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For example the column for auto manufacturing shows the resources required for building automobiles ie. Input — Output models typically includes separate tables showing the amount of labour required per rupee unit of investment or production.

Consider a simple economic model consisting of two industries A 1 and A 2 where each produces only one type of product. Assume that each industry consumes part of its own output and rest from the other industry for its operation. The industries are thus interdependent. Further assume that whatever is produced that is consumed. That is the total output of each industry must be such as to meet its own demand, the demand of the other industry and the external demand final demand.

Our aim is to determine the output levels of each of the two industries in order to meet a change in final demand, based on knowledge of the current outputs of the two industries, of course under the assumption that the structure of the economy does not change.

Let x 1 and x 2 be the rupee value of the current outputs of A 1 and A 2 respectively. Let d 1 and d 2 be the rupee value of the final demands for the outputs of A 1 and A 2 respectively. Hawkins — Simon conditions ensure the viability of the system. If B is the technology matrix then Hawkins — Simon conditions are. I — B must be positive. Example 1. An economy produces only coal and steel. Similarly 0. No capital inputs are needed.

Do you think that the system is viable? Economists are interested in examining types of relationships. For example an economist may look at the amount of money a person earns and the amount that person chooses to spend. This is a consumption relationship or function. As another example an economist may look at the amount of money a business firm has and the amount it chooses to spend on new equipment. This is an investment relationship or investment function.

A function tries to define these relationsips. It tries to give the relationship a mathematical form. An equation is a mathematical way of looking at the relationship between concepts or items. These concepts or items ar represented by what are called variables. A variable represents a concept or an item whose magnitude can be represented by a number, i.

Variables are called variables because they vary, i. Thus a variable can be considered as a quantity which assumes a variety of values in a particular problem. Many items in economics can take on different values. Mathematics usually uses letters from the end of the alphabet to represent variables. Economics however often uses the first letter of the item which varies to represent variables.

Thus p is used for the variable price and q is used for the variable quantity. An expression such as 4x 3 is a variable. It can assume different values because x can assume different values. In this expression x is the variable and 4 is the coefficient of x. Coefficient means 4 works together with x. Expressions such as 4x 3 which consists of a coefficient times a variable raised to a power are called monomials.

A monomial is an algebraic expression that is either a numeral, a variable, or the product of numerals and variables. Monomial comes from the Greek word, monos, which means one. Real numbers such as 5 which are not multiplied by a variable are also called monomials. Monomials may also have more than one variable. In this expression both x and y are variables and 4 is their coefficient. One or more monomials can be combined by addition or subtraction to form what are called polynomials.

Polynomial comes from the Greek word, poly, which means many. A polynomial has two or more terms i. If there are only two terms in the polynomial, the polynomial is called a binomial. The coefficients of the terms are 4, -2, and 3. The degree of a term or monomial is the sum of the exponents of the variables. The degree of a polynomial is the degree of the term of highest degree. In the above example the degrees of the terms are 5, 3, and 0. The degree of the polynomial is 5.

Remember that variables are items which can assume different values. A function tries to explain one variable in terms of another. Consider the above example where the amount you choose to spend depends on your salary.

Posted in Mathematics category - 17 Apr [ Permalink ]. LaTeX is longer because it is intended for more complex mathematical formulas, and those require more control over typesetting. Once people write math professionally, they need to know LaTeX, and the best way to learn it is to start using it on simple formulas Mike: I agree with you that "real" mathematicians should know LaTeX.

But for the other AsciiMathml and TeX where created for very different purposes: TeX was created by Donald Knuth for preparing books and articles to be printed. Users are espected to invest a lot in learning a system to help them publish their books or papers. AsciiMathml was created by Peter Jipsen as a sort of "natural language parser" that would parse the emails his students were sending him using approximate calculator syntax. The "users" that created the formulas were not expected to invest anything in learning it.

It was meant to be good enough to handle most of the formulas people write like text without intending it to be parsed and displayed as a formula. Asciimathml is much more convenient for communication even for people that know how to compose TeX.

And it has another advantage, that there are no syntax errors in AsciiMathml, because all expressions are syntactically correct. Several years ago I played with making an email interface display math formulas with Asciimathml. Here's a screenshot of a trial email I sent myself from my Gmail account that contains formulas and the same email without rendering formulas.

The interface is Fastmail. Since no one else I knew could read formulas natively in their email client I had no use for this. It's a pity that communication software can be considered "fully internationalized" without any support for the language common to most of humanity: Mathematics.

Is it still possible to "inject your own javascript" in Fastmail. I couldn't find it in their documentation. But until all email services provide a math option, it's not worth doing as you found. Your blog URL can be left blank. Notify me of followup comments via e-mail. Your comment:. Preview comment.

Name optional. From Math Blogs. Our math tutors are available 24x7 to help you with exams and homework. Send us your math problem and we'll help you solve it - right now. I've been wanting this for a long time now. Creating math in document editors like MS Word is also a clumsy process. For example, consider this fraction, surrounded by braces.

