Graph Theory, Sage, and LaTeX page


I've added another page to the website. It's still in the beginning stages but it will cover graph theory, $latex \LaTeX$ and Sage. You can find it here and it's listed on the sidebar or click here. From this documentation at the Sagemath website you can see the way Sage works with $latex \LaTeX$ to produce graphs. This method is quite different than what you'll find in the Altermundus tkz-berge package despite the fact that Sage uses that package. The information I just posted has to do with the creating a graph in the simplest and cleanest way. I opted for the 'Normal' representation of graphs to allow for a choice of labels inside or outside. A vertex is created as follows:


where R1 is what the vertex will be referred to by the program and the factors which determine the label are handled in the options:

LabelOut to put the vertex label outside the vertex. Lpos is the label position. It's the angle of rotation around the center of the vertex (0 is east of the vertex, 90 is north of the vertex, etc). L= will be the label, and x=, y= handle the placement of the vertex. Simple and efficient. You can read more on the new page where I've posted the code for two 'Normal' graphs, with labels out and with labels in.

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

  • 11alive covers Tennessee phasing out Common Core. "Common Core standards ignited a political brawl last year when state lawmakers, who saw the standards as federal overreach, pushed to scrap them. In response to cries for state-specific standards, Gov. Bill Haslam authorized a review of the state's English and math standards."
  • St Louis Post Dispatch reports "Missouri became the latest state to adopt a new set of education benchmarks to replace the national Common Core standards, ditching the benchmarks Tuesday following conservative backlash.". Common Core is not so common anymore.
  • EAGnews has a piece on  Tennessee students "Parents and community leaders in Murfreesboro are fuming after police arrested numerous elementary students at school over a fight that occurred off campus several days prior....Several students at Hobgood Elementary School, ranging in age from about 6 to 13 years old, were then handcuffed and arrested, and hauled to a juvenile detention center before their parents were even notified, WKRN reports.....“Here’s the catch, the girls were just bystanders in the video. They were not fighting, they were not instigating it, they were just standing in the video. And there was actually no technical fight in the video,” he said. “But the claim and the accusation is that they didn’t stop the fight, so they should be arrested.”"
  • RT has a piece where the title says it all: "Teacher tackles pupil to the ground in ‘deeply disturbing’ classroom attack".  A violent, profanity laden assault that will hopefully lead to jail time.
  • But it's better overseas, right. Not all the time. RT has video footage of  "A teacher in China bore the brunt of a vicious classroom uprising after he tried to forcibly collect a student’s exam paper in a shocking case of school violence caught on camera."
  • Don't even think about messin' with Colorado schools. ABC news reports, "A suburban Denver school district is arming its security staff with military-style semiautomatic rifles in case of a school shooting or other violent attack, a move that appears unprecedented even as more schools arm employees in response to mass violence elsewhere."
  • Chalkbeat reports  "Facing widespread backlash after years of controversies and testing glitches, one of the world’s largest testing companies is taking an unusual approach to quieting critics: It’s opening its doors." The Washington Post covers some of the problems here.
  • The Altibox Norway Chess 2016 tournament has 4 rounds in  the books. Magnus in first but with Kramnik, Giri, and MVL lurking around the tournament is wide open. You can follow it here. Click on the "Live Streaming" button at the top of the page to follow it live.
  • There are just 2 rounds left in the US Chess Championship. You can watch it live here. Caruana leads for the championship section, and Abrahamyan for the women. Irina Krush doesn't control her fate anymore as she competes for another title.

Altermundus: circle-circle intersections


I've added information on getting the intersection of 2 circles using the tkz-euclide package. The tkz-euclide package gives a macro \tkzInterCC to find the intersection of 2 circles. As there are multiple ways to input a circle, the macro can be used in different ways.

\tkzInterCC(D,B)(A,C) \tkzGetPoints{M}{N}

finds the intersection of circle centered at D containing point B along with the circle centered at A containing point C. The two intersection points are recovered with \tkzGetPoints macro. Likewise

\tkzInterCC[R](A,1 cm)(B,1 cm) \tkzGetPoints{M1}{N1}

finds the intersection of circle centered at A with radius of 1 cm along with the circle centered at B with radius 1 cm. Note the R option.

You can download the code, with comments, here.

