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Have you ever considered just how much of an influence Maths has on our everyday lives?
We're not talking about fractions or completing worksheets, but Maths in the form of logic and problem-solving crop up constantly outside of the classroom. Mathematics is more a part of our everyday lives than many would think, and allows us to better understand the world around us.
Math helps us think analytically and have better reasoning abilities. Analytical thinking refers to the ability to think critically about the world around us. The reasoning is our ability to think logically about a situation. Analytical and reasoning skills are essential because they help us solve problems and look for solutions.
While it may seem far-fetched to believe that solving the worksheet problems can help you solve a problem in your life, the skills that you use in framing the problem, identifying the known(s) and unknown(s), and taking steps to solve the problem can be a very important strategy that is applicable to other issues in life.
Mathematical Functions
You may heard about the word 'function' before which is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.
In mathematics, we represent functions in many different ways; we can use words, tables, mappings, equations, and even graphs. Consider this example: If a state has a 6% sales tax, then we can use a function to calculate it. We can use the following equation to represent this function:
T = 0.06x
If we purchase a product for x dollars, then to calculate the tax, we would multiply x by 0.06, or the tax rate in decimal form. For instance, if you bought a shirt for $25, then you can calculate the sales tax by plugging in 25 for x.
T = 0.06(25) = 1.5
We see the sales tax is $1.50.
We can also represent this function using our other representations. Because our purchase price can be any number, we could never list all of the inputs and outputs! Using a table or mapping wouldn't be the best method in this situation, but we can easily represent it graphically by simply graphing the equation T = 0.06x.
So, we can use functions to describe many things that happens every day in our world. We can know the height of something by measuring the length of their shadows. The length of a shadow is simply a function of its height and the time of day. Shadows can be used to find the height of large objects such as trees or buildings.
We also can use functions to describe real life physical systems like knowing the velocity of a car travelling as a function of time. We can also know the kinetic energy of a body, which is the energy that is possessed by a body due to its state of motion, by knowing its velocity.
We can use functions in other fields like economics and programing language. They are very helpful in our life.
Contradiction with our life
As we know. Our life depends on continuity. Imagine that you are holding a pen in your right hand and you throw it to your left hand. Of course, the pen doesn’t disappear from your right hand and goes to your left hand.
Let us call the position of the pen in your right hand “Point A” and your left hand “Point E”. So, the pen must go throw all the points between A and E so that it could reach the point E in your left hand.
Different kinds of functions were discovered from real-world applications. However, during the seventeenth century, Mathematicians started creating functions using only mathematical logic with complete Isolation from the real world. One of them is the absolute value function, f(x)=|x|.
Give a deep look at this function, there’s something strange! The derivative at point zero doesn't exist which means that there’s no rate of change at point zero. This causes a complete contradiction with our world. Why?
We said that our life depends on continuity which means there is a change is happening and therefore a rate of change. So, how could this function describe a physical system in our real life that depends on continuity?
Is this mean that mathematical functions derived only from mathematical logic isn’t useful? Are all of the mathematicians work during the 17th century until now isn’t useful for us?
Our understanding of the world and how our universe is working is not constant. Every day we discover something, we study something, we invent something, and we explore something. Our world is changing every day.
It’s important for mathematicians to work on discovering new functions even if those functions have contradictions with our life and even if our current mind doesn’t believe it. Maybe someday in the future, our understanding of the world will change and therefore our understanding of the functions will also change. At this time.
We can call those functions that we didn’t believe in, and use them to describe our new life.
- Written by Amr Abdalkhalek Meshref (EMN Community Member From Egypt)
- Edited by Mridul Goyal (EMN Community Member From New Delhi, India)
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