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A Visual, Intuitive Guide to Imaginary Numbers

A Visual, Intuitive Guide to Imaginary Numbers
Imaginary numbers always confused me. Like understanding e, most explanations fell into one of two categories: It’s a mathematical abstraction, and the equations work out. Deal with it.It’s used in advanced physics, trust us. Just wait until college. Gee, what a great way to encourage math in kids! Focusing on relationships, not mechanical formulas.Seeing complex numbers as an upgrade to our number system, just like zero, decimals and negatives were.Using visual diagrams, not just text, to understand the idea. And our secret weapon: learning by analogy. It doesn’t make sense yet, but hang in there. Video Walkthrough: Really Understanding Negative Numbers Negative numbers aren’t easy. But what about 3-4? Negatives were considered absurd, something that “darkened the very whole doctrines of the equations” (Francis Maseres, 1759). What happened? Rather than saying “I owe you 30” and reading words to see if I’m up or down, I can write “-30” and know it means I’m in the hole. Uh oh. Wrong. or

MIT's free online classes can carry credit The Massachusetts Institute of Technology has offered free online courses for the last four years with one major downside: They didn't count toward a degree. That's about to change. In a pilot project announced Wednesday, students will be able to take a semester of free online courses in one of MIT's graduate programs and then, if they pay a "modest fee," earn a "MicroMaster's" degree, the school said. The new degree represents half of the university's one-year master's degree program in supply chain management. The fee for the MicroMaster's degree amounts to what it now costs to receive a "verified certificate" for finishing online classes, the university said. "The rising cost of education, combined with the transformative potential of online teaching and learning technologies, presents a long-term challenge that no university can afford to ignore," MIT President L. MIT didn't immediately say when the new pilot project would launch.

Hillary Clinton to unveil $350-billion plan to make college more affordable Hillary Rodham Clinton outlined a plan Monday to slash student loan interest rates while aiming to guarantee students could attend college without needing to take out loans in the first place, tapping into an issue that has risen in prominence among Democrats. Under Clinton’s plan, state governments, higher education institutions and students would play roles alongside the federal government in addressing the affordability of higher education and the debt that can come from it. “We need to make a quality education affordable and available to everyone willing to work for it without saddling them with decades of debt,” she said. The $350-billion plan Clinton outlined at a New Hampshire town hall meeting was the most expensive and expansive policy proposal of her campaign thus far. States that agree to increase spending on higher education would be eligible for federal grants to help reduce the gap between what families can afford to pay and full tuition. Sen. Former Maryland Gov.

Privately educated graduates 'earn more' than state school colleagues - BBC News Privately educated UK graduates in high status jobs earn more than their state school counterparts, says a study. The report, by the Sutton Trust and UpReach, examined those in careers such as law and financial services. It found that, on average, three years after graduation, those who attended fee-paying schools earned £4,500 more. The government said it was "determined... to ensure every child, regardless of background, reaches their potential" through its policies. The report put the earnings gap down to factors such as the university attended, but also suggested non-academic factors, such as assertiveness, were at play. The research also found salaries of the privately-educated increased more quickly, growing by £3,000 more over the same three-and-a-half year period. Average salaries, six months after graduation, were more generous for those who had attended independent schools - £24,066 compared to £22,735, a difference of £1,331.

Teacher grade forecasts are 'too optimistic' - BBC News Teachers are often too optimistic when predicting pupils' grades, suggests a new analysis of exam board data. In future, these forecasts will be crucial to universities when offering places to pupils. That is because A-levels results in in England will depend solely on exams taken at the end of two years' study. The forecasts "will be the only thing universities will have to go on", said Cherry Ridgway of the Association of Teachers and Lecturers (ASCL). But the accuracy of teachers' forecasts is falling, the study suggests. The researchers compared GCSE and A-level results from the OCR board with predictions sent in by teachers just before the exams. At A-level some 43% were correct in 2014, down from 48% in 2012 For GCSEs, 44% of predictions were accurate in 2014, compared with nearly 47% in 2013. New exams Currently universities use AS-level results when making offers - but from next year they will no longer count towards the final A-level grade. Selective schools

Students doubt fees value for money - BBC News Many students are unconvinced they have received value for money from their university courses, according to an annual survey. And a large majority do not think they have been given enough information about how tuition fees are spent. The survey suggests students average 12 hours per week "contact" time, when they are taught by staff. The findings are part of a survey of 15,000 students in the UK, carried out by higher education think tanks. The Student Academic Experience Survey, carried out by the Higher Education Policy Institute and the Higher Education Academy, examines levels of consumer satisfaction among undergraduate students. Information gap The survey suggests 59% of students are "fairly satisfied" with their course - and a further 28% are "very satisfied". But, with "the benefit of hindsight", more than a third said they would have chosen a different course. "If it doesn't happen soon, it could be forced on universities by policymakers," he said. Contact hours

