Plotting with sagetex: implicit plots revisited


Earlier I had looked into Implicit Plots and found a way to do them which depended on whether they were connected or disconnected. Recently I found a way of determining the points that Sage is using to construct the plots. This eliminates the need for two cases BUT we have to take more care in plotting the graph. I've added information on plotting implicitly to the Plotting with Sagetex page. The key breakthrough was determining a way to determine the points that Sage used in plotting functions implicitly.  Sage is using a grid of points, which I called gridDim. The gridDim is the number of points on each side of the side of the grid. Since the plot is going from x=-3 to x=3 and y=-3 to y=3 there are (250)x(250) points that will be turned "on" by Sage if they are on the curve and "off" if they are not on the curve.Since an implicit plot is solving the equation f(x,y)=0, in order to have it plotted by the computer I chose to consider the point on the curve if it was "close" by making sure

if abs(C1.xy_data_array[i][j])<.02:

The value .02 was chosen from my experiments with plotting; change to .01 and the plot thins out too much for my liking while .03 starts to thicken the plots too much. You can find a more in depth discussion as well as 2 sample templates to experiment with, on the Plotting with Sagetex page.

Here are some stories which caught my eye recently:

  • hosts a piece on micoagressions.There is increasing pressure on college admin to think "correctly".From the article, "Early this year, the University of California’s president, Janet Napolitano, asked all deans and department chairs in the university’s ten campuses to undergo training in overcoming their “implicit biases” toward women and minorities. The department heads also needed training, according to the UC president, in how to avoid committingmicroaggressions, those acts of alleged racism that are invisible to the naked eye. A more insulting and mindless exercise would be hard to imagine. But Napolitano’s seminar possesses a larger significance: it demolishes any remaining hope that college administrators possess a firmer grip on reality than the narcissistic students over whom they preside."
  • The New York Times has an excellent piece on "The Singular Mind of Terry Tao". Terry Tao is considered to be one of the top mathematicians alive today. From the article, "But it turned out that the work of real mathematicians bears little resemblance to the manipulations and memorization of the math student. Even those who experience great success through their college years may turn out not to have what it takes. The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians. Tao now believes that his younger self, the prodigy who wowed the math world, wasn’t truly doing math at all. ‘‘It’s as if your only experience with music were practicing scales or learning music theory,’’ he said, looking into light pouring from his window. ‘‘I didn’t learn the deeper meaning of the subject until much later.’’
  • has another piece on the LA public school system's attempts to get a star teacher fired."Esquith, who teaches low-income and minority fifth graders, made a joke about the difficulty he was having raising enough funds for the yearly Shakespeare production, which he finances through donations to his non-profit. As I previously noted, “While reading a passage from Huckleberry Finn in which ‘the king came prancing out on all fours, naked,’ Esquith remarked that if he couldn’t raise additional funds for his annual production, he supposed ‘the class would have to similarly perform naked.’” The joke was overheard by another teacher, who deemed it inappropriate and reported Esquith to the principal, Jonathan Paek....Paek made Esquith sign a humiliating letter of apology:...Esquith was suspended anyway, and now sits in one of the infamous “rubber rooms” while he waits for the district to decide his fate. Officials are doing their best to dig up dirt on him".
  • The reports on "The federal government is spending $125,000 to study adjectives that could be perceived as sexist or racist.". A good use of taxpayer money?
  • reports on "How 'Adjunct' Professors are Exploited". From the article, "According to data collected by the Chronicle of Higher Education, adjuncts at one college and two universities near my home in Southeast Florida earn between $1,380 and $3,000 to teach a fifteen-week, three-credit course. My own university’s published rates range from $1,500 to $3,000. A national survey found the average pay for a three-credit course to be $2,700...Given that the typical equation for calculating preparation and grading time for a three-credit course is three hours for every one hour of class time, it’s safe to assume that adjuncts put in a good 135 hours during a semester. That works out to just over $10 an hour for someone making the lowest rate and about $22 an hour for the higher rate based on the rates listed above...A report from the University of California at Berkeley found that nearly a quarter of all adjunct professors receive some form of public assistance, like food stamps or Medicaid. Many must, as grown educated adults with advanced degrees, live with their families, and struggle to afford basic food requirements. One adjunct professor reported, “I lived off of fried potatoes and onions for the semester. I actually lived better as a grad student than I do now.”.."

tkz-euclide: Snell's Law



Snell's Law is a formula in basic physics which follows easily from Calculus. This makes it worth deriving in your class. I've put together 2 diagrams (the PDFs can be downloaded from the Graphics page) and I've posted the approach to designing these graphics using just the basics of Altermundus' tkz-euclide package. That's posted here and the tex files are attached for you to modify/adjust the colors or notation.

Here are some stories that caught my eye this week:

  • livescience has an article "New Brain-Like Computer May Solve World's Most Complex Math Problems" which looks at a new type of computer design, "In contrast, Massimiliano Di Ventra, a theoretical physicist at the University of California, San Diego, and his colleagues are building "memcomputers," made up of "memprocessors," that both process and store data. This setup mimics the neurons that make up the human brain, with each neuron serving as both the processor and the memory...Now, Di Ventra and his colleagues have built a prototype memcomputer they say can efficiently solve one type of notoriously difficult computational problem. Moreover, they built their memcomputer from standard microelectronics...The new memcomputer solves the NP-complete version of what is called the subset sum problem. In this problem, one is given a set of integers — whole numbers such as 1 and negative 1, but not fractions such as 1/2 — ."
  • The Journal Gazette reports, "A 15-year-old high school student visiting Boston's Museum of Science has uncovered a math error in the golden ratio at a 34-year-old exhibit....Joseph noticed minus signs in the equation where there should have been plus signs. He left a message at the desk and later received a letter from the museum's exhibit content developer, Alana Parkes, informing him the equation would be corrected. Parkes wrote the mistake had been there for a "very long time" without being noticed."
  • The Daily Beast notes "Only one in eight Common Core-aligned textbooks actually meet Common Core standards—and none by textbook giants Pearson or Houghton Mifflin Harcourt—but they were repackaged and sold to public schools anyway, at taxpayers’ expense."
  • The Statesman Journal tells the story of a letter sent by a school to parents "The third paragraph of the letter begins: "Children must be picked up on time. If they are not picked up on time we will call DHS and you will then have to pick them up at court the next day." The letter also talks about dropping children off in the morning. "We will be serving breakfast at 7:45 a.m. at no cost," the letter said. Cafeteria will close at 8:15 a.m. for breakfast. If your child is running late, please feed them at home before sending them to school. Please do not drop your children off before this time. There will not be supervision. If children are dropped before 7:40 the staff will call the authorities."". Parents are upset and a district spokesman says the letter was sent in error. So----they said it but didn't mean it.
  • RT reports on the politicization of history in school. "In addition, the books will teach that the Civil War was caused by “sectionalism, states’ rights and slavery" ‒ in that particular order so as to emphasize the idea that slavery was not the main driver of war, and that, in the context of the 1860s, states' rights and slavery were not intertwined. Slavery was "a side issue to the Civil War," conservative state education board member Pat Hardysaid in 2010 when the board was considering new standards. “There would be those who would say the reason for the Civil War was over slavery. No. It was over states’ rights.""
  • has the article, "'Free' Community College Already Costs 50 Percent More than Originally Estimated". From the article, "For those who missed the whole thing, here are the basics: President Barack Obama and several leading Democrats want to make community college free for students who would then transfer to four-year colleges for bachelor's degrees and for those who are in training programs for occupations that the state determines to be part of an "in-demand industry sector." The federal government will pay two-thirds of the cost, but states will have to chip in one-third to participate...None of these plans seem to seriously deal with the fact that its government subsidies to education that have driven up these costs. That massive debt middle class students are racking up isn't paying for instructors. It's paying for boatloads after boatloads of administrators making plum salaries for managing these reform programs that the government insists will make colleges better. The government isn't making college cheaper. It's making it even more expensive.". Quantity of education doesn't equal quality so this seems like an even bigger waste of money. Remember this post? where you'll find the quote from a Michael Snyder article, "In Japan, Finland and the Netherlands, young adults with only a high school degree scored on par with American Millennials holding four-year college degrees, the report said". The article also says "It also mandates community college systems provide plans for "institutional reforms and innovative practices to improve student outcomes." I suppose writing on a slip of paper "Grade inflation!" would not qualify."  If they could deliver a quality public school education that resulted in literate students with good math skills there'd be no need for this. But they can't. So what's the quality of education that students will get in a school that needs to "improve student outcomes". No question mark there because it's more of the same low quality education. Excellence in education is found mainly in private schools and public schools in affluent areas where the parents help to assure the quality.
  • Solve my maths has a post Concentric Circles Problem that would be useful for a lot of math teachers. The Humor section of the site has some nice content too.
  • notes, "A bill introduced in the New Jersey State Senate last month seeks to put a three-year moratorium on the growth of charter schools in the state.In a blistering op-ed this week in NJ Spotlight, Dale Caldwell, the head of school at the Village Charter School in Trenton, argues that the New Jersey Education Association (NJEA), the state's largest teachers union, is behind the legislation. The union's goal: to preserve its monopoly over public education in the state.". The posted video is worth your time. The "blistering op-ed" piece is here.