We needed a cross-browser, cross-platform math rendering system which didn't use images. Enter MathJax. MathJax MathJax promises "beautiful math in any browser without plugins" and essentially that's what it delivers. What does LaTeX look like? Here's the same fraction I used above. We needed a solution that brought these 2 approaches together - and now it's here. You can see example pages where most of the math has been created this way here: Division of Algebraic Expressions fractions Split Functions piecewise-defined functions For new development, this system is so much more productive than using images, or using LaTeX input.

I'm a happy camper. Comparison of math Web publishing options Publishing math on the Web can be a challenge. Mathematics, teamed with patience, builds stock market wealth more reliably than "big score" attempts. Gaussian math calculates random fluctuations of uncorrelated entities. This sounds ideal for playing the undulating stock market, except that stock market transactions are all correlated. Gaussian logic, therefore, cannot predict sudden crashes. Power law, on the other hand, calculates how changes in the value of one quantity affect another quantity, such as how a company's value affects stock prices in its industry.

This helps calculate standard deviations, which can help traders better understand potential risks and allow them to buy or sell accordingly. Computer-based quantitative analysis, which studies how amounts, or quantities, relate to each other, is the most common mathematical model used by trading houses. The field includes algorithms, which study patterns of behavior in entities such as the financial sector.

These calculations can help identify potential risks ahead, but overreliance on quantitative models and algorithms can lead to wild speculation, imprudent investing and "flash crashes. At the center of everything we do is a strong commitment to independent research and sharing its profitable discoveries with investors. This dedication to giving investors a trading advantage led to the creation of our proven Zacks Rank stock-rating system.

These returns cover a period from and were examined and attested by Baker Tilly, an independent accounting firm. Visit performance for information about the performance numbers displayed above. Finance Menu. More Articles 1. Probabilities No mathematical system, however advanced, can predict the actual future. Losing Less Often Successful stock traders such as Warren Buffet often give the impression that successful trading means percent accuracy.

Gaussian Laws vs.

You can choose the input variables yourself, but the output variables are always determined by the rule established by the function. You'll also see functions in the form of one variable often y equal to an expression involving another variable x. A simple example is. A function is a rule that relates each input value to one and only one output value. Mathematicians often compare the idea of a function to a coin stamping machine. The coin is your input, and when you insert it into the machine, the output is a flattened piece of metal with something stamped on it.

Just as the machine can only give you only one flattened piece of metal, a function can give you only one result. You can test a mathematical relation to see if it's a function by inputting various values and making sure you get only one result for the output. If you graph a function, it may generate a straight line or a curve, and a vertical line drawn anywhere on the co-ordinate plane will intersect it at only one point.

Mathematicians call the set of all input values for a function its domain. The domain is an integral part of the function. In many mathematical problems, it includes all real numbers, but it doesn't have to. It does have to include all numbers for which the function works, though. To create an illustration from the non-mathematical world, suppose your function is a machine that gives all bald people a full head of hair. Its domain would include all bald people, but not all people. In the same way, the domain for a mathematical function may not include all numbers.

For example, the domain for the function. The range of a function includes all the possible output values, so it's determined by the domain as well as the function itself. For example, suppose the function is "double the input value," and the domain is all real, whole numbers. You would write the function mathematically as.

No mathematical system, however advanced, can predict the actual future. But sophisticated mathematics can calculate the probability of events. This works in the stock market by helping traders minimize the likelihood that something bad might happen before a certain date or other precursor. It works like insurance: Actuarial tables cannot predict the date or cause of your death, for example, but they can give insurers a better general idea of the time frame or nature of your demise.

Successful stock traders such as Warren Buffet often give the impression that successful trading means percent accuracy. But most successful traders are right only half the time at best. Simple mathematics shows that "winning" on only four or five of every 10 trades can put a trader ahead, depending on how much was won versus how much was lost. Mathematics, teamed with patience, builds stock market wealth more reliably than "big score" attempts.

Gaussian math calculates random fluctuations of uncorrelated entities. This sounds ideal for playing the undulating stock market, except that stock market transactions are all correlated. Gaussian logic, therefore, cannot predict sudden crashes. Power law, on the other hand, calculates how changes in the value of one quantity affect another quantity, such as how a company's value affects stock prices in its industry.

This helps calculate standard deviations, which can help traders better understand potential risks and allow them to buy or sell accordingly. Computer-based quantitative analysis, which studies how amounts, or quantities, relate to each other, is the most common mathematical model used by trading houses. The field includes algorithms, which study patterns of behavior in entities such as the financial sector. These calculations can help identify potential risks ahead, but overreliance on quantitative models and algorithms can lead to wild speculation, imprudent investing and "flash crashes.

At the center of everything we do is a strong commitment to independent research and sharing its profitable discoveries with investors. This dedication to giving investors a trading advantage led to the creation of our proven Zacks Rank stock-rating system.

The input and output tables are diagrams used to convey basic functional concepts. They are based on a functional rule. When the table is full. Input-output analysis (I-O) is a form of macroeconomic analysis based on the interdependencies between different economic sectors or industries. Wassily bulv.shelu.xyzef. Input Output analysis is a form of economic analysis based on the interdependencies between economic sectors. The method is.