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

  • What happens in Vegas may stay in Vegas, but in Mexico---not so much. RT has a piece on "A prestigious fee-paying school in Mexico has failed to separate twerking from working, allegedly forcing a 24-year-old teacher to resign after she participated in a dance competition while on spring break. The primary school teacher, known only as Clarissa, was in the popular Mexican holiday spot Cabo San Lucas when she decided to channel her inner Miley Cyrus and grind on one of the judges."
  • Listverse has "10 Strange Cold War Tales Left Out Of The History Books"
  • RT on "Flint, Michigan has become the epicenter of the lead water crisis in the United States, but hundreds of schools across the country have tested positive for unsafe lead levels in their water over the past three years, according to a new report."
  • Reuters on "Meet the Thai math prof whose copyright case is headed for SCOTUS – again"
  • Technology review looks at  "A chip that can’t guarantee that every calculation is perfect can still get good results on many problems but needs fewer circuits and burns less energy, he says...A chip that can’t guarantee that every calculation is perfect can still get good results on many problems but needs fewer circuits and burns less energy, he says....In a simulated test using software that tracks objects such as cars in video, Singular’s approach was  capable of processing frames almost 100 times faster than a conventional processor restricted to doing correct math—while using less than 2 percent as much power."
  • The US Chess Championship (closed) has begun. Caruana, Robson, and So are tied for first after 3 rounds of the scheduled 11 rounds. Follow it live here.
  • IndyStar's Russ Pulliam looks at who won common core, and with the number of states using common core down to 21 you get the idea that failure has been achieved.
  • WTHV11 has a report and video on one of those states that has moved away from common core , "In nine days, 85 Arkansas teachers across the state revised 65 percent of the Common Core Math Standards. They hope these revisions turn confusion into a statewide understanding."
  • looks at the teacher shortage in Detroit, "Two moms want answers. How can it be that in public schools in this country - kids can go months without a math teacher?" Answer: The priority of the system isn't about providing a good education for the kids. If they'd remove the numerous hoops to jump through requiring money and time they'd have plenty of people. Certified does not mean qualified. And many qualified teachers are denied certification. Until they fix the Orwellian double-speak you won't have meaningful change.
  • A cougar in LA might not be uncommon, but a mountain lion at an LA high school is. RT has the the details and video that led to a school lockdown.

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.

Handout: counting factors


If you teach some combinatorics in your classes you're probably familiar with the Fundamental Principle of Counting, otherwise known as the Multiplication Rule, and the typical problems (how many ways to roll a 7 with a pair of dice, how many outfits to where, how many different pizzas given specific topping choices). Some of that is fine, but I also like to link it to things they should already know: factoring numbers. I've created a handout on determining the number of factors of a number. For example, there are 9 factors of 100 (1, 2, 4, 5, 10, 20, 25, 50, 100).  Typically schools teach students to try dividing the the numbers 1,2,3, ....n into the number n and pairing the factors along the way but that's certainly not the way a math person would do it, especially as the numbers get bigger. For a number with a lot of factors, such as 6!, it's too easy to miss some factors unless you have a methodical way of finding them. Getting the prime factorization of the integer will let you use the Fundamental Principle of Counting to quickly get the answer: no trial and error. You can find the details in the PDF is posted on the Handouts page. Most students don't know the basics, which is a good enough reason to combine it with combinatorics, so factors and primes and other basic concepts need to be reviewed.

I've added a link to OER Commons, covered in the last post, to the sidebar.

Here are some stories that caught my eye this week:

