# Modern Day Algebra Essay

1237 Words 5 Pages
Abstract: This paper is a report on the development of algebra throughout time. It’s slow, but nevertheless, unyielding progression brings us to the algebra we know today. However, it was not always based on the abstract, rather, it was born out of necessity. The need to calculate unknown quantities gave rise to algebraic methods and techniques practiced and taught even today. And, even though nowadays, algebra is a rather abstract mathematics, this was not always the case. It was through centuries of work from remarkable individuals with an undying passion and curiosity that algebra slowly but surely evolved.

Introduction

In modern day mathematics, the term algebra denotes the manipulation of abstract symbols, solving equations for unknowns,
This issue guided much of the progress attained in the 17 and 18th centuries [Allen]. It was during this time period that many noteworthy mathematicians with an unquenchable thirst for mathematical knowledge spent countless amounts of time in the development of modern day algebra. During this time, radicals were still a great issue. It was thought than no solutions by radicals could be accomplished and many expended their efforts in so proving this. However, as often times occurs, through the processes utilized in these efforts, other theories arose. The theory of substitutions, for example, was arrived at by the theory of equations. By the 20th century, algebra was much more than verbal solutions, or illustrated examples. It became the “study of mathematical structures with well-defined operations” [Allen]. This gave rise to the emergence of “groups, fields and rings,” the “basic units” of algebra [Allen]. These concepts undoubtedly, integrated and related many areas of mathematics, amongst these, topology, theory and analysis [Allen].

The Fundamental Theorem of
And as remarkable mathematicians made new discoveries, algebra developed and progressed as a mathematical science. Prodigious individuals such as Descartes and Fermat were founders in the creation and development of analytical geometry, including theory on

• ## Justification Of Knowledge

There exists a plethora more of other early traces of Calculus, such as Exodus’ concepts of limits (408 B.C.) and Archimedes 's integral calculus (287 B.C.). The reasoning behind the math of these mathematicians is something could not be argued upon at the time, thus their concepts of math came to be known as justifiable truths. It has been centuries since the idea of limits was discovered but it is something that, to this day, is still taught and explored within modern day…

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• ## Dirichlet And Legesgue, Henri Lebesgue's Contribution To Mathematics

Abstract—The idea of Riemann integration is now popular and very helpful in mathematics. In this paper we explore the background of mathematicians Henri Lebesgue, Peter Gustav Lejeune-Dirichlet and Bernhard Riemann. We discover some of their contributions to mathematics and how they all contributed to this famous concept of Riemann integration. Index Terms— Bernhard Riemann, Henri Lebesgue, Peter Gustav Lejeune-Dirichlet, Riemann integration I. INTRODUCTION Even though the idea of calculus was already in the air, the clear definition of it or its concepts could still be improved.…

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• ## Modern Day Math Research Paper

The Moscow Papyrus for example, is a mathematical text that is filled with what we would call word problems or math stories in modern day. These word problems not only taught algebraic functions, they were also used as a source of entertainment. One essential element that the Egyptian Papyrus introduced, was the use of a standard algebraic symbol to represent an unknown number, such as X. The Rhind Papyrus, also a mathematical text taught students how to work with multiplication, divisions and fractions. Although written in the language of Egyptian scholars, the texts left behind demonstrate the sophistication and progress of mathematics throughout Egypt.…

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• ## Why Are Mathematicians Important To The World

Though he worked on the calculus theory a lot, there is a debate as to whether he or Sir Isaac Newton truly discovered calculus. After much debate, most scholars agree that Leibniz and Newton worked on the theory and development at the same time. Leibniz also discovered what a matrix was, which helped with finding solutions to many mathematical problems. One of his other great contributions was inventing a practical calculating machine. This helped with adding, subtracting, multiplying, and dividing numbers.…

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• ## Philosophy Of Education Research Paper

What is so fascinating to me is that there are a lot of problems in mathematics that have a long way and a short way to solve the problem. The long way teaches you the concept and gives you a complete understanding of the problem. The short way helps you do the problem faster and efficiently and the short way is sometimes mind-blowing. Above, is the definition I gave of mathematics before I entered into this program. Now I would like to discuss the importance of mathematics.…

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• ## Algebra Geometry And Trigonometry

Abstract: - Mathematics is a fascinating subject filled with concepts and ideas that have been formed and developed throughout time. This paper focuses on the contributions made by Islamic mathematician Muhammad Al-Khwarizmi to the difference subjects of algebra, geometry and trigonometry. Ideas discovered by Al-Khwarizmi are discussed as well as other concepts that serve as proof of his understanding of various complex ideas we use nowadays. These concepts include simplifying equations, completing the square and trigonometric tables. Key-Words: - Islam, Mathematics, Algebra, Geometry, Trigonometry 1 Introduction Throughout time, cultures and societies have created and discovered amazing concepts that have been passed down and are now considered…

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• ## Logic And The Importance Of Logic In Mathematics

The rules of Logic specify the meaning of mathematical statements, it is the basis of all mathematical reasoning (Rosen, 2012). Its application in the area of computer science is very vast that even the computer itself defends on it, True or False, 1 or 0, and the presence or absence of bit. The study of Logic will increase your knowledge in formulating logically statements for the reason that program statements and expressions is built from repeated application of logical operators. This module will help you to analyze arguments to determine the truth value of it. Objectives: After completing this module, you should be able to: 1.…

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• ## Archimedes: Nikhita Guntu And Laya Biddala

His methods anticipated the integral calculus 2,000 years before Newton and Leibniz. He introduced the concept of Pi . Archimedes also produced formulas to calculate the areas of regular shapes, using a revolutionary method of capturing new shapes by using pre-existing shapes. During this time period, his understanding of geometric shapes and volume was extraordinary. One of Archimedes most famous works is Measurement of the Circle.…

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• ## How Did Pythagoras Use Math

There are many famous and influential mathematicians that have done many wondrous and extraordinary things, some of these range it Einstein, newton and to pascal. But one interesting one in particular is Pythagoras. Pythagoras is one of the many famous mathematicians that has lived on the earth. What he did in math helped shape math to what it is today. Some things he did was learn math and science as much as he could, create the useful Pythagoreanism, and help progress the advancement of mathematics.…

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• ## Narrative Essay On Mathematical Modeling

I have my high school days to thank for that. Answering all those reviewers I can say that I have gained sufficient experience to answer basic problems such as algebraic and trigonometric problems. A good foundation in those branches in mathematics has proven really helpful for higher math. Such as in Calculus, new concepts may have been introduced but basic manipulation of the expression requires algebra. As for the fourth and fifth which are modeling mathematically and representing mathematical entities, I still need improvement but I am starting to grasp and get the hand of it.…

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