This website uses cookies to ensure you have the best experience. Learn more

The Nature Of Mathematics Essay

1403 words - 6 pages

The Nature of Mathematics

Mathematics relies on both logic and creativity, and it is pursued
both for a variety of practical purposes and for its basic interest.
The essence of mathematics lies in its beauty and its intellectual
challenge. This essay is divided into three sections, which are
patterns and relationships, mathematics, science and technology and
mathematical inquiry.

Firstly, Mathematics is the science of patterns and relationships. As
a theoretical order, mathematics explores the possible relationships
among abstractions without concern for whether those abstractions have
counterparts in the real world. The abstractions can be anything from
strings of numbers to geometric figures to sets of equations. In
deriving, for instance, an expression for the change in the surface
area of any regular solid as its volume approaches zero,
mathematicians have no interest in any correspondence between
geometric solids and physical objects in the real world.

A central line of investigation in theoretical mathematics is
identifying in each field of study a small set of basic ideas and
rules from which all other interesting ideas and rules in that field
can be logically deduced. Mathematicians are particularly pleased when
previously unrelated parts of mathematics are found to be derivable
from one another, or from some more general theory. Part of the sense
of beauty that many people have perceived in mathematics lies not in
finding the greatest richness or complexity but on the contrary, in
finding the greatest economy and simplicity of representation and
proof. As mathematics has progressed, more and more relationships have
been found between parts of it that have been developed separately.
These cross-connections enable insights to be developed into the
various parts; together, they strengthen belief in the correctness and
underlying unity of the whole structure.

Mathematics is also an applied science. Many mathematicians focus
their attention on solving problems that originate in the world of
experience. They too search for patterns and relationships, and in the
process they use techniques that are similar to those used in doing
purely theoretical mathematics. The difference is largely one of
intent. In contrast to theoretical mathematicians, applied
mathematicians, in the examples given above, might study the interval
pattern of prime numbers to develop a new system for coding numerical
information, rather than as an abstract problem. Or they might tackle
the area/volume problem as a step in producing a model for the study
of crystal behavior.

The results of theoretical and applied mathematics often influence
each other. Studies on the mathematical properties of random events,
for example, led to knowledge that later made it possible to improve
the design of...

Find Another Essay On The Nature of Mathematics

The origin and development of Mathematics

1063 words - 4 pages Rhind Mathematical papyrus as well as the Moscow mathematical papyrus. The totality of these are considered the Pythagorean theorem and they are seen as the most ancient and popular mathematical development since the arithmetic and geometry (Struik, 1987). It is the purpose of this paper to inform the readers of the origin and development of mathematics, the writing and communication practice of this specific field so that valuable information can

The History of Mathematics in Africa

1502 words - 6 pages The history of mathematics has its roots on the African continent. The oldest mathematical object was found in Swaziland Africa. The oldest example of arithmetic was found in Zaire. The 4000 year old, Moscow papyrus, contains geometry, from the Middle Kingdom of Egypt, Egypt was the cradle of mathematics. The great Greek mathematicians, including Pythagoras, Thales, and Exodus all acquired much of their mathematics from Egypt, including the

The Teachings of Mathematics Education in America

987 words - 4 pages The Teachings of Mathematics Education in America Math educators in the United States should stress the understanding of the learners and teach them to process certain understanding to succeed in mathematics. The connection between math understanding and the reading of math problems should be raised in smaller grade levels so students have a better understand of math at younger ages. Yet it is not all the students’ part in learning the math

The Progression of Mathematics in School

936 words - 4 pages The educational system grooms children to be productive members of society. First coined in the days of one-room schoolhouses, the phrase “reading, writing, and ‘rithmetic” has become a common mantra of education. The third of these three r’s is mathematics, an infamous subject. It is incumbent in many professions, from accountants and doctors to physicists and teachers. Both hated and adored by many, math is complex, essential, and encompasses

The Rich Cost of Poor Mathematics Education

932 words - 4 pages , after college it is rarely used on the level in which it is taught. Although mathematics is essential learning material for any pupil, mandatory Consumer Economics classes would better suit graduates of this era by assisting in living in the real world, keeping their finances in order and preventing scholars from drowning in an increasing sea of debt. Consumer economics is widely known now as just another Home Economics class. It is based

