Mathematics, the language of the universe, is one of the largest fields of study in the world today. With the roots of the math tree beginning in simple mathematics such as, one digit plus one digit, and one digit minus one digit, the tree of mathematics comes together in the more complex field of algebra to form the true base of calculations as the trunk. As we get higher, branches begin to form creating more specialized forms of numerical comprehension and schools of mathematical thought. Some examples of these are the applications into chemistry, economics and computers. Further up the tree we see the crown beginning to form with the introduction of calculus based organization. Calculus, a theoretical school of mathematical thought, had its creation in the middle ages with Newton. The main use of calculus is its application in advanced physics. Mathematics is everywhere because that is where we put them, everywhere. We, humans, represent everything with numbers, which therefore means that we impose mathematics on to the universe.
Starting at childhood, education begins with the forced mind track of comparison. Parents teach their offspring to be fair or equal, and that they should share to make it fair. This is the beginning of the mathematical state of mind which stays with the child for the rest of his/her life, the summing up of what they themselves have and comparing it to what the other person has, so that both sides can be equal. This lesson is considered essential in the raising of children and since everyone is supposed to understand, people assume that everyone does. This assumption is a flaw that begins early. An example of how this can have a not so positive effect on people is if the “spoiled brat” wants to have more toys than the other children, and thus becomes, mathematically superior.
When one plus one is taught to be two, two plus two to be four and so on, the idea of a pattern emerges. Patterns are another rudimentary concept taught early to assist in the comprehension of numbers. When a child sees a cat being chased by a dog that is followed by his unhappy owner, the child subconchisly devises the pattern, cat-dog-owner, or a-b-c, a link to the alphabet. Such as in the film ?, where the main character believes that there are patterns in nature, the child begins to seek out o...
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...thematical systems or ideas were created with the formation of the universe in the Big Bang, they were thought up by mortal men with mortal minds. With this fact in mind, there is no way to totally understand the universe or for example, predict what will occur when a material is cooled to absolute zero on earth. The human race devised the language of mathematics and numerals and digits in the same fashion we developed the exorbitante amount of spoken languages which litter the planet. To state that the universe imposed mathematics upon humanity is upsurd, nearly to the extreme of lunicy. The point of mathematics is to be able to represent the universe in numbers, which are the most rudimentary language in the know world, and organize everything to the point of universal enlightenment. Humans begin their knowledge of the world in a comparison view, two is greater than one, and mom does not equal dad, but how can we compare our world to anything else? We cannot, there is nothing to compare our world to. With this perspective, people are submerged into a universe of mathematics where everything is represented with numbers and units infused upon the surrounding environment by humans.
Earthquakes are caused by tectonic plates moving in the earth's crust. They either move apart or pull together at faults. Two forms of faults are normal faulting where the hanging wall moves downward causing rocks to be pulled apart by tension and reverse faulting, which is the opposite where the hanging wall moves upward casuing rocks to be forced together by tension. These movements cause tectonic plate boundaries called divergent boundaries, convergent boundaries and transform boundaries. Each boundary is different and play a
It consistently affects the urban development of neighborhoods. Even though there are positives in gentrification such as social and economic development of communities but there are also negatives specifically lower income families are forced to move out of their homes because of high rent prices. This also causes people to become homeless because they can’t afford the newly inflated rent prices. In my opinion, I believe there should be some sort of system where apartments and houses are made based of what you can afford so families have places to live. Landlords shouldn’t raise their prices just so they can get people they desire to live in their homes. Even though it's understandable that landlords want to make more money but they shouldn’t force families out. There should only be a legitimate reason for families to be evicted out of their homes. Even though Gentrification has been around for a long time, hopefully there is some positive change in the
I also learned that mathematics was more than merely an intellectual activity: it was a necessary tool for getting a grip on all sorts of problems in science and engineering. Without mathematics there is no progress. However, mathematics could also show its nasty face during periods in which problems that seemed so simple at first sight refused to be solved for a long time. Every math student will recognize these periods of frustration and helplessness.
In literature and in life, people endure events which are the effects from the relationships between a parent and their child. In Death of a Salesman written by Arthur Miller it is evident how the relationship between Willy and his sons creates the downfall of the dysfunctional Loman family. Miller depicts the possessiveness that exists in humans through Willy Loman. In the 1949 era to preserve a healthy household it was important for the father-son relationship to be strong. If conflicts were to arise in their relationship the entire family would collapse and fail. Biff and Happy constantly idolize and praise their father, however, they realize that he is flawed and how as a father he failed to prepare them for the real world. Willy Loman is a man that is happy and proud in one moment and suddenly angry in another, which exhibits how the inconsistencies in his character make it difficult for anyone to have a strong relationship with him. In the play it is evident that the tension between the father and son relationship is the factor that causes the protagonist’s tragedy. The dispute between the father and
According to Piaget’s theory of cognitive development, grade 5 children are at concrete operational stage. They are able to solve hands-on problems in logical fashion, understands laws of conservation and is able to classify and seriate objects, and understands reversibility ( Hockenberry, 2014b). Grade 5 students write reflections in their health education class. They understand there could be more than one answer to each questions. In addition, they know how to group similar objects, how to arrange (seriate) numbers from increasing and decreasing order, and how to calculate multiplications like 2*4=4+4=8, and they can answer the question even when the numbers changed position to 4*2=8. Furthermore, when they discuss about a book, they
Thermodynamics is the study that shows the relevance between the work and the heat. Thermodynamics has 2 laws. The first law declares that the heat and the work are mutually interchangeable. The second law states that a entropy of a secluded regulation can never decrease, because the secluded regulation always develops toward the equilibrium thermodynamic. These two laws attitudinize the process of a heat engine.The first law is the implementation of the preservation of energy to the regulation. The second law defines the potential eligibility of the machine and guidance of the energy flow.