Resource: Internet Archive


Who doesn't like quality, free resources? The Internet Archive explains on their About page: "The Internet Archive is a 501(c)(3) non-profit that was founded to build an Internet library. Its purposes include offering permanent access for researchers, historians, scholars, people with disabilities, and the general public to historical collections that exist in digital format.

Founded in 1996 and located in San Francisco, the Archive has been receiving data donations from Alexa Internet and others. In late 1999, the organization started to grow to include more well-rounded collections. Now the Internet Archive includes: texts, audio, moving images, and software as well as archived web pages in our collections, and provides specialized services for adaptive reading and information access for the blind and other persons with disabilities.".

What separates the Internet Archive from other resources is threefold: the quality of their resources, the range of resources (books, software, audio, video) and the ability to read through many of the books by flipping through the text (as well as downloading it in a variety of formats). Take a look at Kotov's "Grandmaster at Work"


Notice the 2 red boxes? The box at the bottom displays a variety of formats that you can download the book in. The box near the top right surrounds the "Full screen" button. Press that button to go into full screen mode.


Clicking on the right hand page flips the book forward, while the left hand page flips you back. So you can browse the resource online. Notice that the screenshot above has two more red boxes. The one in the top right hand corner will activate the voice reading of the book. The red square in the bottom left hand corner is a slider that can quickly get you to deep inside the book without flipping each page.


My only complaint is that the Search feature wasn't as helpful in finding the resources. I failed to find some books through searching "mathematics" which turned up in other unrelated searches.Here are some links to get you started:

Spivak: Calculus book, Supplement for the book, Dugopolski: Precalculus, Beginning and Intermediate Algebra,lots of CK-12 series books CK 12 AlgebraCK 12 Algebra II with Trigonometry, MOOCulus Sequence and Series Textbook, Advanced Math 2Python Programming, Soltis: What it takes to become a chess master, Botvinnik: Half a Century of Chess, Alburt: Test and Improve Your Chess, Kosikov: Elements of Chess Strategy, lots of old Schaum's books, and so much more! I've added the link to the Internet Archive to the sidebar.

Here are some stories which caught my eye the last week:

  • The Intercept looks at "NO CHILD LEFT UN-MINED? STUDENT PRIVACY AT RISK IN THE AGE OF BIG DATA". From the article, "“What if potential employers can buy the data about you growing up and in school?” asks mathematician Cathy O’Neil, who’s finishing a book on big data and blogs at In some of the educational tracking systems, which literally log a child’s progress on software keystroke by keystroke, “We’re giving a persistence score as young as age 7 — that is, how easily do you give up or do you keep trying? Once you track this and attach this to [a child’s] name, the persistence score will be there somewhere.” O’Neil worries that just as credit scores are now being used in hiring decisions, predictive analytics based on educational metrics may be applied in unintended ways. Such worries came to the fore last week when educational services giant Pearson announced that it was selling the company PowerSchool, which tracks student performance, to a private equity firm for $350 million. The company was started independently; sold to Apple; then to Pearson; and now to Vista Equity Partners. Each owner in turn has to decide how to manage the records of some 15 million students across the globe, according to Pearson."
  • reports on famous author Judy Blume warning about censorship in today's world.
  • Huffington Post has a piece on Dr. John Urschel, professional football player, on why more kids don't like math.
  • Microagrressions, which I mentioned in this post, are back again. Although I learned "America is a melting pot", that's now a color blindess microaggression because it denies a person of color's racial/ethnic experience. The College Fix can help get you up-to-date on on the latest witch hunt. From the article, "University of Wisconsin-Stevens Point officials have advised faculty that the term “America is a melting pot” is a racial microaggression. The common phrase was among a list of examples of so-called racial microaggressions used “as a discussion item for some new faculty and staff training over the past few years,” a campus official told The College Fix in an email. Other phrases on the list included: “You are a credit to your race,” “where are you from,” “there is only one race, the human race,” “I believe the most qualified person should get the job” and “everyone can succeed in this society if they work hard enough.”. Take some time and look at the lists from University of Wisconsin and University of California. Lots of the examples on the list are ambiguous in the sense that it presumes you know WHY a comment was made. So the example, to a woman of color about "I would never have guessed you were a scientist." is considered a microaggression. because it's assumed you said it because she's a woman which means it could be perceived as insulting her intelligence. Apparently it's okay to to say it to a white male, though, because it wouldn't be an attack on his intelligence....wait, what? Or if you've mistaken a faculty of color mistaken for a service worker then it assumes you've done it because they are of color and not because of how they were dressed, where they, or who they looked like. Heck, I've been mistaken for someone working in a store that I was shopping in for who knows what reason.  Should I have been insulted? HOLDING AN OPINION that, "Affirmative action is racist" IS FORBIDDEN because it makes it seem like one group gets extra privileges. And the common practice of empathy, such as a someone saying, "As a woman, I know what you go through as a racial minority" is enough to cause a problem. How can a woman possibly know what racial discrimination is like. Your AMBIGUOUS ACTIONS are now under assault. "A person asks a woman her age and, upon hearing she is 31, looks quickly at her ring finger" is a problem because the reason WHY you did that was you thought "Women should be married during child-bearing ages because that is their primary purpose.". If faculty are being taught that examples like they've listed are transgressions then you get an indication of how today's young are looking at the world. It's a less tolerant, "he/she said this which made me feel ___, therefore they must pay the price". Imagine spending money to get an education and coming out less educated and less tolerant. ZeroHedge has a piece on how "hate speech" is used to destroy "freedom of speech".
  • There's an annoying piece that's getting a lot of play. From the Western Morning News we hear "Myth that men are naturally better at maths than women debunked". Now you'd think that such a conclusion would be based on some test scores which would show that women scored just as well (or better) than men. No such case. From the article, "US psychologist Dr Shane Bench, from Washington State University, who led a study that involved assessing the ability of men and women to predict their performance in maths tests, said: "Gender gaps in the science, technology, engineering and maths fields are not necessarily the result of women's underestimating their abilities, but rather may be due to men's overestimating their abilities." His team conducted two studies of 300 undergraduates who were asked to have their maths skill tested before guessing how well they had fared. In the first study, participants received feedback about their real performance before they were again asked to take a test and predict their scores. For the second study, the students only sat one test without receiving any feedback, and were questioned about any plans to pursue maths-related courses Across both studies, men were consistently found to overestimate the number of problems they solved correctly while women's appraisal of their own abilities was more accurate. After receiving feedback about how well they did in the first study, men were then better at estimating their scores in the second test.". Got that? With no information on actual math scores, what does this mean?? Suppose, for example, women scored 75% on the test and then estimated they scored about 75% whereas men scored 80% and estimated they scored 85%. Then the women are more accurate at gauging their performance, but since their performance is worse, how would that debunk the claim that men are better than women at math. And to make things worse, the research said "After receiving feedback about how well they did in the first study, men were then better at estimating their scores in the second test.". I'm not sure how this "research" proves anything. It only seems to show that, without feedback on performance, women are better at appraising their performance than men. But with feedback on performance (which is what happens in the real world as students get feedback on each test throughout the semester) men are better at appraising their performance. But none of this has to do with mathematical expertise.
  • The PC climate claims another high school teacher. has the report, "An Illinois high school teacher was fired after stepping on the American flag to prove a point about free speech. The teacher, Jordan Parmenter, had been using a flag as a pointer during class on May 15. At least one student accused him of being disrespectful toward the national symbol, so Parmenter dropped the flag on the ground and stomped on it, according to Word quickly spread, and soon enough, demonstrators appeared outside Martinsville Junior-Senior High School. Parmenter wrote a letter of apology, but the school board voted 6-0 to fire him....The school board had a golden opportunity to show kids that honoring the values the flag represents is more important than honoring the flag itself. Instead, they imparted a different lesson: that no act of defiance goes unpunished by the government. Perhaps that’s an important lesson as well.".  Beware the angry mob.
  • The PC climate claims a college teacher as well. The Advocate has the story of an LSU professor, Teresa Buchanan, fired for using salty language. The teacher is fighting back with a lawsuit. From the article, "She said the university is trying to dictate how she teaches and in the process is impinging on her academic freedom. “The occasional use of profanity is not sexual harassment,” Buchanan said. “Nor is the occasional frank discussion of issues related to sexuality, particularly when done in the context of teaching specific issues related to sexuality.” LSU spokesman Ernie Ballard declined comment Friday on Buchanan’s dismissal, saying it’s a personnel matter and involves possible litigation. Buchanan was fired even though a committee of five faculty members that presided over an 11-hour dismissal review hearing held on March 9 recommended that she keep her job. While the committee found that her adult language and humor violated university policies that protect students and employees from sexual harassment, it found no evidence Buchanan’s comments were “systematically directed at any individual.” The committee recommended she be censured and agree to quit using “potentially offensive language and jokes” that some found offensive."



