’t magically inject her with more knowledge, the two aforementioned studies indicate it significantly boosts her odds of overcoming an obstacle increasingly critical to future success: high-school graduation." WTF? Schools cheat but hey that may be a good thing because kids graduate. Isn't it obvious that increasing inflating a students grade would increase the chance of their graduating? And, news flash, it's probably likely that some of the inflation is done precisely to get that failing senior out of the school system. But when about 40% of the graduating classes are college ready perhaps high school graduate as an indicator of future success will lose its value as a high school degree is no longer proof that you can read and write. This is an absurd article on a lot of levels. And the nonsense continues, "Indeed, a growing body of international research suggests that the prospect of a raise—or the threat of sanctions—seldom induces teachers to fudge their students’ test scores. Altruistic motivations appear to be at play." And I've got a bridge in Brooklyn to sell you. The school system is so broken and most of the people in charge aren't interested in fixing it.
  • Yet another Common Core defector wanna-be: Michigan. Truth in American Education says, "Michigan’s Common Core Repeal Bill just made it over a a major hurdle. The Senate Education Committee voted to pass SB 826, a bill that would repeal Common Core and replace them with Massachusetts pre-Common Core standards."

Sage Interact: Generate Continuous Data


We already know it's not math, but like (physics, engineering, chemistry, etc) it's an important application of math. But we've seen, "David Moore, statistics educator and former president of the American Statistical Association , gives the following four compelling reasons why statistics is a separate a.discipline from mathematics:......

  • The standards of excellence in statistics differ from those of mathematics"

Truth be told, the standards of the pseudo-science of statistics differs from real science as well. Data analysis is, as my graduate analysis teacher used to say, more of an art than a science. Now there's an understatement! As statistics infects the high school math curriculum you might find yourself having to teach it, in which case you'll find the pseudo-math field of statistics needs data---lots of data.

Luckily, the brief foray into statistics at the high school level doesn't get too involved. A lot of the descriptive statistics in high school doesn't venture into the BS dubious areas of statistics; they tend to focus on mean/median/mode/standard deviation and plotting a bunch of graphs by hand even though in the real world they'd use Excel to process the data and put out charts. To eliminate some of the drudgery I've put together a Sage Interact that generates data for some continuous probability distributions (normal, exponential, gamma, beta). As you can see from the screenshot above, you can pick how many items to include in your data set as well as specify the number of digits shown. Finally you can specify the number of bins to use in the histogram. Be aware that the figure might be cut off (as below) and to see the rest of it you'll need to find and use the scroll bar underneath the histogram.


The total output is a histogram, the data set, and some common statistics (sample mean and standard deviation, mode, minimum, and maximum). A simple copy and paste will get you data for a test/quiz/example along with the answers to prevent any mistakes.

You can find the code on the Python/Sage page. Copy and paste the code into a Sage Cell Server (such as on the Sage Sandbox page), press "Evaluate" and generate the data sets you need quickly and easily.

Here are some stories that caught my eye this last week:

