Introduction to Mathematics-History, Branches, And Scope

What is Mathematics?

Mathematics is the study of structure, order, and relationships. Over time, the fundamental techniques of counting, measuring, and describing the shape of objects have evolved.

It studies quantity, structure, space, and change. By rigorous deduction from appropriately chosen axioms and definitions, mathematics involves finding patterns, formulating conjectures, and establishing truth.

The entities that are stipulated with certain properties called axioms include arithmetic, geometry, algebra, number theory, formulas, formulas, calculus, proofs, and abstractions from nature.

A mathematical proof consists of a succession of applications of rules that have already been proven, as well as some basic properties that are considered to be the true starting points of the theory.

Mathematics comes from the Greek word “Mathema” which means measure, ratio, and knowledge.

Who is the Father of Mathematics?

Ancient Greek mathematicians introduced mathematics to the world. Several topics from various parts of the world were contributed by mathematicians at the same time. Nobody is credited with inventing mathematics.

Archimedes is famous for being a Greek mathematician who is regarded as the father of mathematics. He is considered the Father of Mathematics for his significant contribution to the development of mathematics.

Notable inventions of Archimedes are His method to find the circumference of the circle by using the method of exhaustion to find the area of the circle and his use of the formula πr2 (the famous pi or pi) to calculate the area of the circle.

History of Mathematics

Mathematics has been part of the physical sciences for hundreds of years. Quantitative aspects of the life sciences have been assumed by it.

The history of mathematics deals with the beginnings of mathematical methods and how they were used in the past. The Egyptians did mathematics before the modern age, and the spread of knowledge, in this version. 

The examples of their new mathematical developments were written down in a few places. The importance of citations is very important in mathematics and statistics. The basis for referencing mathematical research can be provided by them. 

When presenting the results of a mathematician’s own publication, it is customary to cite the original work of that mathematician. 

For purposes of taxation, commerce, and trade and also to record time and formulate calendars, the states of Mesopotamia, Akkad, and Assyria, as well as Ancient Egypt and the Levantine state of Ebla, began using arithmetic, algebra, and geometry from 3000 BC.

The history of Mesopotamian and Egyptian mathematics is based on the original documents written by the scribe. Although there are very few documents left in Egypt, these are all of a type and leave no doubt that Egyptian mathematics was, on the whole, elementary and profoundly practical in its orientation. 

Mesopotamian mathematics was much more advanced than Egyptian mathematics. It had a combination of both writing and math, and it had a large number of clay tablets, which showed the mathematical achievements of a much higher order than those of the Egyptians.

The oldest copies of the Greek mathematical documents are in Byzantine manuscripts dating from the 10th century, and from the period before Alexander the Great, no Greek mathematical documents have been preserved except for fragmentary paraphrases. 

This is completely different from the situation described in Egyptian and Babylonian documents.

The invention of printing has solved the problem of obtaining secure texts and has allowed historians of mathematics to concentrate their editorial efforts on the correspondence or the unpublished works of mathematicians.

Historians can only treat the major figures in detail for the period from the 19th century on, because of the exponential growth of mathematics. There is a problem of perspective when the period gets closer to the present.

The birth of mathematics was thought to have occurred among the ancient Greeks until the 1920s. What was known of earlier traditions, such as the Egyptian as represented by the Rhind papyrus (edited for the first time only in 1877).

Significance Of Mathematics In Sight Of Scientists

Mathematics has long been recognized as an essential and indispensable field of study. As it has a wide range of applications in diverse fields such as science, engineering, economics, and art. 

Its significance has been acknowledged by numerous prominent scientists throughout history. Here are some views on the importance of mathematics, from Bertrand Russell’s famously skeptical quote to Gauss’s declaration that arithmetic is the queen of all mathematics.

•  “The subject in which we never know what we are talking about, nor whether what we are saying is true”. (Betrand Russell-1901)
• “Mathematics is the queen of sciences and Arithmetic is the queen of all mathematics”. (Gauss)
• “Mathematics is an indispensable instrument of all physical research”. (Kant)
• “Mathematics is the gateway and key to all sciences”. (Bacon)
• “Mathematics is the language of physical sciences and certainly, no more marvelous language was created by the mind of man”. (Lindsay)
• “Mathematics is a way to settle in the mind a habit of reasoning”. (Locke)
• “Mathematics is engaged, in fact, in the profound study of Art and the expression of beauty”. (j.B.Shaw).

Branches of Mathematics

Mathematics can be broadly grouped into the following branches:

Arithmetic

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Arithmetic is about adding, subtracting, multiplying, and dividing. For the sake of simplicity, we will denote these operations by the given symbols.