Sagetex: Definite Integrals


I've added two definite integrals to the Sagetex: Integrals page. The first problem creates two random parabolas in different directions and the area between the two curves must be calculated. This requires them to find the intersection points as well to set up the integral properly. The second integral gives a random exponential in e along with (random) endpoints of integration.


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

  • USA Today reports "Texas is decriminalizing students' truancy": "Gov. Greg Abbott has signed into law a measure to decriminalize unexcused absences and require school districts to implement preventive measures. It will take effect Sept. 1. Reform advocates say the threat of a heavy fine — up to $500 plus court costs — and a criminal record wasn't keeping children in school and was sending those who couldn't pay into a criminal justice system spiral. Under the old law, students as young as 12 could be ordered to court for three unexcused absences in four weeks. Schools were required to file a misdemeanor failure to attend school charge against students with more than 10 unexcused absences in six months. And unpaid fines landed some students behind bars when they turned 17."
  • There's a wrinkle in a story from my last post. A teacher who was reported to have been removed from his position because he read from Mark Twain was actually removed for making an inappropriate joke (relating to a Mark Twain passage). LA Times has the details: "In his first interview since he was pulled from his fifth-grade class, Esquith told The Times on Monday that controversy stemmed from a joke he made in the classroom. He said he quipped with students that if he could not raise enough money for the annual Shakespearean play, they would all have to perform their parts naked like the king in Mark Twain's "The Adventures of Huckleberry Finn." After another teacher complained, he said he explained the context of the joke to his principal at Hobart Boulevard Elementary. The principal, he said, told him he had nothing to worry about. Nonetheless, Esquith was removed from the classroom in April."
  • EducationWeek reports on the L.A. Unified budget has reduced the spending on police. This was a victory for The Dignity in Schools Campaign which, "..demanded that the school district, which is the second largest in the country, redirect $13.1 million in funds it had planned to spend on policing practices during the 2015-16 school year into jobs and programs aimed at improving school climate. (The district is still budgeting about $54 million for school police from other parts of its budget.) Though the district school board adopted the revised budget, campaign organizers don't yet know how much of the redirected money will go toward their specific funding recommendations, which include using $8 million for restorative justice measures like technical assistance and staff training, as well as $5 million for hiring prevention and intervention staff in alternative schools to create counselor-student ratios of 1 to 50. Such investments have been proven to positively transform school climate, whereas school-based policing has not, said Ruth Cusick, an education rights attorney at Public Counsel."
  • Huffington Post's piece "Meet the 63rd Black Woman in American History with a Physics Ph.D." provides a glimpse into "the challenges faced by marginalized communities in science".
  • Put this on your radar: has an update on a case making its way through the legal system: "A little over a year ago, a group of nine California students with the help of the activist group Students Matter won an amazing victory in California Superior Court in the case of Vergara v. California.As I reported at the time:

    Judge Rolf M. Treu reasoned that the challenged teacher rules—regarding permanent employment status, dismissal procedures, and a "last in first out" rule for layoffs—do indeed damage California children's constitutional right (on the state level) to an education. He wrote that the challenged statutes "cause the potential and/or unreasonable exposure of grossly ineffective teachers to all California students" and "to minority and/or low income students in particular, in violation of the equal protection clause of the California constitution."

    Naturally, the losers appealed, and Judge Treu stayed actual enforcement of his ruling pending appeal. Today, the Students Matter side filed their brief in the appeal process in the Court of Appeal for California, 2nd appellate district....In a press conference call this morning announcing the brief, lawyers on the Students Matter side say they still need to wait for the teachers side to file its response brief and then await an actual court date. Once the hearings are over, though, a decision must come within 90 days, but that could still be a very long time away--more's the pity for California public school students.". There's a decent video that's posted on the page.

  • The Norway Chess Tournament 2015 ended with victory for Topalov. The tournament was marred by some blunders and a short draw between Anand and Topalov in the final round. But most newsworthy is what Chessbase reports here,"...this is easily the worst tournament ever played by Carlsen after obtaining his GM strength."
  • The 43rd Sparkassen Chess Meeting Dortmund 2015 has begun; it features players such as Kramnik, So, Hou Yifan, Naiditsch.
  • American chess lost an icon recently. The NY Times has a piece on Walter Browne who passed away in Las Vegas at the age of 66.
  • Michael Krieger posts on "Salt “Black Markets” Emerge in Indiana School System as Students Seek to Avoid Bland Michelle Obama Lunches"

Resource: SymPy Gamma


It's not considered important enough to be implemented in Sage but I think every teacher sees the educational value if Sage were able to show the steps of its calculations. SymPy Gamma shows how it could be implemented for (some) derivative and integration problems. I've typed in the command integrate(ln(x)) which results in the screenshot above (where it annoyingly writes ln(x) as log(x)). In addition to that information it plots the graph of the solution and even finds the root.