How US students get a university degree for free in Germany - BBC News While the cost of college education in the US has reached record highs, Germany has abandoned tuition fees altogether for German and international students alike. An increasing number of Americans are taking advantage and saving tens of thousands of dollars to get their degrees. In a kitchen in rural South Carolina one night, Hunter Bliss told his mother he wanted to apply to university in Germany. Amy Hall chuckled, dismissed it, and told him he could go if he got in. "When he got accepted I burst into tears," says Amy, a single mother. Across the US parents are preparing for their children to leave the nest this summer, but not many send them 4,800 miles (7,700km) away - or to a continent that no family member has ever set foot in. Yet the appeal of a good education, and one that doesn't cost anything, was hard for Hunter and Amy to ignore. "For him to stay here in the US was going to be very costly," says Amy. "The healthcare gives her peace of mind," says Hunter. 'Mind blowing'

Graduate jobs: University degrees no longer relevant to some employers University degrees aren’t as valued by employers as they once were, which is great, or terrible, news, depending who you are. BIG employers are going cold on university degrees, leaving students and jobseekers to wonder if their qualifications are worth the investment and extra study. This week, international publishing house Penguin Random House decided to drop degrees as a requirement for job applicants, following in the footsteps of major consulting firms Ernst and Young and PricewaterhouseCoopers. The move comes as smaller employers are shifting away from hiring graduates or university students, believing kids are coming out of university with “no real skills” or simply being taught the wrong things. Penguin hasn’t been so harsh, saying the shift in requirements is simply a move “to make publishing far, far more inclusive than it has been to date”. “Simply if you’re talented and you have potential, we want to hear from you.” “I think it’s a good thing. Loaded: 0% Progress: 0%

MIT Dean Takes Leave to Start New University Without Lectures or Classrooms Christine Ortiz is the dean for graduate education and a professor of materials science and engineering at the Massachusetts Institute of Technology. In a conversation with The Chronicle, she discusses her ideas about building a new type of college from scratch. Christine Ortiz is taking a leave from her prestigious post as a professor and dean at the Massachusetts Institute of Technology to start a radical, new nonprofit university that she says will have no majors, no lectures, and no classrooms. Many details about the new university are still undetermined, she says, but the basic idea is to answer the question, What if you could start a university from scratch for today’s needs and with today’s technology? Her venture is not the only effort to create a new kind of college — there’s the Minerva Project, created by a tech entrepreneur in San Francisco, and MOOC providers like Udacity, started by a former Stanford University professor. But those are for-profit businesses. Q. A. Q. A. Q.

Why American Students Are Flocking to Germany — and Staying BONN, Germany — How do you say "sign me up" in German? The number of Americans studying in Germany has risen sharply, recent figures show, driven in part by the low cost of higher education compared to the United States. More than 10,000 U.S. students are presently enrolled in the country's higher education programs, according to data from the Institute for International Education. It's an increase of almost 9 percent compared to the previous academic year, and 25 percent more than in 2008-2009. Natasha Turner, 25, from Rochester, New York, came to Germany on an exchange program three years ago but decided to stay when she realized how "cheap it was to study here." She is now working on her master's degree in American Studies at the University of Bonn. "For my undergraduate studies in the United States, I needed a lot of loans," she said. Students in Germany pay a fee to cover university administrative costs and to support student unions.

Why so many are alarmed by the ongoing controversy at Mount St. Mary’s In rural Maryland, a battle is taking place over the future of religious colleges in the U.S. What began as a public relations flap in a student newspaper has boiled over into a national controversy, with the editorial board of The Washington Post joining the faculty of Mount St. Mary’s in calling for university president Simon Newman to resign. To recap: the student newspaper of Mount St. Mary’s, a Catholic liberal arts college in Emmitsburg, Md., published an article investigating efforts by university leaders to improve the school’s retention rate, a key metric used in rankings systems such as U.S. The imbroglio worsened when Newman abruptly fired two faculty members who had opposed his plan, with academics from across the country signing an online petition protesting what appeared to be political retribution for their disagreement. [The controversy at Mount St. Late last week, the faculty of Mount St. All of that led to the genesis of the first modern research universities. Mount St.

Why are so many smart people such idiots about philosophy? There’s no doubt that Bill Nye “the Science Guy” is extremely intelligent. But it seems that, when it comes to philosophy, he’s completely in the dark. The beloved American science educator and TV personality posted a video last week where he responded to a question from a philosophy undergrad about whether philosophy is a “meaningless topic.” The video, which made the entire US philosophy community collectively choke on its morning espresso, is hard to watch, because most of Nye’s statements are wrong. Not just kinda wrong, but deeply, ludicrously wrong. He merges together questions of consciousness and reality as though they’re one and the same topic, and completely misconstrues Descartes’ argument “I think, therefore I am”—to mention just two of many examples. And Nye—arguably America’s favorite “edutainer”—is not the only popular scientist saying “meh” to the entire centuries-old discipline. “It often gets back to this question: What is the nature of consciousness?”

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