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million units in the English Vs Math

English Vs. Math

To most people English or Language Arts is a creative course and math is just a logical, you get it or you dont class. My purpose writing this paper is to change your mind. I believe that Math is just as, or more creative than English. I will demonstrate this through a couple of examples.

First, we must understand what is behind the creative aspect in English. Most people consider that English is the, creative, subject because of titles such as creative writing and creative thinking and in contrast there is no creative something in math. In English when we are, lets say, going to write a creative short story we use our imaginations and there are no limits. Now on the other hand in math when faced with a problem such as; if you have 300 meters of fence and have to enclose a rectangular field. What would be the dimensions of the field that would yield the largest area? When mathematicians go to solve one of these they have to be creative in their problem solving.

Perhaps, one of the best ways to demonstrate creativity in math is through an identity question. An identity question is where you have an equation and you try to manipulate each side individually without touching the other side and get them to be equal. We start off with something like sin squared theta over cos theta plus cos and the objective here is to prove that it is identical to sec theta. At first looks there is no connection but by using creative methods and hours of work eventually we figure out the way to do it.






Sin? + Cos ?  |  Sec ?
Cos ?  |


First I would make everything over Cos  ?

Sin ? + Cos ?   | Sec ?
   Cos ?       |            


Then I would apply a law

1     |   Sec ?
    Cos ?    |  


Then a simple law

Sec ?    |   Sec ?


You can prove that it is creative because a computer cant solve this equation, (a computer thinks logically). Technically a computer could solve this equation but it could just tell you if they were equal and not to the same level of accuracy. A computer would input a value for ? on both sides and if the answer is equal then the equation is equal. The problem with this is that when you get into trigonometry there could be a difference in the decilionth decimal place. A computer cant work with the abstract which is what is in my example. A computer may take 2 seconds or a million years to find an answer or it may give the wrong answer! The other point is that a computer can only perform things in a certain order it cant guess or have a feeling about a question, which brings in the creative aspect.

Another example happened during one of my Calculus classes that I believe to be the most abstract and creative of the maths. A fellow student and me figured out pie. We figured out that the integral from 0 to1 of the square root of x minus 1 is equal to half of pie. We had huge problems figuring out this equation but persistence eventually won out and we solved it. Later we found out that this was a University Calculus level question and we shouldnt have been able to solve it due to our lack of skills in this area. Creativity then can be the only culprit for our derivation of the solution.

 

Finally one of my strongest points is that on some of the more creative math units the more creative people usually the artsy type do a lot better than in the other units and by no means because these units are easier. Remember that I am not saying that English isnt creative, just that Math is more creative than anyone gives it credit for. ... more

million units in the

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US Economy Expansion

The
million (or should we say 'billion' now) dollar question is whether or not the
United States' economy will stay in it's record 107 month expansion (according
to the index of leading indicators) or come out of the boom and take a downturn
into a recession. Nobody, including the Chairman of the Federal Reserve, Alan
Greenspan has a crystal ball to provide insight as to what will happen if
interest rates are raised, lowered, or left alone. However, Economists have
developed a set of indicators to aid in predicting when a recession is about to
occur and when the economy is in one. Indicators should not be mistaken for
predictors. They are simply forecasting tools, and like any forecast can be
misleading. The index of leading indicators that is reported in the popular
press shows our economy is still in an expansion. For the purposes of our
evaluation of the economy, we chose the Principle Economic Indicators tracked by
the Bureau of Economic Analysis and the U.S. Census Bureau under the Economics
and Statistics Administration at the U.S. Department of Commerce. There are
thirteen Principle Economic Indicators, and they fall into five major
categories: National Output and Income; Orders, Sectoral Production, and
Inventories; Consumer Spending; Housing and Construction; and Foreign Trade.
National Output and Income The first of the five major categories directly
relates to measuring the growth of the U.S. economy. National Output and Income
consists of the Gross Domestic Product (GDP), Personal Income, and Corporate
Profits measurements. GDP is the primary measurement of growth and measures the
total amount of goods and services produced by governments, businesses, people,
and property located within the United States. Both real (adjusted for
inflation) and nominal (current value in dollars) data is collected for
computing the GDP. The base year for the real data is 1997. The GDP is normally
reported as an annualized quarter-to-quarter change. The reason this measurement
is vital to tracking the growth of the U.S. economy is self-explanatory. When
the economy is growing, both total income and total output are increasing.
Furthermore, a steady increase in the GDP is healthy for the economy. According
to the U.S. Department of Commerce, U.S. economic output has grown at an annual
rate of 2.5 to 3.5 percent since 1890. The preliminary estimate of GDP in the
fourth quarter of 1999 rose at a 6.9 percent annual rate, which is the strongest
gain since a similar increase in mid-1996. This is an increase from the initial
estimate of 5.8 percent and is consistent with the expectations of analysts. It
is also a reflection of the widespread upward increases among the major spending
components, including consumer spending, goods exported, and state and local
government spending. In the third quarter of 1999, GDP rose 5.7% as a result of
increases in Personal Consumption Expenditures, nonresidential fixed investment,
and exports. Personal Income is a measurement of total pretax income earned by
individuals, non-profit organizations, and private trust funds. It is expressed
at an annual rate also. The more Personal Income increases the greater the
potential for the American people to spend and save money, which directly
influences the growth of the U.S. economy. Personal Income rose .7 percent in
January, following an increase of .3 percent in December. The average monthly
increases in 1999 were .5 percent. Some extenuating factors affected income in
recent months, including cost of living increases in federal transfer payments,
a federal pay raise, and agricultural subsidy payments in January. Real
disposable income, income after taxes and adjusted for price changes, increased
by .7 percent. There was no change in December. The individual personal saving
rate rose from 1 percent in December, which was its low, to 1.4 percent in
January. Savings rates generally go down in the months October through May due
to Holiday spending (includes "paying off" credit cards). There are
two methods in which Corporate Profits are reported by the government.
"Tax-based" profits are derived from corporate tax returns, and
"adjusted" profits reflect earnings from current production. Just as
increases in Personal Income are vital to the growth of the U.S economy,
increases in Corporate Profits are just as important on an even larger scale.
The greater the profits, the more potential for growth. This in turn has a
direct effect on employment rates, spending, etc. Profits reported from current
production increased $3.7 billion in the third quarter of 1999. This is a
dramatic improvement from a decrease of $6.5 billion in the second quarter.
Profits would have been about $10 billion more than they were in the ... more

million units in the

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