But the explanation for how it got the answer was most impressive:


The main problem is that there were plenty of times in my experimentation that the steps weren't given--as I said already, it shows the solution for some problems. Before you rush out and try it I need to mention I that while most of the output is provided quickly, some of the information (usually the plot) can take a lot more time to show up-maybe a minute or so. And sometimes it just "times out" without giving all the output. So if you're willing to put together problems that result in a solution you've got a great teaching tool for calculus. I've added SymPy Gamma to the links on sidebar.

Here are some issues that caught my eye this week:

  • There's growing opposition to the growing budget for police protection in Los Angeles schools. Southern California Radio has the story: "Superintendent Ramon Cortines proposed growing the school police budget by about $2 million, bringing the department's total funding to $59 million for the 2015-2016 school year. The district runs the largest school police department in the country with more than 350 officers. The armed staff supervise students who walk to and from school under a safe passage program and perform other duties related to campus security....Last fall, school police estimated they would need 80 new officers to protect students walking home from school with iPads. The department later retracted the statement....Students living in communities such as Watts are more likely to feel harassed than protected by police, according to Ruth Cusick, an attorney for Public Counsel, a legal advocacy group....The school police department drew scrutiny last fall after reports that it owned an armored tank, grenade launchers and more than 60 assault rifles from the military surplus program. The district later returned some of the weapons.". While police protection sounds great, the harassment mentioned above hearkens back to 2012 when police were issuing citations to kids as young as 6 for fighting and, for example, "...two boys who were stopped by officers near their school, minutes late, and were searched, handcuffed and allegedly intimidated inside a squad car before officers took them into school and wrote them curfew tickets.". As covered in more detail here, "Students at schools with some of the highest dropout rates have reported staying home if they were running late — rather than risk meeting up with police and getting tickets that can rise to $400 once court fees are tacked on.". The vote on the budget is set for Tuesday.
  • Connie St Louis, one of the women who led the campaign to oust Tim Hunt from his job explains her side of the story to Scientific American. Her agenda goes even deeper: "I didn’t just call out Hunt in that first tweet, however, but also the Royal Society, the U.K.’s national academy of science, where he is a fellow. Sexual inequality in the STEM fields continues in part because the Society continues to take very little action....I felt it would be a waste if the uproar ignored the forest for trees—rebuking only Hunt and not higher orders of power as well—so my next action was to present a framework for systemic change:...The Royal Society was founded in 1660 there has never been a female president, so I went to and set up a petition called, “Its time to elect a female president to lead the Royal Society.” So far there have been only 68 signatures .... Condemning one mans’ sexist remarks is not enough. It is important that this episode also affects change for women in science.". Racism and sexism will always exist--but is the playing field so unfair when the targeted group can bully the system to remove a former Nobel Prize winner and use that issue to push for a female president of the Royal Society? It seems like "the system" is on her side. Indeed, in her own article (link above) she recalls a "disturbing" dream where she's confronted by reporters: "They are all shouting the same question: “How did you think you would get a way with publically calling to account a prominent white male scientist?”". No such problem in the real world.
  • In an earlier post, Jerry Seinfeld expressed his displeasure with the extreme PC environment on college campuses. A college student wrote in to Huffington Post to explain comedy to Jerry Seinfeld. Comedian Bill Maher takes aim at these 'idiots' and dispenses his verbal beat down of the college student as only a comedian could. It can make you laugh or maybe it will offend you--view at your own discretion.
  • LA Times reports on a "nationally recognized" teacher who was removed from his post for reading a passage from Mark Twain's book "The Adventures of Huckleberry Finn". The PC climate, again. Great literature forces can force you confront some uncomfortable questions whether it's "Lord of the Flies", "1984", "To Kill a Mockingbird" and other numerous books that are targeted for banning. The American Library Association's website notes "Each year, the ALA's Office for Intellectual Freedom records hundreds of attempts by individuals and groups to have books removed from libraries shelves and from classrooms.". How many of those classic books have you read?
  • The French government is warning it's citizens about the US attitudes/culture. From the article,"Along with warnings about slower speed limits, higher drinking ages and hurricanes in Texas, the French foreign ministry adds a note of warning against being too “Latin.”“It’s recommended to adopt a reserved attitude toward those of the opposite sex,” it says. “Comments, behavior, and jokes, which might be harmless in Latin countries, can lead to criminal cases,” the ministry’s website says....Reinforcing French views of American prudishness, the website notes that even minors can be accused of sexual harassment, and asks that children use toilets reserved for their sex in the U.S....Among other advice to the French in America: “keep calm in all circumstances” since some states authorize the carrying of weapons. It asks visitors to avoid raising their voice or making sudden or aggressive gestures at the police."
  • With 4 out of 9 rounds down, the Norway Chess Classic 2015 is drawing attention for Carlsen's poor showing. As Chessbase notes, "This disaster, however, is simply unprecedented.". Round 1 started with magnificent play by Magnus to achieve a winning position. But he lost on time because he didn't know the time control for the tournament(!!!). It's been downhill from there. He was outplayed by Caruana and Anand. You can follow the games at the tournament site here.
  • The Daily Caller reports on the "fiasco" while implementing Common Core in Nevada: "Under No Child Left Behind, states are supposed to test children in grades 3-8 each year in mathematics and reading. At least 95 percent of students must take the tests, or else a state can face federal sanctions such as a loss of millions of dollars in funds. Nevada, on the other hand, was only able to test 37 percent of the 213,000 students it was supposed to, thanks to a cascade of glitches and computer problems that left students unable to complete their exams. In Clark County, which contains the Las Vegas metro area and over half the state’s students, only 5 percent were successfully tested. Because so few were tested, Nevada’s department of education says it will be unable to issue grades for individual schools based on performance, like it is supposed to. The failure means Nevada is at risk of losing millions in federal funding, but such sanctions are unlikely in this case because the state made an honest effort that simply undone by technical shortfalls.". There is, of course, a scramble to assign blame.
  • WND has a piece on author Alex Newman calling for a debate with Huffington Post writer "...Rebecca Klein over her June 4 article, “5 of the Most Extreme Claims Made Against Common Core In The Last 5 Years.”One of her claims was Newman’s contention in March 2014 that Common Core was part of a global agenda to “transform American children, and students around the globe, into what globalists refer to as ‘global citizens’ ready for the coming ‘green’ and ‘sustainable’ world order.” He is asking for her to investigate the claim for herself. For example, in a 2010 speech at the Sustainability Summit, Duncan bragged that his Education Department was “taking a leadership role in the work of educating the next generation of green citizens and preparing them to contribute to the workforce through green jobs.” In a separate 2010 speech given to UNESCO, Duncan proclaimed the U.S. must partner with foreign countries to tackle global challenges. Newman also addressed another one of Klein’s five “extreme” claims: that Common Core will turn kids into communists and/or socialists. She accused Glenn Beck and Rep. Jim Bridenstine, R-Okla., of making those assertions. However, as Newman pointed out, that’s not exactly what Beck and Bridenstine said." . Two very different perspectives that should give a lively debate. Will she rise to the challenge or give the other side "bragging rights" by refusing. Stay tuned!


Sagetex: plotting templates


The plotting templates that are posted on the Handouts page should be good enough for most of your plotting needs--they're convenient because you don't need sagetex and Sage to use them. But lately I've found myself graphing functions that can't be done with those templates, such as the Cantor function, and decided to make sagetex driven versions of those 2 templates. The image above shows the version with the magnifying glass--the zeta function, Weierstrass function, and a Fourier series have been plotted simultaneously. I've made the main tick marks thicker but the important change is seen in the circular magnified portion. The templates incorporate comments by reader Lazza posted on the Plotting with Sagetex page to get around a problem of having enough points to make the graph look good but not too many that it won't compile. The complicated functions would look like this (step size .01):

SagetexSPYorigThe Fourier plot doesn't look smooth and the Weierstrass function looks too smooth. Lazza's comments apply to the regular template as well.