  • The NY Post has a story on teachers taking a public stand: "Renegade city public school teachers have been sending emails to parents the past week encouraging them to boycott the state English and math Common Core exams being administered citywide starting Tuesday,...some teachers at the Earth School on the Lower East Side emailed a four-page letter to parents slamming the exams and applauding the 73 percent of parents who opted out last year,...A city Department of Education official warned that teachers “may be subject to discipline” if they cross the line in prodding parents to opt out. Teachers complained DOE has imposed a gag order."
  • The New Scientist has a piece on the knew movie on Ramanujan's life and it's not positive: "Ramanujan’s journey is the subject of a new film, The Man Who Knew Infinity, based on a book of the same name....the film attempts to give us a glimpse of an unknowable mind traversing the realm of abstract thought, while also humanising its subject. And frankly, the formula is starting to wear thin....The Man Who Knew Infinity isn’t bad, it’s just safe, cramming Ramanujan’s colourful life into a well-established, sellable format."
  • Common Core is dead, according to the Federalist. It's not official yet, though: "The big postmortems will roll out in a year or two, but it’s already clear this education monstrosity is eking out its last gasps....Common Core has by now not only failed academically, it has failed operationally. This is a horrific outcome...Common Core’s failure should indict every single Common Core cheerleader and prompt a revival of genuine education reforms we’ve known for decades would actually help children but aren’t sexy to the consultant class that makes a living as “education innovators” (i.e. experimenting on children for fun and profit)...Researcher Ze’ev Wurman looked at several other indicators of student achievement and found none have improved since Common Core went into effect. In fact, SAT and ACT scores are slightly down....Common Core tests’ rapid (and predictable) disintegration has negated politicians’ central justification for the (unconstitutional) federal requirement that states give annual math and reading tests: “public accountability.” That’s because it’s impossible to compare Common Core test results to those that came before them. It would have been possible had educrats cared enough about accountability to require the proper testing translations, but they didn’t. Common Core test results cannot even be compared to themselves yet because they have not generated enough reliable data....Obama’s dictatorial flourishes of the pen have forced tens of thousands of people to spend hundreds of millions in tax dollars and millions of man-hours essentially shuffling paperwork. It’s trickle-down bureaucracy. (That’s why half of school employees are not teachers, but instead mostly paperwork shufflers. Thanks, feds!) " A good piece with a lot of information. Why does every educational plan fail after 5-7 years time and time again so the educational experts people can spend a lot of money to come up with another plan? That's rhetorical, of course
  • EAGnews on reports on "Parents are removing their children from Bear Branch Elementary School after the principal allegedly banned them from school grounds and threatened violators with arrest....District officials issued a prepared statement to Fox 26 about the situation that supported Ray’s supposed goal of a safe dismissal....Parents said they do not believe the old dismissal process was unsafe, and believe the principal is on a power trip.
  • ZeroHedge hosts a piece by Jim Quinn: "The Department of Education was created in 1979 and now has an annual budget of $73 billion, with 5,000 government bureaucrats roaming its hallways. When you include all Federal, State and Local spending on public education it totals about $700 billion per year, or $13,000 per student. ...According to the 2007 California Academic Performance Index, research show that 57% of students failed the California Standards Test in English.... 50% of the unemployed between the ages of 16 and 21 cannot read well enough to be considered functionally literate" If doctors or lawyers had such poor results they'd be sued for malpractice.

Sagetex: Rational Functions 4


The latest addition to the website is the sagetex randomized problem on rational functions. It's posted on the Sagetex: Functions page. This one involves functions of the form f = ((a*x^2+abs(d))*(x-b))/((x-b)*(c*x+d)*(x-d)) where a,b,c,d are random integers. Unlike the previous rational function problems you'll see that (x-b) cancels so there will be a hole in the graph, as shown in the picture above.

$latex \LaTeX$ god Alain Matthes, designer of the Altermundus packages, left a comment on this page. It sounds like providing an English version of his documentation is on his mind but, admittedly, no time frame is given. Keep your eye on the CTAN feed....

Here are some things that caught my eye this week:

