Math Term Paper Sample: Algebra

Historical Sketch of Algebra

Historical Sketch of Algebra is an example of a sketch that is resembles the sketches that are in the book The Maths through the Ages. Algebra sketch is one of the basic functions of mathematics. It is a discipline that has been used over the years to cover different concepts in the real life. In this regard, this is a functional discipline that has been applied in different subjects that involve the use of mathematics in order to come up with analytical means of communicating especially through the use of equations. Algebra traces its roots to the early days of mathematical development. The development of mathematics into an abstract point of view led to the development of classical algebra. This was as a result of the developments in science and technology that were taking place over the years. This necessitated the use of algebra to solve major problems and computations.

The concept of algebra started in the medieval times. This perpetuated the need for medieval algebra. This was as a result of the works of different mathematicians. These included Abu Kamil and Al-Khowarizmi (Klein 218). From their works, they came up with algebraic concepts that consisted of different elements. The main problems included linear and quadratic algebraic expressions that were easy to be solved. They also came up with algebraic solutions and how to simplify these operations effectively. This also prompted the development of rules regarding solving equations, using positive and negative numbers and their functions in algebra and how to operate using the rules of False Position (Gallian 200). During these medieval times, the algebraic functions and equations were used for different purposes. These included the use of algebra to solve logistic, legal, business and industrial problems.

In the early renaissance algebra the main mathematician Nicolas Chuquet was essential in coming up with more analytical forms of algebra. This involved the invention of symbols particularly for the use of solving algebraic expressions. These symbols were for solving the unknown functions in algebra and for finding squares and cubes of different levels. This form of algebra allowed the use of algebra as exponents and coefficients. These were also found to be necessary in finding solutions to different problems (Rashed 219).

Early modern algebra saw the development of algebra into other levels. This enabled the creation of rules that facilitated the solving of different cubic equations. The development of algebra facilitated the combination of different cubes and squares in solving quadratic equations (Rashed 226). This method was effective as it facilitated the reduction of cubic equations into quadratics thus enhancing the solving of these problems effectively.

Francois Viete in the 17th century came up with the most valuable developments in algebra. Through different researches he decided on coming up with effective symbols that would be used in algebraic expressions. He suggested the use of the + sign to denote addition and the use of the word ‘in’ to show multiplication. He suggested the use of a consistent notations of vowel letters such as A, I, O and Y to denote values for quantities that are unknown in nature of problems (Klein 296). On the other hand he suggested that consonants such as D, C and K among others should be used to denote the known or given quantities in problems.

The development of algebra into modern analytical systems came in the years around 1800 to 1900s. This saw the use of algebra and algebraic expressions effectively to come up with notable solutions to problems. This therefore involved the use of the symbols and notations already developed to come up with effective roots and coefficients of equations. This was important in facilitating the use of theorem as facilitated by Albert Girard. This theorem stated that “Every algebraic equation admits of as many solutions as the denomination of the highest quantity indicates.” (Klein 313). This enhanced the use of algebraic equations in different complex situations as the times demanded. All these developments have led to the sophistication of algebra and the use of the same to come up with intricate solutions to different problems.

The importance of having such intensive backgrounds and developments of algebra is seen in the application of algebra in real life. These developments have facilitated the use of algebraic expressions in different scenario to come up with effective means of solving technical and complex problems. As a result, many people in engineering and other disciplines that use mathematics to solve equations have found it necessary to apply algebra in their daily mathematical operations.

For a closer look at the use and development of algebra over time; different books and readings have been suggested to effectively cover this topic in totality. These books will be able to shed more light on the development of algebra in the past and modern world.

A good example of such a book is Math through the Ages: A Gentle History for Teachers and others, by Bill Berlinghoff

This is a book that brings into perspective the different sketches that are found in the field of mathematics. Another book include:

Hoyrup, John, Babylonian Algebra from the Viewpoint of Geometrical Heuristics. Roskilde University Centre, Roskilde, 1985.

This is a book that brings into view the elements of Babylonian algebra and the effects it has on modern algebra.