Mathematics is everywhere we look, so many things we encounter in our everyday lives have some form of mathematics involved. Mathematics the language of understanding the natural world (Tony Chan, 2009) and is useful to understand the world around us. The Oxford Dictionary defines mathematics as ‘the science of space, number, quantity, and arrangement, whose methods, involve logical reasoning and use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis of mathematical operations or calculations (Soanes et al, Concise Oxford Dictionary,
Calculus, the mathematical study of change, can be separated into two departments: differential calculus, and integral calculus. Both are concerned with infinite sequences and series to define a limit. In order to produce this study, inventors and innovators throughout history have been present and necessary. The ancient Greeks, Indians, and Enlightenment thinkers developed the basic elements of calculus by forming ideas and theories, but it was not until the late 17th century that the theories and concepts were being specified. Originally called infinitesimal calculus, meaning to create a solution for calculating objects smaller than any feasible measurement previously known through the use of symbolic manipulation of expressions. Generally accepted, Isaac Newton and Gottfried Leibniz were recognized as the two major inventors and innovators of calculus, but the controversy appeared when both wanted sole credit of the invention of calculus. This paper will display the typical reason of why Newton was the inventor of calculus and Leibniz was the innovator, while both contributed an immense amount of knowledge to the system.
Research has shown that ‘structured’ math lessons in early childhood are premature and can be detrimental to proper brain development for the young child, actually interfering with concept development (Gromicko, 2011). Children’s experiences in mathematics should reflect learning in a fun and natural way. The main focus of this essay is to show the effectiveness of applying learning theories by Piaget, Vygotsky and Bruner and their relation to the active learning of basic concepts in maths. The theories represent Piaget’s Cognitivism, Vygotsky’s Social Cognitive and Bruner’s Constructivism. Based on my research and analysis, comparisons will be made to the theories presented and their overall impact on promoting mathematical capabilities in children. (ECFS 2009: Unit 5)
Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
Mathematical logic is something that has been around for a very long time. Centuries Ago Greek and other logicians tried to make sense out of mathematical proofs. As time went on other people tried to do the same thing but using only symbols and variables. But I will get into detail about that a little later. There is also something called set theory, which is related with this. In mathematical logic a lot of terms are used such as axiom and proofs. A lot of things in math can be proven, but there are still some things that will probably always remain theories or ideas.
Differential calculus is a subfield of Calculus that focuses on derivates, which are used to describe rates of change that are not constants. The term ‘differential’ comes from the process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, “We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).” Not only are derivatives used to determine how to maximize or minimize functions, but they are also used in determining how two related variables are changing over time in relation to each other. Eight different differential rules were established in order to assist with finding the derivative of a function. Those rules include chain rule, the differentiation of the sum and difference of equations, the constant rule, the product rule, the quotient rule, and more. In addition to these differential rules, optimization is an application of differential calculus used today to effectively help with efficiency. Also, partial differentiation and implicit differentiation are subgroups of differential calculus that allow derivatives to be taken to more challenging and difficult formulas. The mean value theorem is applied in differential calculus. This rule basically states that there is at least one tangent line that produces the same slope as the slope made by the endpoints found on a closed interval. Differential calculus began to develop due to Sir Isaac Newton’s biggest problem: navigation at sea. Shipwrecks were frequent all due to the captain being unaware of how the Earth, planets, and stars mov...
What is math? If you had asked me that question at the beginning of the semester, then my answer would have been something like: “math is about numbers, letters, and equations.” Now, however, thirteen weeks later, I have come to realize a new definition of what math is. Math includes numbers, letters, and equations, but it is also so much more than that—math is a way of thinking, a method of solving problems and explaining arguments, a foundation upon which modern society is built, a structure that nature is patterned by…and math is everywhere.
As mathematics has progressed, more and more relationships have ... ... middle of paper ... ... that fit those rules, which includes inventing additional rules and finding new connections between old rules. In conclusion, the nature of mathematics is very unique and as we have seen in can we applied everywhere in world. For example how do our street light work with mathematical instructions? Our daily life is full of mathematics, which also has many connections to nature.