  • The always entertaining Kevin Knudson of Forbes on a new type of puzzle called Sweet 16.
  • Who could miss the NY Times clickbait "The Wrong Way to Teach Math"? At first I was going to ignore the trashy article, and then after seeing how a hack was given a forum to sell/hype a book I figure I should probably say something. But let's give mathematician Dr. Keith Devlin a standing ovation for stepping in to inflict a brutal beat down: he's got 2 pieces, one on the Huffington Post and the other on Devlin's Angle. The pieces are similar but there are some important differences. From the Huffington Post article he's a bit more restrained: "Since Hacker clearly has a valuable connection to the nation's premier national newspaper, it is then a pity he pitched his article the way he did....There is always a danger in setting oneself up as an advocate for change in a discipline one does not know. Hacker is not a mathematician. He is a retired college professor of political science, who has taught some courses in mathematics to non-majors....Unfortunately, since Hacker plainly does not understand what algebra is, or more generally what mathematical thinking is, he instead proposes we throw away the healthy but neglected baby along with the depressing pool of lukewarm, dirty bathwater it currently hides in....In reading an advance copy to write my review, I annotated 20 pages (out of a total of 200) where he makes significant errors due to a lack of knowledge of, or a misunderstanding of, mathematics. That's an error rate of 10%; way too high for significant errors.". In the Devlin's angle piece you'll see a recap of Huffington Post along with his analysis. But here he gives a couple more blows to the head followed by a $latex \pi$ to the face: "Not only does Hacker give no indication he is familiar with the Common Core—the real one, not the azimuth-strewn, straw-man version he creates—he gives every indication he does not understand mathematics as it is practiced today. (He also does not know that pi is irrational, but I’ll come to that later.) will be jolted by Hacker’s fundamental lack of knowledge of mathematics. He writes, “Along with phenomena like earthquakes and cyclones, nature also has some numbers that control or explain how the world works. One of them is pi, whose 3.14159 goes on indefinitely, at least as far as we know.” Yes, you read that last part correctly." Oooooooh...SNAP! Isn't it great to find out someone with a lack of basic prealgebra knowledge on the irrational number $\atex \pi$: writes a book on removing algebra from high school, has a forum to voice his ignorance at the NY Times, and teaches math at the college level. Shame on the the NY Times for giving this cr@p a forum and  to Queens College, City University of New York for having someone with a "fundamental lack of knowledge of mathematics" teaching math. THANK YOU DR. DEVLIN!!!
  • EAGNews on how "School officials in Huntsville plan on tracking students’ social media accounts as part of a new system that will also levy punishments based on posts, regardless of whether they’re private or public....The “procedure” involves tracking the social media posts of violent students or any school officials deem to be a risk to school safety. The superintendent can then use the social media posts – regardless of whether they posted publicly or privately – to take action against students. "
  • The kids really are different these days: with the story that "A 16-year old Nashville resident is accused of shooting his grandmother, sister and nephew because he did not want to leave his bed to head to school. He also tried to shoot his mother, but she managed to escape."
  • Those kids start young, too. EAGNews on "Police recently busted a drug dealer inside Marlin Elementary School – a 9-year-old who brought in several prepackaged bags of marijuana to hawk to classmates."
  • with a piece on how Denver Public Schools are using district wide credit cards. "The Problem Solvers focused on purchases totaling around $2 million that appeared to contradict school policy but were approved by the finance department anyway.....Auditors sampled 197 employee credit card transactions and found something wrong with 154 of them -- a 78 percent fail rate....That also made it easy to question certain purchases that were culled from a computer database that was built that contained all the credit card purchases in the past couple of years.
    • Party City: $23,511
    • Flowers: $7,806
    • Jewelry: $3,900
    • Gift cards: $110,638

    Putting nonstudent-related food on credit is supposedly under tight control, but when we searched for receipts linked to "BBQ" or "Famous Dave's," there were $73,917 in credit card purchases by school employees. Einstein Brother’s Bagels came out to $174,222. Pizza restaurants were at $451,658."

  • The Periodic Table of Elements in Pictures would be useful for any chemistry teacher.
  • PC zealots are alive and well at Kansas University where the Daily Beast reports that another faculty member has been removed. "You would think that Quenette must have perpetrated an egregious act of harassment or obvious discrimination to provoke her students to publish an open letter demanding her immediate termination. The letter, written by five of Quenette’s students—some, but not all of them, black—alleges that Quenette violated the university’s policies prohibiting racial discrimination...We students in the class began discussing possible ways to bring these issues up in our classes when COMS 930 instructor Dr. Andrea Quenette abruptly interjected with deeply disturbing remarks. Those remarks began with her admitted lack of knowledge of how to talk about racism with her students because she is white. “As a white woman I just never have seen the racism… It’s not like I see ‘Nigger’ spray-painted on walls…” she said....But she did not use inappropriate language to describe any of her students—or to describe anyone else. She was describing her own blindness to racial animus. Could she have used different language? Sure. Should she have? Probably. But genuine self-reflection isn’t usually rehearsed. This wasn’t a public address—it was a classroom discussion about a controversial topic. Some imprecision should be expected, and tolerated.". The potential impact of this generation on free speech in America is frightening.
  • John King, President Obama's choice for the new education secretary, is apparently not well liked by a lot of "progressives". According to Alternet, an open letter to the Senate was published in the Washington Post asking for his rejection, "The letter is signed by world-renowned scholar Noam Chomsky, along with journalist Naomi Klein, Chicago Teachers Union president Karen Lewis, Green Party presidential candidate Jill Stein and a host of other prominent scholars and activists, including some of the most established pro-public education voices. A variety of teachers’ and public education organizations signed the letter as well, including New York for Public Education, Save Our Schools and Time Out From Testing. The signatories warn King’s policies “have been ineffective and destructive to schools, educators, and most importantly students.”..."The American public deserves a Secretary of Education who will advocate for their interests, not those of the testing corporations who profit from the Common Core,” the letter reads.""
  • Alternet again, this time warning, "The FBI Has a New Plan to Spy on High School Students Across the Country...The FBI’s justification for such surveillance is based on McCarthy-era theories of radicalization, in which authorities monitor thoughts and behaviors that they claim to lead to acts of violent subversion, even if those people being watched have not committed any wrongdoing...The FBI’s instructions to surveil and report young people not for wrong they have committed, but for violence they supposedly might enact in the future, is likely to promote an intensification of this draconian practice."