Note that for the zeta function above, the red circle shows that the zeta function doesn't go to the bottom of the screen with step size .01. This issue, which was previously mentioned on the Plotting with Sagetex page, can sometimes be solved by increasing the number of points. But if there are too many points, the code doesn't run. Lazza's improvement allow for decreasing the step size in just the areas where more points are needed. For the zeta function, the problem area is before 1, so the x coordinates could be calculated as:

x2_coords = srange(LowerX,.8,.001)+ srange(1.2,UpperX,step)

Without step of .001 the function doesn't make it to the bottom but .01 is adequate for the right hand piece. Also, starting at 1.2 avoids all the non-plotted points in between the two pieces. And of course, you could break this into 3 intervals so that the step size of .001 is only used closer to .8, say .75 to .8, eliminating even more points. Once the x coordinates are determined the y coordinates follow easily with a simple statement:

y2_coords = [(zeta(t2)).n(digits=6) for t2 in x2_coords]

The two templates can be found on the Plotting with Sagetex page along with more information, such as how the graph paper feature can be turned off or having a frame instead of axes. With these templates you can have the same look and feel for whatever you're graphing plus the additional power of Sage.

So many stories that caught my eye over the past week!

  • The NY Post tells us that a Brooklyn high school was caught giving students science credits they needed to graduate by taking math classes. "The scheme was engineered following the February transfer of the only 12th-grade science teacher at Lafayette HS, where most of about 350 students are immigrants, the source said...Principal Jon Harriman didn’t return a call seeking comment — and on Friday sent out an e-mail instructing school faculty not to speak with reporters.". Seems likely this story will continue to evolve.
  • ProPublica has an audio interview with theJohannes Bohannon, Ph.D., mentioned in an earlier post, about how he was able to convince the world that chocolate can help you lose weight.
  • I used to have tissues and antibacterial lotion for students to use, if they wanted, when they came into class. IFLScience explains "Why You Should Never Use Hand Sanitizer".
  • has the crazy story of a Thomas Jefferson high school student at the center of controversy: "The Korean media dubbed Sara Kim the “Genius Girl.” A young math whiz so brilliant that two elite universities, Harvard and Stanford, offered her dual admissions. Her father, an exec at Korean game company Nexon, must have been proud! Other people, however, were suspicious. ..., which ran the original story, received similar denials from both Harvard and Stanford in afollow-up report published today. In this latest update, Kim allegedly still says she is not lying and is sticking with her story that she has been accepted into both universities....While reporting this story, today writes it received an email on Monday signed by Harvard Public Affairs and Communications official Anna Cowenhoven, stating that Sara Kim had been accepted by the Ivy League university. The following day, Cowenhoven told the paper that the email was also a forgery.".
  • Do you let kids eat in class or give out food to them? The NY Post also reports, "A Harlem boy allergic to peanuts died after school staff inadvertently gave him a nut-based candy bar and then failed to immediately administer an antidote or call an ambulance, his devastated mother charges...The tragedy was compounded by the fact that Brandon, the eldest of three kids, was due to be a bone-marrow donor for his younger brother, Tyler, who suffers from sickle cell anemia, ...."
  • The Washington Post writes, "A Woodbridge teenager admitted in court Thursday that he was the secret voice behind a pro-Islamic State Twitter account, which once counted more than 4,000 followers, and that he helped another teen travel to join the Islamic State in Syria. Ali Shukri Amin, 17, a former student at Prince William County’s Osbourn Park High School who was arrested earlier this year, pleaded guilty to conspiring to provide material support to a terrorist organization. As part of a deal with prosecutors, he admitted that he helped arrange a successful trip to Syria for an 18-year-old Prince William County man who wanted to fight with the Islamic State."
  • The tragic story of high school student Kalief Browder, first mentioned here,  who spent 33 months in prison without a trial before charges were dropped has a tragic end: he committed suicide recently. The damage of torture and starvation haunted him after he was freed. "At Rikers, Browder spent two of his three years in solitary confinement. There, as he frequently recounted later, Browder was routinely brutalized and starved by guards and subjected to virtually unrestrained violence by other prisoners....After a visit with Browder in the psych ward at St. Barnabas Hospital in January, Gonnerman described him as “gaunt, restless and deeply paranoid.”She added: He had recently thrown out his brand-new television, he explained, “because it was watching me.” Condolences to his family on their unnecessary, tragic loss.
  • ZeroHedge posts on BioMed Central: "A major publisher of scholarly medical and science articles has retracted 43 papers because of “fabricated” peer reviews amid signs of a broader fake peer review racket affecting many more publications."
  • A school in Idaho is arming staff to protect students. According to the Guardian, "A tiny school district in Idaho far removed from law enforcement has purchased firearms and trained a handful of staff to use them should the same school shooting rampage that has occurred across the country take place. It takes at least 45 minutes for officers to reach the Garden Valley School district – a district made up of less than 300 students all taught in the same building – where limited funds have prevented the school from being able to afford hiring police officers to patrol the building during school hours."
  • The NY Times reports on the crippling education budget problems in Arizona: "In the rural Saddle Mountain Unified School District 50 miles west of Phoenix, three new libraries have been locked since last year. In a neighboring county, an elementary school closed last month because there was no money to keep it open, even after the district agreed to shift to a four-day week....In Peoria, a suburb northwest of Phoenix, Curtis J. Smith, the principal at Peoria Elementary, said he had about $42,000 to pay for toilet paper and printing paper; athletic equipment and arts materials; and light bulbs, small repairs and cleaning materials for the school year that ended May 22. It amounts to only $68 for each of his 620 students over the school year. Next year, Mr. Smith will have roughly $32,000, or about $52 per student."
  • There's plenty of buzz for this story which is continues the PC theme in schools mentioned in the last post--but this time it's in the UK. Several articles stand out from the rest: Huffington Post gives one woman's harsh, sarcastic perspective on the tone deaf statements by former Nobel Prize winner Tim Hunt which led to his in "The Illiberal Persecution of Tim Hunt" provides my view: "In a normal world, a world which valued the freedom to make a doofus of oneself, that should have been the end of it. Seventy-two-year-old man of science makes outdated joke, tumbleweed rolls by, The End. But we don't live in a normal world. Certainly we don't live in a world where people are allowed to make off-color comments. And so with tedious, life-zapping predicability, Hunt fell victim to the offence-policers, to the machine of outrage being constantly cranked up by self-styled guardians of what we may think, say, and even joke about....What is truly alarming, what should really send a shiver down every liberal's spine, is not the words that came out of Hunt's mouth but the haranguing of him that followed, the shunning of him by the academy and possibly by the scientific elite itself...The response to Hunt is way more archaic than what Hunt said. Sure, his views might be a bit pre-women's lib, pre-1960s. But the tormenting and sacking of people for what they think and say is pre-modern. It's positively Inquisitorial...The Hunt incident is quite terrifying. For what we have here is a university, under pressure from an intolerant mob, judging a professor's fitness for office by his personal thoughts, his idea of humour. Profs should be judged by one thing alone: their depth of knowledge. It shouldn't matter one iota if they are sexist, stupid, unfunny, religious, uncouth, ugly, or whatever. All that should matter is whether they have the brainpower to do the job at hand. UCL and the mob's hounding of Hunt echoes the university of the pre-Enlightenment era, when only those who were 100 percent Good Catholics had a hope in hell of getting a job. Only now, academics must be unflinchingly in accordance with the commandments of PC rather than with Biblical thinking." Missing from most accounts is provided by one woman who, thankfully, has come to his defense. Sarah Vine of the Daily Mail writes, "His so-called sexist remarks were actually, it turns out, more a veiled mea culpa. His wife (an equally eminent scientist, immunology professor Mary Collins, who, ironically, has done much to further the standing of women in science) was once his student. She was already married when they met over the roaring flame of a Bunsen burner. They had an affair, she divorced her first husband — and she and Sir Tim have been together for the past 20 years. ‘I have fallen in love with people in the lab and people in the lab have fallen for me, and it’s very disruptive to the science,’ he said yesterday, trying in vain to calm the story and explain why he’d said what he’d said. ‘These emotional entanglements make life very difficult.". And after reminding the reader of other cases where men have been taken down for their not being sensitive enough (such as atrophysicist Matt Taylor reduced to tears for wearing "...a shirt emblazoned with scantily clad women of the comic-book variety...") continues, "Don’t get me wrong. I wouldn’t die in a ditch to defend any of these three men as being entirely innocent. You might say they were all a bit silly, or you might say they were just being men. But I would argue that the enraged response from women in all cases was wildly disproportionate...But the feminists aren’t prepared to cut them that slack. They spot a potential target, zone in on their off-the-cuff remark, or their lurid shirt, or their ill-advised joke, and harry away until they achieve their goal: emasculation, defenestration, prostration or gibbering apologies. But what does this tactic actually do for the feminist cause?". But there's an interesting side story from the Huffington Post piece (above): "In a recent article posted on the Science Magazine website, Alice Huang, herself a very successful scientist, dispensed advice to a young female researcher wondering how to cope with the perceived unwelcome advances of a senior male colleague. Dr. Huang's recommendation: put up with it. She went on to say that it was likely that the male colleague likely couldn't help himself and as such, should be forgiven. Following substantial (and in my view, highly warranted) backlash on social media, this article was quickly removed.". Bloomberg Business has that report under the prurient headlines "Academic Journal Deletes Article Telling Woman to Let Adviser Ogle Her Breasts". Like Nigel Short, notice the comments getting twisted in the headlines by a "journalist". Dr Huang, a woman, gets some heat for her advice which isn't PC enough. The original question and answer are posted; no information on whether she'll lose her job. But recognize that a man giving the same advice starts with an extra strike of being a many--so he can be freely labelled and abused (in a way a woman can't) by a reactionary mob. Unfortunately the younger generation has a much different set of acceptable standards than their parents. Check out "The Most Whiney, Thin-Skinned, Easily Offended Society In The History Of The World" posted on ZeroHedge which explains the thinking of today's younger crowd and the  "microaggressions" they are taught to see, such as opening the car door for a woman. Microaggressions and people's need to make the perceived offender pay the price, regardless of the intent behind the comments get taken very seriously by today's schools and, in the US, by more and more businesses and individuals. If you don't have the proper opinion then, man or woman, the situation can get spin out of control very quickly.
  • You can feel relieved now that the family which cheered too loudly at their daughter's graduation is no longer facing arrest warrants and jail time for cheering too loudly. WREG in Mississippi has the original coverage--with video for you to judge just how disruptive they were. Local channel KOAT has a more recent story telling us the school superintendent (Foster) dropped the charges: ""Our purpose in filing the complaints was not to place a hardship of any kind on the four individuals who disrupted the ceremony, but to protect the rights of the class of 2015," Foster said to WHBQ just minutes after dropping the charges.".
  • American Radio Works has some nice podcasts. Here's one: "What Can Japan Teach Us About Teaching?"
  • The NY Post again: "Reading? Math? Nah- let's teach kids to put on a condom". The article beginning sets the tone: "Can anyone spare a banana? New York City public schools are now offering demonstrations of how to put on a condom. Because, you know, they’ve already mastered teaching kids math and reading. So let’s move on to the important stuff. Well maybe not. Thirty six percent of students in the city were proficient in math and 31 percent were proficient in reading. With these teachers in charge of condom demonstrations, I think we’re headed for a lot of unintended pregnancies."

