Sunday, July 7, 2013

Week 3 - What is Algebra (Nature)

What is Algebra?

Algebra is one of the many parts of mathematics, and will always be a base set of theories and ideas that support mathematic’s ever-infinitely expanding field. It involves all basic thought on equations and number theory. Balancing, defining, and solving equations and understanding numbers is what everyone achieves by learning about algebra. 

Algebra uses non-numerical values to represent unknowns in equations. The idea behind solving these has moved into other forms such as vectors, and matrices. Algebraic structures include sets, rings, fields, and groups. Algebra contains arithmetic, and simple calculations.  Many ideas for graph theory stem from algebra, and many students first learn how to graph from algebraic equations that are linear, cubic, quadratic, etc., and this continues into calculus based graphing and other mathematical forms. 

Algebra differs from other branches of mathematics such as calculus, geometry, discrete mathematics, linear algebra, and in a sense; proof-based mathematics, but algebra has its hand in all of these branches in some way. Algebra is really a simpler-to-understand branch of mathematics, but becomes the foundation for all other branches. It’s easy to that algebra is a part of many other fields of math, but not all that fields create algebra. For instance, algebra is learned before calculus because solving something like a differential equation or calculating an integral cannot be done without knowing how to solve an equation to some extent, and the basics for equation-solving comes from learning algebra. However, you don’t need to know how to take a derivative to know how to do any calculation that is algebraic to its most basic sense. Algebra also came fro arithmetic, whereas other developments in other branches of math came from algebra. 

Algebra is a way to connect relationships in math, and it helps develop overall computational skills to help a student in their development. It’s a logical tool that can be used to analyze situations that do not have to be mathematical. Algebra’s evolving as a mathematical tool has paved the way for other subjects, and no other comes to mind more quickly than statistics. Equations and algorithms are all about what algebra is, and nailing down algebraic concepts have lead to advancements in statistics. The logical side to algebra allows students to make better decisions in any aspect of life. It’s easy to figure out simple problems, but a more complex issue that has multiple factors can be rationalized into an algebraic idea and can be solved more efficiently. While every student should learn about algebra, it takes a certain amount of time to develop the skills relating to the subject, and waiting for an appropriate time to learn it is important. I took my first algebra-based course in 8th grade, while most students in the Davison school district took it in 9th grade, and is a requirement to continue to 9th/10th grade math (which is geometry). While I struggled with the concepts of algebra initially, it became more clear as I worked with it, and it helped me mature into a better problem-solver. This is what algebra is and what it does for those that can take advantage of learning about this valuable subject.  

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