Sagetex: Rational Functions 3


This week I've added another example to the Sagetex: Functions page. This one is quite similar to the previous example: there are two vertical asymptotes and one horizontal asymptote. But in this case the horizontal asymptote is a line other than y=0.

Here are some stories that caught my eye over the last week:

  • The Atlantic has an article on how, despite America's poor showing in math, the number of students excelling in math is growing. But wait for it..."Parents of students in the accelerated-math community, many of whom make their living in stem fields, have enrolled their children in one or more of these programs to supplement or replace what they see as the shallow and often confused math instruction offered by public schools, especially during the late-elementary and middle-school years."
  • quoting the Daily Caller, "In the syllabus for her "Creativity In Context" class — a required course for any student pursuing a minor in Innovation — UF professor Jennifer Lee informs students of her four paragraph long classroom "communications policy" that she says will enforce "ethical conduct" in the classroom....The policy mandates that students "[s]peak in a way that does not make assumptions about others based on "norms", stereotypes, or one's own identity or experience."...The syllabus explains that this means replacing the words "boyfriend"/"girlfriend" with the more inclusive "partner" or "significant other." The rule applies to conversations about married couples too: saying "husband" or "wife" is forbidden. Even the words "mom" and "dad" have a more "inclusive" alternative — students are told to use the word 'family" instead.". Around fifty years ago getting a college degree wasn't essential. People learned "the basics" by the end of high school and college was for advanced studies. Now, it seems that typically students are graduating high school unready for college but then go on to college because "you have to" but lacking the education end up taking courses like...well like Creativity in Context. So now, at the end of college they have an enormous debt burden, no real skills, and are learning cr@p. How did education get to this?
  • Good news, class! MedicalNewsToday reports "A math test a day keeps the weight away, by activating brown fat"
  • Who's running the SAT anyway? They've lost a lot of business to ACT because of poor test design. So they've redesigned the test and it looks like they made it worse. From the NY Times: "Chief among the changes, experts say: longer and harder reading passages and more words in math problems. The shift is leading some educators and college admissions officers to fear that the revised test will penalize students who have not been exposed to a lot of reading, or who speak a different language at home — like immigrants and the poor.....College Board officials said the new test was devised to satisfy the demands of college admissions officers and high school guidance counselors for an exam that more clearly showed a connection to what students were learning in school. " What better way to test someone's math skills than by putting a heavy emphasis on reading and vocabulary....winner: ACT.
  • with a piece on a petition in California to get high school credit taking computer classes. Great idea, just don't cut math classes to do it (unless it's statistics...because statistics isn't really math) and get discrete math into the curriculum at the same time.
  • Yet another school shooting. on two teenagers killed this week in an "apparent murder suicide" at an Arizona public school: "Initial reports described the victims as “two teenagers,” but offered no details. One KNXV-TV source said that two female students may have got into an “altercation” at the cafeteria, which ended with gunshots."

Sage Interact: Taylor Polynomials


I've added another Sage Interact to the Python/Sage page. The text can be copied into any Sage Cell Server, like the three that are on the Sage Sandbox page. Just press "Evaluate" and the Sage Interact appears; This Interact allows you to generate Taylor polynomial approximations for a function about some center. It's a little unpolished because you set the function to graph, the center of the expansion, the width (xrange shown is 2*width) and the minimum and maximum y values for the figure in the code itself. The resulting Sage Interact is programmed to handle the Taylor polynomials of degree 1 through 7. Simply click the boxes to display which  the polynomials you want to see. The screenshot above shows the function $latex e^{x}$ with center 1 having a dot on it. Of course you can modify the size or not plot the point if you find it too distracting.

Don't overlook the "TaylorPoly.pdf" in the bottom left.TP2

Right click on the link to download a pdf of the figure for your own use. This is a quick and easy way to generate examples for, say, a Powerpoint beamer presentation.