tkz-euclide: tangents to circles


I've added some more material to the Circles page on Altermundus tkz-euclide package. As I've already mentioned the documentation is in French and having the important information posted in English is both a convenience and necessity when you don't use the package frequently. The material relates to drawing the tangent lines to a circle; there are 2 main cases: Case 1 is to plot the tangent to the circle at a specific point on the circle. The point can be given explicitly, e.g. (-1,1) or chosen at random with one of the macros from the package. Case 2 is to draw one or two tangents to a circle given a specific point outside the circle. That case is shown above; from point C in the picture both tangents have been drawn. You can find the details and the sample files with commentary to walk you through it.

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

  • Chicago public school chief executive resigns from her position," ...amid a federal investigation into a $20.5 million no-bid contract.". Guilt/innocence has not been determined but it highlights yet another problem with a heavy top down educational system: layers of bureaucracy (which drain money from schools), lots of money (so it's easy for a bit to go missing), and the power for people in key positions to direct that money.
  • Caffeinated Thoughts blog has a decent post. From the blog, "Once again, the Common Core Standards are another federal policy which discourages students from memorizing multiplication facts and other basic math theories and formulas.These policies are in place to justify the emphasis on student-centered, discovery, and inquiry methods of instruction which fail because they are laborious, error-ridden, discouraging methods for introducing new concepts to young learners according to research.". My experiences have been similar. Too many people without math backgrounds have too much of a say. They question the need for learning multiplication tables, algebra, homework, and proofs and push for everything to be student centered. There's a time and place for discovery learning as well as drilling. It shouldn't be either/or but both. As classes get more challenging the problems are more complex and you need to be able to finish off the "pieces" of the problem in a reasonable amount of time.
  • reports, "The Farrington Elementary School principal, named a National Distinguished Principal of the year in 2013, resigned within two weeks of the disclosure that mathematics assessment results for 106 students there will be thrown out because of testing irregularities....The school superintendent wrote recently in a letter to parents that two rooms where the tests were administered “inappropriately” contained math “reference sheets and posters.”". Two testing rooms were compromised.
  • King5 news in Washington state reports, on school sexting and blackmail, "The investigation involves two junior high schools, Canyon Park and Skyview. Police say over the past several months, boys were pressuring girls to send nude photos of themselves. In some cases they even threatened to make the pictures public if the girls didn't send more, according to a letter sent home by the district....Sexting with minors can be considered trafficking in child pornography, and police say this case will be referred to prosecutors for possible charges."
  • In California, LAschoolreport informs us of a new educational report which found, "“While most new math textbooks are advertised to be ‘Common Core–aligned,’ few actually are, differing little from their previous editions,” the report stated. “In fact, of the 31 instructional programs formally adopted by the California State Board of Education in January 2014, 10 were reviewed by EdReports, and only one partially met the non-profit organization’s expectations for Common Core alignment.”". It makes me wonder 1. Who determines what material can legitimately be advertised as Common Core? and 2. How come the state didn't have a list of California approved textbooks?
  • Both's piece on a self-described liberal professor who is afraid of his students and conservative commentator George Will's video commentary posted on ZeroHedge mention the power that students have to avoid dealing with speech they don't like. You can even find Jerry Seinfeld and Jay Leno talking about the chilling PC culture on videos here. It all seems to be an extension of a general problem at the high school level as well. Students in the U.S. have a tremendous amount of power and aren't afraid to use it as a weapon. This makes education in the US even more challenging in today's world. I have yet to find a teacher with 2+ years of experience who hasn't felt the unfair power/wrath of kids in the classroom. I've seen some of that overseas as well but the US takes it to a "higher level".  For example, more recently I discovered 2 students (quietly) quizzing each other for some test they were taking later that day. I stopped it and reduced their participation scores for the day. Upon seeing the lower  participation scores posted online, I was told by 1 student it was unfair and they'd tell their parents if the score wasn't changed. I said I'd be happy to talk with the parents. Perhaps the parents agreed with me (I hope so) but it didn't matter: the next day I had admin telling me to change the scores. The student "is a good kid" and admin "had better things to do". This sort of thing would never happen when I taught overseas. The admin would not cave into a student wanting to not pay attention; I doubt the students would even think to approach admin. But not in the US. The above articles and videos indicate this problem is more widescale than you might think.
  • Two California teens arrested for hacking into school computers to change grades. ABC news reports, "The grade-changing incident comes just a few weeks after a senior from Dixon High School in northern California was also arrested for gaining access to his school's computer network, according to police. The student, 18, was arrested on May 13 after school officials learned that over 200 grades of 32 students had been changed, a Dixon Police Department spokesperson told ABC News today. He was charged with unauthorized access of a computer network operated by the government, a felony."
  • reports that presidential hopeful Chris Christie no longer supports Common Core, "Navigating New Jersey interests and a likely presidential campaign, Gov. Chris Christie on Thursday proposed dropping national Common Core education standards he once supported but have since become a lightening rod issue for Republican voters."