Mathematics of the Eye and Color

3192 words - 13 pages . wavelength graph below. It is important not to get hung up on the color names for the cones. These are just given names and do not reflect the complete nature of cones, so I think L, M, S are better names. There are various experimental ways of measuring cone absorbency. For example scientist isolate, then suspend in glass and then measuring the light absorbency of a cone by shining lights of different wavelengths on it. Now a distinction has to be

The Use of Mathematics in the Medical Field

1099 words - 4 pages field relies heavily on mathematics. Elementary mathematics, geometry and algebra are all obviously crucial to advancing in new technology, saving lives and curing diseases. However, most people do not realize the importance math has on simpler tasks performed every day by doctors, nurses, x-ray technicians, pharmacists, and the hundreds of other jobs in this fascinating career field. With the use of basic as well as advanced mathematics, we

The Disadvantage of Using English to Teach Mathematics and Science

1504 words - 6 pages but what can be seen, the lack of PPSMI has overcome all the benefits of PPSMI. Many people do not agree to the implementation of PPSMI. There are disadvantages of using English language to teach Mathematics and Science the effect to Malaysia language, lower student achievement and increase a lot of cost to education. PPSMI been enshrined as a policy decision of the Malaysian government as a result of the Special Cabinet meeting on July 19, 2002

Barriers to female achievement in the field of mathematics

780 words - 3 pages What were the barriers to women's achievement in mathematics in the past? How did some women manage to overcome them? To what extent do these barriers still exist today?Mathematical achievements throughout the ages have been well recognised and held in high esteem. However, the names of Ada Lovelace, Emmy Noether or Sonya Kovalevskaya are rarely highlighted and brought out for public attention, consideration, and admiration. These outstanding

The Impact of Technology on Assessment Practices in Mathematics

4057 words - 16 pages Introduction This essay aims to discuss the impact of Web Based Technology (WBT) on assessment practices in mathematics. WBT refers to and promotes what is known as Web Based Learning (WBL) where the learning is in hypertext format providing the learner with more exploration and interactivity capabilities. Studies in Hong Kong by Khalifa(2002) suggests that this is the most superior form of WBL in comparison to Distributive Passive Learning

The Nature of Women

1733 words - 7 pages service. Riley: Oh, this is going to be fantastic. Two 18th century moral and political philosophers in my living room. Both people, if historical accounts are to be taken seriously, that apparently didn't like each other. Wollstonecraft: Theories on the social standing between Mister Rousseau and myself matter not. Matters of educational theory and their substantial backings do. Rousseau: After all this time you and I still debating the nature

Similar Essays

The Mathematics Of War Essay

1776 words - 7 pages A Mathematics for WarAmong all the chaos and uncertainty inherent in war is a mathematical beauty. The size and frequency of insurgent attacks in any country during any time period is found to obey a certain inverse power-law distribution, following a specific mathematical model. A case of immediate interest is the insurgent attacks in Iraq, which also follows, to a great deal of accuracy, the inverse power law. However, such a law tells us

The Benefits Of Learning Mathematics Essay

962 words - 4 pages , the topics need not be important or of immediate use, but altogether or cumulatively, the topics provide or point to a skill, a mastery of mathematics. Logic and mathematics starting with basic arithmetic showed me how to follow steps, one at a time and one after another, to arrive at the results, one step at a time and after another. I learned that an error in one step will make all the following steps and results wrong. Mathematics like any

The Simple Mathematics Of Cryptology Essay

700 words - 3 pages PLC XOZ OVM QLI LDV PBB IPI FHB FQF PDL FKD QLY BYL QEC RKX KAB XPV. Oops! I'm getting ahead of myself. We'll get back to this sentence in a very short time, but first, lets discuss what roles mathematics plays in cryptology.The simplest type of cipher is the monoalphabetic substitution cipher (Lewand 1). As its name suggests, this enciphering scheme is based on the idea of replacing each character of a message (the plaintext message) with a

The Issue Of Experiment In Mathematics

2305 words - 9 pages mathematics and natural sciences. Physical objects are recognized in the process of our experiencing materialistic reality. The experiment in natural sciences can be defined as a dialogue between the learning subject and the nature, which exists objectively. If we treat the experiment in mathematics in similar way, then there has to be two interlocutors: a mathematician and the field of mathematical objects, subjected to its own rules independent