I also need to mention that Detlef Reimers, the author of the lapdf package for LaTeX, left some comments. One is on the Common Core Questions page where he shares his philosophy behind the lapdf package which and states, "The audience for such a packet full of math, programming utilities (loops) and many complex drawing commands - directly based on the fore runner of PDF, PostScript - would generally be the scientific orientated people.". I agree. If you haven't tried the package then you definitely need to. My complaint at the time was the lack of good documentation--the package has a lot to offer but you have to be willing to puzzle through the details on how to make things work. The good news is that the package is currently undergoing an update which will provide some more documentation and fix the problems I noticed with ellipses. In a second comment, at the bottom of the lapdf packge post, Mr Riemers mentions that lapdf has some ability to draw chess diagrams--you can go to the links and check out some of what he's working on. I'll be looking forward to seeing the the new version of lapdf show up on CTAN.

Here are some stories that caught my eye over the last week.

  • Hikaru Nakamura won the 2016 Tradewise Gibraltar Masters chess tournament on tiebreaks over MVL; both players had 8/10. Nakamura bested MVL 3-2 in speed chess.
  • John Cleese of Monty Python fame was in a ZeroHedge article, "John Cleese says political correctness has gone too far, especially on America's college campuses, where he will no longer go to perform...Cleese, having worked with psychiatrist Robin Skynner, says there may even be something more sinister behind the insistence to be always be politically correct.
    "If you start to say we mustn't, we mustn't criticize or offend them then humor is gone. With humor goes a sense of proportion. And then as far as I'm concerned you're living in 1984.""
    Serious words from a funny man.
  • EAGNews with headlines that over 15,000 Chicago school employees make over $100,000 a year. "So what is the overall record of student learning and achievement in the Chicago district? Absolutely awful. “Four out of ten CPS freshmen don’t graduate,” reported in 2014. “Ninety-one percent of CPS graduates must take remedial courses in college because they do not know how to do basic math and other schoolwork. Only 26 percent of CPS high school students are college-ready, according to results from ACT subject-matter tests.“Education should be the great equalizer; but in Chicago, public education is more of a holding cell than a launch pad.”" Bad education+expensive price tag+ lack accountability =waste of money.
  • The Washington Post reports there is a noticeable performance difference between students taking Common Core with a computer versus those using pencil and paper, "...about one in five took the exam with paper and pencil, and those students — who tested the old-fashioned way — tended to score higher than students who took the tests online...It’s not clear whether the score differences were due to the format of the testing, or due to differences in the backgrounds of the students who took the two different types of test, according to the Feb. 3 Education Week report. But the publication reported that in some cases the differences were substantial enough to raise concerns about whether scores on the exam — the Partnership for Assessment of Readiness for College and Careers test — are valid and reliable enough to be used for teacher evaluations or school accountability decisions." Did you catch that? The differences are, apparently, valid and reliable enough to gauge the student but not the teacher or school.
  • I'd been ignoring this story until the The Columbian piqued my interest with a flashier headline (linking the Babylonians with calculus) for a reprint of a Washington Post piece, "The astronomers of Babylonia, scratching tiny marks in soft clay, used surprisingly sophisticated geometry to calculate the orbit of what they called the White Star — the planet Jupiter. These tablets are quite incomprehensible to the untrained eye. Thousands of clay tablets — many unearthed in the 19th century by adventurers hoping to build museum collections in Europe, the United States and elsewhere — are undeciphered." Until a key breakthrough, "... The calculations merely describe Jupiter’s motion over time as it appears to speed up and slow down in its journey across the night sky. Those calculations are done in a surprisingly abstract way — the same way the Oxford mathematicians would do them a millennium and a half later. “It’s geometry, which is itself old, but it’s applied in a completely new way, not to fields, or something that lives in real space, but to something that exists in completely abstract space,” Ossendrijver said. “Anybody who studies physics would be reminded of integral calculus.”Which was invented in Europe in 1350, according to historians.""

Sagetex: Rational Functions 2


I've added another problem to the Sagetex: functions page. This is a rational function with two vertical asymptotes, a horizontal asymptote and no holes. In the coming weeks I'll work on putting a problem together that has a hole in it.

