Al-Khwarizmi Essay Example | Topics and Well Written Essays - 1250 words

Al-Khwarizmi - Essay Example The early Arab mathematician and astronomer al-Khwarizmi has been considered by some to be the founder of algebra, a branch of mathematics dealing with equations containing unknown quantities and variables. While this has been disputed, it is certain that his publications on the subject were among the earliest available to the Arab world, and were highly influential among later audiences. (Sen, 2) One of the most well-known early Arab scientists, he wrote his famous treatise, "The Compendious Book on Calculation by Completion and Balancing," by the year 830. Later, this work had a great impact on Western mathematics and science; Latin translations of his work were quite important to scholars and businesspeople during the Middle Ages. Al-Khwarizmi is also known for bringing the Hindu system of fixed numerals to international attention. He wrote an Arab-language text that explained Hindu methods of calculation, which depended upon written numerals rather than the more primitive counting techniques that were widely used at the time. The 'publication' of the book of al-Khwarizmi at the beginning of the ninth century-between 813 and 833 -is an outstanding event in the history of mathematics. For the first time, one could see the term algebra appearing in a title to designate a distinct mathematical discipline, equipped with a proper technical vocabulary. Muhammad ibn Miss al-Khwarizmi, mathematician, astronomer and distinguished member of the 'House of Wisdom' of Baghdad, had compiled, he wrote, 'a book on algebra and al-muqbala, a concise book recording that which is subtle and important in calculation' (Gandz, 263-277). The event was crucial, and was recognized as such by both ancient and modern historians. Its importance did not escape the mathematical community of the epoch, nor that of the following centuries. This book of al-Khwarizmi did not cease being a source of inspiration and the subject of commentaries by mathematicians, not only in Arabic and Persian, but also in Latin and in the languages of Wester n Europe until the eighteenth century. But the event appeared paradoxical: to the novelty of the conception, of the vocabulary and of the organization of the book of al-Khwarizmi was contrasted the simplicity of the mathematical techniques described, if one compares them with the techniques in the celebrated mathematical compositions, of Euclid or Diophantus, for example. But this technical simplicity stems precisely from the new mathematical conception of al-Khwarizmi. Whilst one of the elements of his project was found twenty-five centuries before him with the Babylonians, another in the Elements of Euclid, a third in the Arithmetica of Diophantus, no earlier writer had recompiled these elements, and in this manner. But which are these elements, and what is this organization The goal of al-Khwarizmi is clear, never conceived of before: to elaborate a theory of equations solvable through radicals, which can be applied to whatever arithmetical and geometrical problems, and which can help in calculation, commercial transactions, inheritance, the surveying of land etc. Al-Khwarizmi begins by defining the basic terms of this theory which, because of the requirement of resolution by radicals and because of his know-how in this area, was only concerned with equations of the first

Small and Medium Enterprises Essay Example | Topics and Well Written Essays - 3000 words

Small and Medium Enterprises - Essay Example The economic downturn brought about financial difficulties in SMEs and at the same time, lenders could not guarantee access to additional funds. Some of the SMEs were forced to shut due to financial difficulties and bankruptcy. The level of investments in SMEs also declined due to lack of funds for investments (Stokes and Wilson, 2010). One of the factors that limited the ability of SMEs to access credit during the recession was the tight credit controls. The government efforts to control the level of money supply lead to high interest rates. Banks had to raise their lending rates and tighten their credit policies to comply with government regulations. Consequently, the SMEs that could not meet these new credit terms could not access funds from banks to finance their operations. SMEs were more vulnerable to the negative effects of the recession of business operations compared to large firms. This is because SMEs lack resource and market manpower to withstand sudden environmental chan ges. The changes in the global economic environment brought about by the 2008 recession had severe effects on SMEs especially on the young and new business (Stokes and Wilson, 2010). The 2008 recession forced organisations to lay off many employees to survive. The level of production reduced and layoffs were used as a way of reducing the cost of production. SMEs were not spared from this move and they too had to lay off a significant number of their employees. This means that they would later incur additional labour costs of recruiting and training new employees after the economic recovery. The performance of SMEs in terms of output production and revenues was severely affected during the recession. The effects on performance were more severe in high risk SMEs relative to low risk SMEs. High risk organisations tend to have high debt to assets ratios. These organisations were forced to take drastic measures of laying off their employees and reducing the dividends paid to shareholders (Stokes and Wilson, 2010; Richard 2011). The profitability of SMEs reduced during the recession and the level of competition increased as well. The demand for products was low and thus, firms intensified their marketing activities to attract customers. However, the effectiveness of the marketing strategies was limited by the reducing purchasing power of the consumers during the recession. The SMEs across Europe faced excessive regulations administration, lack of skilled human resources and high costs of productions (Richard 2011). Question 2: Reasons why small firms dominate some market structures There are many theories that explain why small firms dominate certain market structure. The technical efficiency theory argues that the existence of small firms in a certain market will depend on economies of scale. Industries with large economies of scale compared to the market size tend to have many small firms and a few large firms that control the market. However, the number of small firms in such markets may increase if the concentration ratios and the economies of decline. The size of a market or its geographical distance has an effect on its composition. A large geographical distance will results in high transportation costs for large firms. Such a market will also have diseconomies of scale. Consequently, there will be more small firms than large firms in the market.