Problem: "Puzzle math"


I've added the following puzzle to the Problems page: For the 8 squares below (corners aren't included) squares are adjacent up/down/left/right/diagonally. Fill in each square with a number from 1 through 8 (one time each) so that adjacent squares don't contain consecutive integers. I found the problem here. You can reason it out logically but I ended up using graph theory to get the answer.

Lots of stories this week:

  • A MUST READ article by John Bohannon: "I Fooled Millions Into Thinking Chocolate Helps Weight Loss. Here's How". From the article, "It was, in fact, a fairly typical study for the field of diet research. Which is to say: It was terrible science. The results are meaningless, and the health claims that the media blasted out to millions of people around the world are utterly unfounded." and the key to generate bad conclusions from good data is "...If you measure a large number of things about a small number of people, you are almost guaranteed to get a “statistically significant” result. Our study included 18 different measurements—weight, cholesterol, sodium, blood protein levels, sleep quality, well-being, etc.—from 15 people. (One subject was dropped.) That study design is a recipe for false positives.". And the p-value is instrumental in the deception, "It’s called p-hacking—fiddling with your experimental design and data to push p under 0.05—and it’s a big problem. Most scientists are honest and do it unconsciously. They get negative results, convince themselves they goofed, and repeat the experiment until it “works”. Or they drop “outlier” data points.". This article is a great resource if you teach statistics.
  • Magnus Carlsen won a 3 board blindfold (with clock) exhibition. The video is posted on Chessbase.
  • Caruana and Nakamura earned their place in the upcoming Candidates tournament to determine the next challenger for the World Chess Championship by taking the top two places at Khanty-Mansiysk 2015.
  • The editor in chief of the Lancet, one of the world's most prestigious medical journals has stirred up some controversy. "Dr. Horton recently published a statement declaring that a lot of published research is in fact unreliable at best, if not completely false. “The case against science is straightforward: much of the scientific literature, perhaps half, may simply be untrue. Afflicted by studies with small sample sizes, tiny effects, invalid exploratory analyses, and flagrant conflicts of interest, together with an obsession for pursuing fashionable trends of dubious importance, science has taken a turn towards darkness.. Yes, statistics isn't really math.
  • Forbes has one of those REALLY annoying posts by someone who really lacks basic knowledge about what they're writing about--something all too common in mainstream media where even robots now generate worthless content. Although posed as a question "Should We Stop Teaching Calculus in High School?" the author is clearly saying "yes". "The list of high school math courses in the U.S. hasn’t changed for decades. My daughters are taking the same courses I took long ago: algebra, geometry, trigonometry, and calculus. These are all fine subjects, but they don’t serve the needs of the 21st century.". But the author goes on to say, "...the vast majority will never use calculus again. And those who do need it – future engineers, physicists, and the like – can take it in college.". So the courses do serve the needs of the 21st century. The author makes the point that we are awash in data today so the author asks, "What math courses do young people really need? Two subjects are head-smackingly obvious: computer science and statistics.". Huh? Who believes computer science is math? And anyone reading this blog knows (e.g. see here and here) that statistics isn't math either. Yes, theoretical stats is basically analysis but the statistics he's talking about (confidence intervals, p-values, etc) isn't. Whether (see the links) you want to look at schools having a "department of math and statistics", or that bigger schools have a separate statistics department, or that AMSTAT news says statistics isn't a subfield of math, or as is mentioned in the second link that statistics books and teachers have been presenting p-values incorrectly. If you believe stats is math then please explain what other branch of math teaches you the wrong way to do something as has been done with p-values? There is a different reasoning process for stats. But back to the article. With respect to statistics, "Most high schools don’t offer either one. In the few schools that do, they are usually electives that only a few students take.". Let's mention that statistics is covered in Common Core. The Common Core Standards are posted here and this government site notes, "The recently adopted Common Core State Standards for Mathematics (CCSSM) contain a large amount of statistics in the middle and high school grades and some at the elementary school level.". Not being a math teacher, this author is unaware how much things have changed: more statistics, mathematical proofs in geometry have been largely removed (I even had to teach probability(!) in my geometry classes), and 4 ways to subtract (which has confounded parents) are some noticeable changes. Assuming that because his daughters are taking the same courses he took decades ago means there hasn't been any change in content is, at best, sloppy journalism. To be clear, let me agree that computer courses in high school would be great. Python is such a natural choice that could be useful--but you don't sacrifice core math classes for that; you eliminate or consolidate less relevant courses to make room for it. The removal of most proof content from geometry is tragic because proofs are the essence of mathematics. As Alfred Renyi said, "A mathematician is a device for turning coffee into theorems". The author opting for computer science and stats as math classes while neglecting discrete math is, I suspect, based in the ignorance of not knowing discrete math is the math of computer science. The author continues, "Convincing schools to give up calculus won’t be easy. I imagine that most math educators will scream in protest at the mere suggestion, in fact. In their never-ending competition to look good on a blizzard of standardized tests, schools push students to accelerate in math starting in elementary school, and they offer calculus as early as the tenth grade. This doesn’t serve students well: the vast majority will never use calculus again.". There's some truth in here but since he hasn't taught high school he can't properly interpret what's happening. High schools get awarded numerical scores according to a formula for "performance" (which often get translated into star ratings for the school). Admin look at how they can increase scores (to make their performance look better). More students taking AP exams means a higher score is given, regardless of how poorly the students do. That's why school admins get teachers to encourage students to sign up for AP classes and that's why schools often pay for the student to take the AP exam--it's an easy way to raise the school's score. The consequence is that it's commonplace for students who struggle with fractions to be taking AP Calculus. But no matter, just require a graphing calculator to give students a chance. The child feels smart, the parents feel proud, admin performance improves, and some business makes a lot of money selling expensive calculators when you can buy a laptop computer for $200. The only problem is the child still has poor math skills that they'd be put to shame by a typical student from another country at a lower grade level that has a fraction of the resources but has parents making sure kids learn multiplication tables and basics and not giving them a calculator to use as a crutch at lower levels. But the issue isn't about producing quality in the US, so it's no surprise we never get it. They're looking to maximize performance under the rules they've been given so wasting taxpayer money on improving the school's score gets the admin credit for improving school quality even though no real quality has taken place. Same thing with attendance. Some schools have poor scores due in part to poor attendance. Since that poor attendance is, in cases, predictable (before Christmas break) schools often have incentives (such as a drawing for a free computer) for students who attend. This expenditure of taxpayer money has nothing to do with quality. There's so much to criticize in this article but you get the idea. His argument that "here’s a simple fix: get rid of high school calculus to make way for computer programming and statistics" is nonsense.
  • The controversy of why women don't perform as well as men in chess, which I first raised here, continues with a new study (authored in part by women). The data itself is interesting: "“Hard” sciences such as physics and statistics on average have a larger gender gap than social sciences and humanities – no surprise there. However, this is only part of the story. According to 2013 data from the National Science Foundation in the United States, there is large variation within each category: whereas women earned only 19% of PhDs in physics and 18% in computer science, they earned no less than 54% of PhDs in molecular biology – amounting to gender parity. Within the humanities and social sciences, those numbers ranged from 78% in art history and 72% in psychology to a dismal 27% in philosophy and 28% in music theory and composition.". I think the conclusions drawn off the data are suspect, to put it lightly. "The key claims of Leslie and Cimpian’s paper are: 1. that fields vary in the degree to which its practitioners believe that innate ability (“genius” or “brilliance”) is required for success; and 2. that society often promotes the notion that men have greater innate abilities than women.". If women were doing well in those fields then I don't see how they would be "bluffed" out of continuing. It makes more sense to me that they weren't doing well, didn't like it, found their "passion" somewhere else (as jobs opened up in other more desirable fields), etc.. The fact is that women used to hold a large percentage of computer science job. The claim that women would somehow give up pursuing a job in these lucrative white collar fields  because  society has told them men have greater innate abilities seems demeaning to women and contrary to the general rise of women in the workforce over the past 40 years. Women have faced harassment in many areas and haven't quit. More believable to me is that the radical change in the field took computer science out of their comfort zone: computer science today is so much different than back in the 80's. Note also that the study separates Statistics from math (as it should) and the resulting percentages for the two are quite different.
  • The chronotope blog comments on the (included) recent John Oliver video on student test in high schools. Make sure to check out the video!
  • Ravens guard John Urschel analyzes the extra point rule change in football.
  • The Hindu notes on the passing of chess legend Anand's mother. Grandmaster R.B. Ramesh has a fitting quote, "Without Anand it’s tough to imagine Indian chess. Without his mother, it’s tough to imagine Anand”.
  • CinemaBlend posts on a Tobey Maguire starring as former World Chess Champion Bobby Fischer in "Pawn Sacrific". Check out the movie trailer.
  • Hundreds of SATs go missing. If they aren't found soon the teenagers will have to take them again. Let's hope nobody has their college plans derailed.
  • reports  "Wisconsin may be the first state in the country to certify teachers who don't have bachelor's degrees under a provision put in the state budget....Under the change, anyone with relevant experience could be licensed to teach non-core academic subjects in grades six through 12. They would not need a bachelor's degree and they could even be a high school dropout.". This doesn't sound like a good idea.