Here are some stories that caught my eye this week:

  • It's not math and it's not chess--but if you play chess you probably will have some interest in's story on a Google designed artificial intelligence based computer, called AlphaGo, crushing the "...reigning three-time European Go champion Fan Hui....However, AlphaGo is not going to stop. Next time it will face one more Go guru – the legendary Lee Sedol, “the top Go player in the world over the past decade.". Some decent videos are posted on the page and don't skip the link to Google's official blog posting on the event.
  • The Tata Steel Chess Championship is almost over. Magnus has assured himself with at least a tie for first. Caruana is the only player to have a chance to catch him but he's losing against Tomashevsky on move 61.
  • According to, a federal judge took aim at some policies at Iowa State University, "As far as Iowa State University President Steven Leath was concerned, censoring the T-shirts of a campus group advocating the legalization of marijuana was simply good politics, a way of maintaining friendly relations with state officials. It was also clearly unconstitutional, according to a federal judge who last week told Leath and his subordinates to cut it out....."We are gratified that the court understood that ISU bowed to political pressure when it imposed special restrictions on NORML ISU," said First Amendment lawyer Robert Corn-Revere, who represented Gerlich and Furleigh. "This violated the most basic First Amendment requirement that the government cannot discriminate against a student group or its members because it disagrees with their viewpoints. This decision vindicates the right to freedom of expression not just for the courageous students who brought this case, but for the students of all public universities.""
  • The inspiring words of Martin Luther King were under attack recently. From the Daily Emerald, "“I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin, but by the content of their character. I have a dream…".....The quote is not going to change, but that decision was not made without some hard thought by the Student Union Board." Maybe next year?!?
  • USAToday on "...a new study made public Tuesday scratches beneath the surface to pin down just how many students in major U.S. metropolitan areas can actually read or do math proficiently. The results: Startlingly few. If all of Detroit’s fourth-graders took the well-respected National Assessment of Educational Progress (NAEP) tests, just 120 African-American fourth-graders across the entire city, by researchers’ estimates, would score “proficient” or above in math.“This is not a misprint,” the authors warn.....In Atlanta, just 60 Hispanic fourth-graders and 40 Hispanic eighth-graders would score proficient or above in reading." More depressing stats can be found in the article.
  • The USAToday link above might get you thinking why public schools are so shockingly bad. Truth in American Education has presidential candidate Carly Fiorina weighing in: "...all these programs, some of them have come out under Republicans too – Common Core, No Child Left Behind, Race to the Top, they are all bad ideas. Because guess what they are? They are big bureaucratic programs coming out of Washington and, by the way, there are a bunch of interests who helped write those programs.  In the case of Common Core guess who helped write it? Text book companies and the testing companies it’s all crony capitalism folks. It’s alive and well under Republicans and Democrats. We have to take our country back,” Fiorina answered." According to a spokesperson for Ms Fiorina, "As she has said, there is absolutely no evidence that the work of a big, centralized bureaucracy in Washington makes things better. In fact, there’s loads of evidence to the contrary. The Department of Education has been growing in size and budget for 40 years and the quality of our education continues to deteriorate." Sounds on the mark to me.
  • reports on the teachers union protecting their turf from charter schools. "Nebraska is one of seven states without charter schools. Previous attempts to authorize them under state law haven’t gotten far, in large part because of stiff opposition from the union representing public school teachers: the Nebraska State Education Association...There are no charter school bills in the current session of the Legislature, but Sen. Bob Krist’s Legislative Bill 26, carried over from last session, would allow donors to receive tax credits for contributing to scholarships that allow low-income students to attend private schools." Why not stick to education and stop working towards eliminating school choice? Perhaps if unions there would work on teacher quality and get rid of poor teachers there would be no demand for charter schools.
  • has a piece responding to the recent call to ban chess by Saudi Arabia's grand mufti. "Far from being a waste of time, chess can be of great benefit to children's minds. Several academics have looked into this extensively. Chesshas been persuasively linked with improving children's concentration, problem-solving, critical, original and creative thinking - and even mathematical abilities. It is also said to help with memory storage and how young brains manage information - and should not only be perceived as a game for gifted children. Children with special educational needs can improve their abilities to learn and interact with other children if they become involved in school chess programmes and chess clubs. Children are also equal in a chess match regardless of things that might divide them. Their age, gender, ethnic backgrounds and religious affiliations are of no significance. Chess can cross socio-economic and cultural boundaries and give otherwise disadvantaged children a chance to compete on equal terms."