Nature of Mathematics.docx

Nature of Mathematics

• Patterns and Relationships

Mathematics is the science of patterns and relationships. As a theoretical discipline, mathematics explores the possible relationships among abstractions (can be anything from strings of numbers to geometric figures to sets of equations).

• Mathematics, Science and Technology

Mathematics is abstract. Because of its abstractness, mathematics is universal and it finds useful applications in many other fields of human thought.

• Mathematical Inquiry

Normally, people are confronted with problems. Mathematics can be used in expressing an idea to a concrete concept.

• Abstraction and Symbolic Representation

Mathematics as being abstract in form can be represented by symbols such as numbers, letters, other marks, diagrams, geometrical constructions, or even words.

• Manipulating Mathematical Statements

After abstractions have been made and symbolic representations of them are selected, those symbols can be combined in various ways according to precise defined rules. Typically, string of symbols is combined into statements that express ideas and propositions.

• Application

Mathematical processes can lead to a kind of model of a thing from which insights can be gained about the thing itself. Any mathematical relationships arrived at by manipulating abstract statements may or may not convey something truthful about the thing being modeled

The Role of Mathematics in Some Discipline

As posted by Angel Rathnabai (2014), mathematics is not only number work or computation, but is more about forming generalization, seeing relationships, and developing logical thinking and reasoning.

Here are some main disciplines in which the role of mathematics is widely accepted:

• Mathematics in Physical Sciences, Chemistry, and Biological Sciences

Mathematical calculations occur at every step in physics, its concept is involved like in Fluid Dynamics, Physical Oceanography and many others. The field of chemistry also use a significant amount of math such as Binding Theory and Kinetics. The use mathematical programming and reliability theory is used in Biosciences, Bioengineering, and Bioelectronics

• Mathematics in Engineering Technology

Mathematics is considered as foundation of engineering. Its application is used in dealing with surveying, levelling, designing, estimating, construction and many others.

• Mathematics and Economics

The level of mathematical literacy required for personal and social activities is continually increasing. According to Marshall – ‘The direct application of mathematical reasoning to the discovery of economic truths has recently rendered great services in the hand of master mathematicians.

• Mathematics in Philosophy

The function of mathematics in the development of philosophical thought has been very aptly put by the great educationist Herbart, in his words, ‘The real finishers of education is philosophy, but it is the office of mathematics to ward off the dangers of philosophy.

According to Ian Stewart (1995), we live in a universe of patterns. Human mind and culture have developed a formal system of thought for recognizing, classifying, and exploiting patterns. We call it mathematics. By using mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature’s patterns are not just there to be admired, they are vital clues to the rules that govern natural processes.

A regularity (Collins, 2018), is the fact that the same thing always happens in the same circumstances.

A pattern is a discernible regularity in the world or in a man-made design as such the elements of a pattern repeat in a predictable manner

Patterns in nature are visible regularities of form found in the natural world

VARIOUS PATTERNS:

• Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes

Symmetry, trees, meander, cracks, tessellation, waves, stripes

• Logic patterns are usually the first to be observed. It deals with the characteristics of various objects while another deals with order.

• Number patterns are encountered through the concept of functions, which is a formal description of the relationships among different quantities

The formula for the nth term of the sequence 9, 12, 15, 18, 21, 24, …. is 3n + 6 because if the variable n is a counting number from 1 to 6 then:

3(1)+ 6 = 9; 3(2) + 6 = 12; 3(3) + 6 = 15; 3(4)v+6 = 18; 3(5) + 6 = 21; 3(6) + 6 = 24

• Geometric patterns are motif or design that depicts abstract shapes like lines,

polygons, and circles, and typically repeats

Here are additional facts about patterns and regularities

• Patterns and counting are correlative. Counting happens when there is pattern.

• A pattern also shows what may have come before

• A pattern organizes information so that it becomes more useful

• Mathematics is the study of patterns. That is why those who use patterns to analyze and solve problems often find success compared those who cannot

Who is Fibonacci? The Fibonacci Sequence Leonardo of Pisa, also known as Fibonacci, is one of the best-known mathematicians of medieval Europe. In 1202, after a trip that took him to several Arab and Eastern countries, Fibonacci wrote the book Liber Abaci. In this book Fibonacci explained why the Hindu-Arabic numeration system that he had learned about during his travels was a more sophisticated and efficient system than the Roman numeration system. This book also contains a problem created by Fibonacci that concerns the birth rate of rabbits.