Algebra

The branch of mathematics that helps in the representation of problems or situations in terms of mathematical expressions is called Algebra. Adding, subtracting, multiplication and division are some of the mathematical operations that involve variables, x, y, and Z. 

The use of the branches of mathematics such as trigonometry, calculus, coordinate geometry, and so on is referred to as Algebra. Here’s a very simple example of an equation: (3x) x (2x) = 12

Geometry

Geometry is a branch of mathematics that deals with the shapes and sizes of things.

It also studies how shapes fit together and how things relate to other things.

It is the most practical branch of mathematics. The basic elements of geometry are points, lines, angles, surfaces, and solids.

Trigonometry

The study of angles and their applications to calculations is referred to as trigonometric. It’s also referred to as the geometry of angles. The three basic functions in trigonometry are sine, cosine, and tangent. 

The other three functions that are cotangent, Secant, and Co Secant are derived from those three functions. These functions are the basis for all trigonometric concepts.

Calculus

Calculus is the branch of mathematics that deals with instantaneous rates of change. In the 17th century, two mathematicians, one from England and the other from Germany, created calculus.

Scope of Mathematics

There are lots of options for a career in mathematics. Many fields are related to social sciences, medicine, engineering, and natural science. 

Business problems, scientific problems, and economic problems are some of the things mathematics is used for. Here are some career opportunities a mathematician can pursue in:

• Professor
• Statistician
• Mathematician
• Data Analyst / Business Analyst
• Chartered Accountant
• Investment Banker
• Data Scientist
• Astronomer
• Programmer/ Software Engineer/ Blockchain Developer
• Economists
• Engineering
• Physicist

Studying mathematics can be highly beneficial for our mental development, as it fosters discipline and logical reasoning skills. Moreover, possessing mathematical knowledge is essential for comprehending various other academic subjects, including science, social studies, and even the arts.

By delving into mathematics, we can enjoy a range of advantages that positively impact our minds. These include the cultivation of analytical thinking, the acceleration of mental processes, the enhancement of practical problem-solving skills, and the applicability of mathematical principles to everyday life.

It’s worth noting that mathematics is a ubiquitous presence in our daily routines.

• Mathematics plays a fundamental role in bringing order to our daily lives. It nurtures essential qualities such as reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability, and effective communication skills in those who study it.
• By helping us comprehend the world around us, mathematics serves as a powerful tool for cultivating mental discipline.
• Mathematics teaches you how to approach problems with logic and reason, fostering your problem-solving abilities, creativity, abstract thinking, and communication skills.
• Mathematical literacy is an essential attribute for leading a successful life. It encompasses fundamental skills such as computational proficiency, quantitative reasoning, spatial ability, and more.
• In marketing, quantitative analysis is a valuable tool. It enables us to discern patterns, forecast trends, and quantify relationships. Math helps us interpret the world around us and uncover interconnections that exist between things, demonstrating how one element is linked to another.
• Mathematics is a versatile discipline utilized in numerous fields and industries, including science, engineering, and economics. It plays a critical role in resolving issues and understanding intricate concepts.

Applications Of Math In Different Fields

Mathematics plays an important role in every field of life. Here are some applications of mathematics:

Math In Environmental Science

In environmental science, math plays a crucial role in tasks ranging from counting the number of species in an ecosystem to solving complex chemistry and physics equations related to energy production. 

Environmental science majors take courses in biology, chemistry, geology, and math. Upper-level courses build on this foundation and apply the knowledge to solve current environmental problems by synthesizing and integrating basic sciences.

Math In Medicine

Mathematics is essential in healthcare. It assists in determining the effectiveness of treatments and medication, evaluating disease spread, and prescribing the correct dosage to patients. 

Probability and statistics play a significant role in validating new drugs, while statistical graphs help to illustrate treatment success rates and other significant data points.

Math In Technology

Mathematics technology includes tools like graphing calculators, spreadsheets, and software designed for math. These tools help scientists and engineers organize and structure their knowledge to create systematic, reproducible, and transmittable knowledge.

Math In Nature

Mathematics plays a significant role in genetics and evolution, enabling us to comprehend the changes and variations in population size and physical characteristics through mathematical models. 

Nature presents numerous examples of mathematical concepts, such as symmetry, which is observed in the six-fold radial symmetry of a snowflake.

Math In Daily Life

Mathematics is the universal language that helps us understand patterns, define relationships, and predict the future.

Banking and financial services rely on math for accuracy in managing money and calculating bills and financial obligations.

Cell phone technology requires basic math skills for phone operations and functions.

Computer science relies heavily on mathematics for data entry, computer operation, and software development.

Technological innovation, such as the Internet, is developed with the help of mathematics.

 Math is widely used in animation design, architecture, sports, population geography, astronomy, music, painting, fashion designing, home decoration, and in the kitchen.

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