Why is Calculus Different from Algebra?

Running as one of the main subjects in academia, mathematics has been an irreplaceable tool in our daily life. Math has been known as the numerical language of humanity in which problems are demonstrated through complicated operations. It seems to be a developmental tree in which one branch has many smaller branches that continue to grow stronger on the root of knowledge. Two of the small section of Pure Math (one of two majors of Math) are Calculus and Algebra. Despite some similarities that they share under the same roof, both Calculus and Algebra strengthen the relationship by contrasting each other in their concentration, sections and application. 

Linear Algebra

               First of all, concentration is an obvious trait that either Calculus or Algebra have in common. To a mathematician, calculus is defined as a study of motions and changes which mainly focuses on the observation of abnormal objects. Calculus is a modern branch of Pure Mathematics while Algebra was first established in 1800 or 1600 B.C.; in other words, Algebra is known as a foundation of Mathematics where many solutions are found. Concentrating on operating algebraic functions, Algebra also gets involved in many other branches of Math, especially Calculus. For example, in order to find a work done of lifting books without constant forces, a scientist sets up an integral based on his calculus knowledge; once the patterns are found, algebra takes a hand in solving it. Even though both of two branches are distinct in their study, they still share some aspects in common. One of the main similarities is an essential ability to comprehend the complication of Mathematics.  Understanding mathematical concepts is very important to develop a necessary skill for obtaining a critical mind in both scientific and non- scientific fields. The failure to operate Math appropriately might create several stumbling blocks in their future study, such as some weaknesses in analytical ability and abstract mind. That is to say, despite the differences among these two categories, both Calculus and Algebra require a learner to wisely comprehend the materials.

Following the concentration, both Calculus and Algebra continue developing Mathematics to a higher level. For Algebra, it’s divided into several categories including Elementary, Universal, Abstract, Linear Algebra; Algebraic Number Theory, Systems, Combinatory, and Geometry. Each section has its own characteristics but still functions in the same logical methods based on algebraic concepts. For instance, the Linear Algebra concentrates on observing the transformation of vector systems and linear properties between spaces; on the other hand, the algebraic geometry focuses on the development of shapes and objects under two or more dimensions. In fact, these two branches still need a hand of Algebra in solving problems, strengthening, and developing their relationship. On the contrary, Calculus simply breaks down into two main categories: differential (derivative) and integral (anti-derivative). Contrast to Algebra, these two sections are opposite to each other in method and application. One studies the rate or change while the other concentrates on finding area and volume of a function. In differentiation, a process of finding derivative of a function, the exponent n will multiply with a new function whose exponent n adds a negative one. In integration, the method is simply inversed in which multiplication is replaced by division and a negative one is changed into a positive one. Even though Calculus and Algebra expand their program in different directions, they still intersect at another similarity which gives us an indication about their relationship. It is an abstract mind to use mathematical knowledge wisely. Once these sections go deeper into their study, it’s necessary to be able to operate rigorous and demanding mathematical functions.    

A failure to operating mathematically

Last but not least, mathematics has been an essential part of humanity in finding the key to natural science. Even though both Calculus and Algebra have the same purpose in practically applying the concepts into realistic problems, they tend to specify their area based on their own concentrated characteristics. For instance, Calculus is mainly applied in solving mechanical functions, or estimating changes of biochemical trials in the medical field. Not only does it help scientists to demonstrate thoroughly the abnormal quantities, shapes or values in STEM careers, but it also helps other non-mathematical fields such as business and politic to visualize changes of society. Unlike Calculus, Algebra expresses itself in everyday usage of numbers. Multiplying, dividing, subtracting, and adding must be seen as familiar to everybody. However, due to a series of different algebraic branches, some parts of Algebra may get involved in complex operations; some may combine with other sections of Math to support theorems. That is to say, the differences between Calculus and Algebra is that they each creates significant characteristics which still carry the main function of Mathematics: practical application.

               In conclusion, Calculus and Algebra have been functioning contrastively to emphasize their program study, branches, and practical exercise even though they still require some common essential skills to escalate Pure Mathematics to another level. Analytical ability, creative thinking, and comprehensive mind allow learners to approach Math in successful manners. In addition, studying Math determines a person’s ability to demonstrate real-world problem by numerical operations and find the solutions; without well-qualified learners, Mathematics seems rough, tough, and meaningless. Why does twenty-two percent of students who primarily major in STEM end up transferring their dream to a non-mathematical field? If Math is an obstacle for the majority of American students, will there be any engineer or doctor in this nation in fifty years?