  • Let's call this now. This is one of the most interesting educational stories you'll read for 2016. It's a lengthy Reuter's article, two parts in fact, on the cheating on the SATs taking place in other countries, while the College Board (the organization that owns the SATs) does nothing. PART 1 and PART 2. From part 1: "A confidential PowerPoint presentation reveals that College Board officials had documented widespread security problems in June 2013...Even so, College Board officials confirmed that some portions of those tainted tests were later administered overseas. And the College Board took no steps to restrict testing in China, the SAT's largest market by far, even as it tightened security in smaller countries where exams had leaked." There is literally too much to quote and I'd strongly urge you to read both articles. There's even a video in PART 1.
  • I've mentioned the corruption in education many times. RT reports "A dozen current and former principals from Detroit Public Schools were among those hit with bribery and conspiracy charges by the federal government regarding a scheme to score kickbacks from school supplies that were rarely, if ever, delivered....Flowers and the 12 principals have been accused of submitting fraudulent invoices for school supplies to DPS that were either never delivered or only partially delivered, according to complaints filed in the US District Court. In exchange for inaccurately reporting the delivery of these goods to DPS, Allstate Sales would receive payments from DPS, while the company owner Norman Shy would deliver kickbacks to the principals as well as Flowers, according to court documents....The charges come as officials in Lansing continue to debate the future of DPS, which currently suffers from a crushing debt in excess of $500 million, in addition to crumbling infrastructure. " Large pools of money and lax oversight is a tempting target for educational professionals crooks.
  • Chess is taken pretty seriously in other parts of the world; RT tells us "A chess duel at a major competition in Ukraine evolved into a fist-fight after a coach became incensed by the way his pupil was being treated....The young woman’s trainer, Mikhail Gerasimenyuk, hurried to help his pupil, but in a way that nobody had expected: he slammed Sakun twice...Sakun had his eyebrow and nose cut, and vessels in his eye ruptured."
  • Students behaving badly, EAGnews reports, "Numerous Glenn Hills High School students face murder charges after a massive 50-person brawl that ended with the death of an 18-year-old man.....Police allege Demajhay Bell, 18, died from being stabbed in the neck during a large street fight involving as many as 50 people, many Glenn Hills students, in Augusta, Georgia March 18. The melee was caught on cell phone video and posted online, providing a harrowing look at a very violent clash involving pipes, bats, and a vehicle barreling through the fracas..."
  • More students behaving badly. Once again from EAGnews, "An Alaska charter school suspended three first-grade girls for plotting to kill a classmate with “poison.” Anchorage police told KTUU three first-graders at Winterberry Charter School planned to poison a classmate with a silica gel packet they believed to be toxic in hopes of killing the young girl."
  • Yet more students behaving badly from EAGnews: "A 16-year-old Syracuse high school student faces two felony assault charges after police allege he punched two teachers in the face for attempting stop him from using his phone in class..The problem stems from a “restorative justice” approach to school discipline that’s designed to reduce punishments for minority students. Large inner-city school districts adopted the approach at the behest of the federal government as a means of reducing suspensions for minority students.....In Syracuse, a December survey of 830 district teachers revealed the vast majority of teachers don’t feel safe in their own classroom, with a third reporting to have been physically assaulted by students, WSTM reports.." Because when admin have caved into students doing what they want, students will do what they want. Do you think that makes it easier for schools to attract qualified people into the teaching profession?
  • The lack of certified teachers is a problem in Arizona. KVOA tells us, "Arizona is simplifying its test for prospective math teachers, in order to help solve its teacher shortage crisis. The State Board of Education has opted to only test teachers on math up to Algebra 2. Teachers will no longer have an exam on trigonometry or calculus, which many educators believe is better than the current alternative."Now a lot of those classes, Algebra 1, geometry, or calculus... Those are being taught by long-term substitutes," said Melissa Hosten, co-director of the Center for Recruitment and Retention of Mathematics Teachers." Certification drives down quality by keeping qualified people out of the classroom. The result is a lousy education run by "experts" who have shown an inability to educate for decades.
  • Some good news. The Federalist has a piece "8 Great Women of Science History".
  • And back to reality. Michael Snyder on just how stupid Americans have become.
  • Do you ever give out candy or snacks to your class? A VERY BAD IDEA if some new regulations get approved. on the consequences: "The federal government is taking steps to fine schools that do not comply with first lady Michelle Obama's school lunch rules....The regulation would punish schools and state departments with fines for "egregious or persistent disregard" for the lunch rules that imposed sodium and calorie limits and banned white grains. A West Virginia preschool teacher was threatened with fines for violating the rules by rewarding her students with candy for good behavior in June 2015. The teacher ultimately did not have to pay, but the school had to develop a "corrective action plan" with training on the policies. The government now seeks to make fines enforceable by regulation. Section 303 of the law requires that the federal government "establish criteria for the imposition of fines" for all the Department of Agriculture's child food programs...The Food and Nutrition Service is targeting schools that refuse to comply with Mrs. Obama's lunch rules and said monetary penalties are a "useful tool" to get noncompliant cafeterias in line...The proposed rule would also apply to private organizations participating in federal childcare nutrition programs, including "institutions, sites, sponsors, day care centers, and day care providers." ." One more problem for those in public schools.