A Historical Sketch

It is imperative to check on the historical sketch of mathematics. This is described as one of the most intricate subjects of all time. Mathematics has been one of the most influential subjects of the world. It has been used in many areas to cover different aspects of life. Used in many disciplines, mathematics is defined as a science that involves numbers. Mathematics describes the combination, interrelation, operation and configuration of numbers. It also involves the manner in which numbers are generalized and configured to make abstractions of situations in different disciplines. It is also defined as the study that involves the study of properties and measurements of space and structure (Robson & Stedall 35). It also involves studying relationships between different quantities and structures through the use of numbers and symbols.

Mathematics involves the study of different disciplines or branches. This includes algebra, geometry, calculus and measurements among others. Mathematics is applied to all these disciplines in order to bring out the essential elements within the subject that amplify it into being one of the greatest subjects of all time. It is considered as important in all disciplines. Many disciplines rely on the basic elements of Mathematics to effectively bring out the essentials of those disciplines. Disciplines such as medicine, engineering, architecture and even art depend on different basics within the subject of Mathematics. The use of elements of mathematics in these different disciplines has been effective in improving the efficiency of these disciplines in explaining different concepts. Mathematics has ceased to be just a discipline of learning; it has become a way of life. It is used in different life situations today such as business and commerce and enhances the manner in which daily lives are lived today.

With regard to learning historical sketches, it is crucial to understand the mathematics history. The need for the use of mathematics is not a current concept. According to studies it started long ago approximately more than 5000 years ago when the need to count especially in barter trade arose. This was the conceptualization of the notion of mathematics. The origin of mathematics was inadvertently caused by the rise in needs of the human people during that time (Gallian 67). As the needs of the society became more complex year by year, the need for mathematical application continued to rise way above basic counting. As such, there was need to involve more use of mathematics in different aspects of life in different countries. Some of the societal needs that were experienced included the need to manage the different assets of the country; building great architectural temples, kingdoms and empires; and solving problems in the management of kingdoms. All these needs required the use of mathematical concepts in order to solve them. As such therefore the need to use mathematical concepts and elements grew from country to country.

Different countries have different mathematical origins. The general mathematical origin is attributed to countries such as Greece and Egypt. The main concepts of the use of mathematics came from the application of these elements in these two countries. This is especially so because of the need to establish great architectural designs for these countries (Robson & Stedall 97). It is for these reasons that these two countries have great historical backgrounds and elements that encroach into the mathematical regime and disciplines. Not only is this important, it is also fundamental ins ensuring that the disciplines associated with mathematics are important in establishing strong concepts of development.

The development of mathematics is one that keeps on evolving from year to year. Mathematics keeps on developing as needs and wants of the society continue to develop and become more complex from time to time. The development of Mathematics is dependent on the development of technology and civilization around the world. This is because of the manner in which it is applied to science and technology in the current world. From the Egyptian and Greek Mathematics to the medieval mathematics, these developments have been used to effectively enhance the development of technology and civilization in the world. The development of mathematics has gone through seven distinct periods. These developments include proto-mathematics, ancient mathematics, classical mathematic, mercantile mathematics, pre-modern mathematics, modern mathematics and post-modern mathematics (Katz 117).

Proto-mathematics refers to the development of mathematics from its origins. This is the type of mathematics that was used with the early people through counting, symmetry and geometry in archeological art as well as keeping tabs with reasoning and logistics. This development occurred through 2000BCE. Ancient mathematics took reign after this. This development occurred as a result of steady developments occurring in the world. This development from an empirical proto mathematical point of view developed into an abstraction point of view. Ancient mathematics is associated with Egyptian and Babylonian mathematics (Katz 129). This is because at this point in time the need to have land planning and surveying, astronomy, planning and engineering was evident in these societies. As such therefore the need to apply geometry and numbers into these different situations was created. This happened between the periods of 2000BCE to 800 BCE. This kind of mathematics needed the use of reasoning and decimal place value. It also created formulas for areas and structures that were both two and three dimensional. This resulted to the building of the hanging gardens of Babylon, the pyramids of Egypt as well as the beautiful granaries of Mesopotamia (Gallian 119).

The next developmental stage was classical mathematics. This was experienced in different countries especially Greece and the Asian countries such as India and China during the periods of 800BCE and 1500CE. . It involved the use of axiomatic geometry and algebra. Greek mathematics presented a paradigm shift from an empirical point of view to a logical point of view. This means that mathematics was viewed as a structure that was appropriated by different laws that engaged thought and structure. In addition, it also ensured that that there was a better representation of the results. This mathematics was applied to geometry, astronomy and engineering…”

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