The pulling power of chaos What is the most efficient way to get a space probe to its target? When Apollo 11 went to the moon in 1969 it followed a conventional Hohmann transfer orbit. Imagine an egg-shaped outline, with the earth at the bottom. As the spacecraft comes up the left-hand side, it burns fuel to accelerate, and swings into orbit around the moon. This was the quickest route – aside from the impractical one of flying straight out by burning fuel the whole time – and, in a manned mission, speed was of the essence. Trajectories such as this exploit the slingshot effect, in which the spacecraft steals energy from a planet. The technique was first used in 1991. It sounded crazy, but Belbruno knew a way to do it. One place where chaotic orbits can arise is somewhere called the “L1 Lagrange point” between the earth and the moon, where the net gravitational force is zero (essentially, objects are “suspended” between the two bodies because of the forces generated by each). The first Oscar
OUHJ Mathematical Studies Programme description Mathematics, statistics and techniques for decision-making are professional and indispensable tools for many types of problems, and continue to enjoy rapid growth in areas of actuarial science, strategic planning, financial investments and operations research analysis. The degree programmes equip students with a strong undergraduate background in the areas of applied mathematical methods, statistics, data analysis, optimization, stochastic and deterministic modeling, and risk analysis. It prepares students for careers or for further study in many technical fields such as statistical analysis, management science, industrial engineering, biostatistics, strategic planning, financial analysis, education. Programme requirements Notes: Choosing the first courses to get started Students with no credit exemption are recommended to begin with MATH S121 or MATH S122.
Thousands of college students in Ontario need help with grade school math | Daily Brew Students complete basic math tests. Reuters photoEnterprising tutors may want to pack up their calculators and head toward Ontario's post-secondary institutions. A recent study by York University and Seneca College in Toronto has found that thousands of Ontario's first-year community college students have signed up for basic math courses in order to brush up on skills they should have mastered in junior high. As Parent Central reports, the study's authors said their findings raise a red flag over the quality of math instruction in the province and could also indicate a growing lack of interest in math that may hurt the economy over time. "We're expressing concern that 8,300 students are taking preparatory and foundational math in first-year college, but the vast majority cover concepts introduced in Grades 6, 7 and 8," co-author and York University professor emeritus of math Graham Orpwood told Parent Central. "If you're illiterate, it's a matter of shame.
Podcasts - One Planet Podcasts - More or Less: Behind the Stats Animation reveals the world's hidden equations MacGregor Campbell, contributor Although they don't actually exist in the physical world, our most powerful tools could be mathematical equations. They underlie much of modern technology, from radio to power generation, to photo compression and electronic musical instruments. In our latest animated explainer, we look at how the wave equation, Maxwell's equations and the Fourier transform came to rule the modern world. For more mathematics-related viewing check out our archive of One-Minute Mathvideos, or watch our previous animations to find out, for example, if supersymmetry could explain everything or why there is no such thing as empty space. Our choice of Maxwell's equations In our feature "Seven equations that rule your world", author Ian Stewart uses Maxwell's equation for electromagnetic waves propagating in a vacuum.
9 Equations True Geeks Should Know Even for those of us who finished high school algebra on a wing and a prayer, there's something compelling about equations. The world's complexities and uncertainties are distilled and set in orderly figures, with a handful of characters sufficing to capture the universe itself. For your enjoyment, the Wired Science team has gathered nine of our favorite equations. Not everything can be quantified, especially when it comes to matters of the human heart and mind. How to design video games that support good math learning: Level 5 « profkeithdevlin Procedures or thinking?Part 5 of a series The vast majority of video games that claim to teach mathematics do not actually do that. Rather, what they do is provide a means for students to practice what they have already been taught. A good example is the first-person shooter Timez Attack. Such games are the low hanging fruit for the math ed video game designer, and like most low hanging fruit, it has pretty well all been picked, leaving game designers coming into the math ed space having to look elsewhere for a useful application of their talents. The difficulty hits you as soon as you decide to go for more than mastery (ideally to fluency) of already taught basic computational skills. This distinction is to a great extent relatively recent. By and large, high school mathematics is still very much based on that earlier tradition, so few people outside the professional mathematical community are aware that in the middle of the 19th century, a revolution took place. Like this:
Podcasts - Woman's Hour: News, Politics, Culture Podcasts - The Life Scientific What do Christian fundamentalists have against set theory? I've mentioned here before that I went to fundamentalist Christian schools from grade 8 through grade 11. I learned high school biology from a Bob Jones University textbook, watched videos of Ken Ham talking about cryptozoology as extra credit assignments, and my mental database of American history probably includes way more information about great revival movements than yours does. In my experience, when the schools I went to followed actual facts, they did a good job in education. Small class sizes, lots of hands-on, lots of writing, and lots of time spent teaching to learn rather than teaching to a standardized test. But when they decided that the facts were ungodly, things went to crazytown pretty damn quick. All of this is to say that I usually take a fairly blasé attitude towards the "OMG LOOK WHAT THE FUNDIES TEACH KIDS" sort of expose that pops up occasionally on the Internet. Well, for me, this is new: Wait? First off, let's establish what set theory actually involves.
Tips for mathematical handwriting John Kerl kerl at math dot arizona dot eduFeb. 25, 2007 Now that you’re majoring in one of the technical disciplines (engineering, science, or math), you’re going to be spending a significant amount of time communicating in writing with others. You may find that previously unimportant details, such as crossing your z’s, now become essential — not only so that others can understand you, but also so that you can avoid mistaking your own 2z for z2 and so on. This is especially important if your handwriting (like mine!) Before I continue, take a fresh look at our Roman alphabet, the digits, and the Greek alphabet: Notice that these mechanically typeset symbols are all clear and distinct (except that lowercase omicron and most of the uppercase Greek letters look like Roman letters — we don’t use these “duplicates”). When we write by hand, though, symbols can become ambiguous — we’re not machines, and things get a little loopy when we hurry. Lowercase Roman letters: Uppercase Roman letters:
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