Sagetex: Indefinite Integrals 3/4


I've added two more indefinite integrals to the Sagetex: Integrals page.

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

  • The NY Times posts on the tragic death of Nobel prize winning mathematician John Nash and his wife on the NJ Turnpike.
  • The Khanty-Mansiysk 2015 chess tournament continues here with Caruana leading the pack with +1 and only two rounds to go.
  • reports on how a principal was "released" after making racially charged comments during graduation exercises. The posted video lets you judge for yourself.
  • Al-Jazeera reports on how Texas is punishing students for skipping school. From the article (video posted, too): "In Texas, truancy is a Class C misdemeanor that carries a possible $500 fine and the threat of jail time if fines go unpaid when a child turns 17. The law has captured the attention of advocacy group Texas Appleseed, whose research found disabled, poor, and black and Latino students are most often sent to truancy court.".  The poor mom is working 2 jobs and now has extra financial stress trying to pay for her truant son. After watching the video this story describes the pathetic state of many of today's kids and their parents who want to be their friends. Why does the child decide whether he goes to school?!?
  • Stitz Zeager Open Source Mathematics has a variety of free, good quality math ebooks as well as the LaTeX source files.

LaTeX: PDF and tex file output


In an earlier post I mentioned how the output from a Sage session could be saved to a file--you just needed to know the path. As I alluded to, it's possible to do the same through Sagemath Cloud using sagetex, too. That means you can create a pdf and tex file at the same time. But why?

If "because it's fun" doesn't make your list, I've come up with a more plausible scenario. The original Sage Test Template provided a starting point for designing a randomized test. The result was a test along with the answer key in a 3 page pdf. But suppose you don't want the PDF to contain the answer key? It's possible to create a PDF for the test while at the same time producing the tex file for the answer key. Although cumbersome, it can be done. You'll need to create a file

f = open(r"SMCtestAnswers.tex",'w')

As with the earlier post, the file is created if it doesn't exist already. Unlike the that example there is no path given. Once the file is created it's just a matter of filling it with the preamble in order to run and then the answers using the choice of random variables from compilation. So the setup and first solution looks like this:

f.write(r"\usepackage{amsmath, amsfonts, amssymb}")
f.write(r"{\large Answers}")
f.write(r"$x=%s$, and $x=%s$"%(a,c))

And you can see why cumbersome is a kind description. Each line followed by a newline character (it didn't work as one line) and when it's time for the solution we insert the appropriate variables. After compiling you get a pdf for the test and you'll have to go check your files to find the newly created SMCtestAnswers.tex. Compile that file to create a pdf just for the answers.


Mission accomplished. I've posted the "proof of concept" file on the Handouts page.

Here are some issues that caught my eye this week.

  • The Khanty-Mansiysk 2015 chess tournament will seed the top two finishers to be in a tournament which will select the next challenger for World Champion Magnus Carlsen. As such you can find many top players competing. Caruana leads after 4 rounds. Tomorrow is a day off. The tournament can be followed at the site here or through Chessbomb (sidebar).
  • Tragedy in Jacksonville where according to this article in the St. Augustine Record, "A girl was left with a gunshot wound through both cheeks. Another girl was struck in the head by a shot. Both survived, but for a moment Thursday, a routine school bus ride home turned into a ride of terror on Jacksonville’s Westside.".
  • Students behaving savagely: ZeroHedge has the story of 50 teenagers beating an adult into the ground: "Richard Fletcher was beaten by a gang after asking two girls to stop fighting on his truck in Dundalk, Maryland. Man, 61, left with horrific injuries and facing $400,000 medical bills after near fatal attack by pack of FIFTY teens, including girls, when he tried to break up a fight. A 17-year-old boy has been charged as an adult for his role in beating a 61-year-old alongside a group of approximately 50 other teens in Baltimore, Maryland, on April 22.". Five students arrested at the time of the story.
  • In a post on Thomas Jefferson high school we saw people suing the school because "...the numbers [of black students] could surely be higher than they are now.". Now from the Washington Post we have, "More than 60 Asian American organizations filed a complaint (see below) with the federal government on Friday alleging that Harvard University discriminates against Asian Americans in the admissions process and calling for an investigation.". The complaint is posted at the link above. Sputnik news has these statistics: "A coalition of 64 organizations is citing research indicating that Asians need to on average score 140 points higher than white students on the SAT, 270 points higher than Hispanic students and 450 points higher than African-American students to equal their chances of gaining admission to Harvard. The exam is scored on a 2400-point scale.". It seems like the reverse discrimination laws to help "level" the field for Asian-Americans is now legal policy to discriminate against them for performing better than other racial groups.