Category Archives: Applied Mathematics

Fun with Dimensional Analysis

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Dimensional analysis (also known as the factor-label method or unit-factor method or UNIT ANALYSIS) is by far the most useful math trick you’ll ever learn. Maybe you’ve learned some algebra, but will you use it? For many people the answer is, “not after the final exam.”

For a fraction of the effort needed to learn algebra, you too can learn “dimensional analysis.” First off, however, let’s get rid of the big words. What this is all about is just conversion—converting one thing to another. This is something you will have occasion to do in real life. This is seriously useful stuff.

This trick is about applied math, not about numbers in the abstract. We’re talking about measurable stuff, stuff you can count. Anything you measure will have a number with some sort of “unit of measure” (the dimension) attached. A unit could be miles, gallons, miles per second, peas per pod, or pizza slices per person.

Source: Fun with Dimensional Analysis

Two Sample Problems (see web site for more):

  • Rate Problems: If you are going 50 miles per hour, how many feet per second are you traveling?
    (Sometimes you need to convert both numerator and denominator)…
  • Mixing Problems: How much bleach would you need to make a quart of 5 percent bleach solution? Continue reading →

An Argument AGAINST the “illogical” metric system! Richard Nilsen

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But when it comes to the arguments for adoption, I demur. No, the metric system is not “more logical” than the so-called English system. And in many ways, it simply fails the test for logic, at least if by logic you mean usefulness.

I admit that when it comes to particle physics and engineering, the fact that you can do a good deal of your math by simply moving a decimal point has a lot in its favor. For the very large and the very small: for astrophysicists and nano-technologists, the 10-based metric system is the logical choice.

But I resent the patronizing tone so many pedants take toward the older system, as if it made no sense at all — when in fact, it makes a great deal of sense. There is a logic to the English system, and one that makes our lives easier — and more human.

Just start with the thermometer. When  Daniel Gabriel Fahrenheit invented the mercury thermometer in 1714, he devised his system of measuring temperature in very human terms. Zero degrees was a cold as he make brine before it froze, and 100 degrees was (he was a little off) body temperature.

And using the Fahrenheit thermometer, when it is 0 degrees F, you know it is cold, and when it hits 100 in the shade, you know you’re hot.

The Celsius, or centigrade system that is used in metric nations, is based on the boiling and freezing points of fresh water. Sounds logical, perhaps, but I’m not water, I’m human. Why should it be considered logical to base your thermometer on water?

via metric system | Richard Nilsen.

Passive Index Funds-Power of Compound Interest (fees)

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First, there is the expense ratio — about 1.12 percent of assets for the average large capitalization blend fund. Then there are transaction costs and distribution costs. Active funds also pay a penalty for keeping a share of their assets in low-yielding cash. Altogether, costs add up to 2.27 percent per year, Mr. Bogle estimates.

By contrast, a passive index fund, like Vanguard’s Total Stock Market Index Fund, costs merely 0.06 percent a year in all.

Of course, Mr. Bogle has a horse in the race. He founded the Vanguard Group. He invented the first index fund for the public. His case is powerful, nonetheless.

Assuming an annual market return of 7 percent, he says, a 30-year-old worker who made $30,000 a year and received a 3 percent annual raise could retire at age 70 with $927,000 in the pot by saving 10 percent of her wages every year in a passive index fund. (Such a nest egg, at the standard withdrawal rate of 4 percent, would generate an inflation-adjusted $37,000 a year more or less indefinitely.) If she put it in a typical actively managed fund, she would end up with only $561,000.

via Americans Aren’t Saving Enough for Retirement, but One Change Could Help – NYTimes.com.

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A Billionaire Mathematician’s Life of Ferocious Curiosity – cf Ilan’s “7 Second Rule” (Before you answer a math problem)

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Down one floor from his office complex is Math for America, a foundation he set up to promote math teaching in public schools. Nearby, on Madison Square Park, is the National Museum of Mathematics, or MoMath, an educational center he helped finance. It opened in 2012 and has had a quarter million visitors.

“I wasn’t the fastest guy in the world,” Dr. Simons said of his youthful math enthusiasms. “I wouldn’t have done well in an Olympiad or a math contest. But I like to ponder. And pondering things, just sort of thinking about it and thinking about it, turns out to be a pretty good approach.”

Dr. Sullivan said that Dr. Simons, in his career, had made a series of seminal contributions and that an early one “revolutionized the consciousness of later generations.” He added that in May 2013, to celebrate Dr. Simons’s 75th birthday, four American math and science luminaries gave lectures about fields he had advanced.

Forbes magazine ranks him as the world’s 93nd richest person — ahead of Eric Schmidt of Google and Elon Musk of Tesla Motors, among others — and in 2010, he and his wife were among the first billionaires to sign the Giving Pledge, promising to devote “the great majority” of their wealth to philanthropy. Continue reading →

So, Who Invented Double Entry Bookkeeping? Luca Pacioli or Benedikt Kotruljević? | Steve Mariotti

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Italian Inventor of Double Entry Bookkeeping luca-pacioli-portrait

Not Luca Pacioli?

Assets = Liabilities + Owners’ Equity.

Ouch! He was right: The first recorded history of the description of double entry bookkeeping was done by Benedikt in 1458 in his work: Book on the Art of Trade.

Although only in a short appendix, it was the first description of what was as one of the world’s great intellectual breakthroughs — modern accounting. This craft enables merchants, entrepreneurs and their investors to keep track of every penny they received or spent.

Thanks to accounting, it allowed people to organize massive amounts of information into journals and then produces summary financial statements — Continue reading →

No Accounting Skills? No Moral Reckoning

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THE GREAT DIVIDE

By JACOB SOLL APRIL 27, 2014

SOMETIMES it seems as if our lives are dominated by financial crises and failed reforms. But how much do Americans even understand about finance? Few of us can do basic accounting and fewer still know what a balance sheet is. If we are going to get to the point where we can have a serious debate about financial accountability, we first need to learn some essentials.

The German economic thinker Max Weber believed that for capitalism to work, average people needed to know how to do double-entry bookkeeping. This is not simply because this type of accounting makes it possible to calculate profit and capital by balancing debits and credits in parallel columns; it is also because good books are “balanced” in a moral sense. They are the very source of accountability, a word that in fact derives its origin from the word “accounting.”

In Renaissance Italy, merchants and property owners used accounting not only for their businesses but to make a moral reckoning with God, their cities, their countries and their families. The famous Italian merchant Francesco Datini wrote “In the Name of God and Profit” in his ledger books. Merchants like Datini (and later Benjamin Franklin) kept moral account books, too, tallying their sins and good acts the way they tallied income and expenditure. Continue reading →