Mathematics is a part of our everyday lives, whether we clean the house, make supper or mow the lawn. Wherever you go, whatever you do, you depend on mathematics daily without even realizing it. It just comes unconsciously. Mathematics can be used to solve very complex problems, far more complicated than that of an apple falling on your head due to gravity. Industries are full of such problems that require mathematic modelling.
Mathematics and the Universe
Mathematical techniques can explain how the universe works and make the world a better place. Mathematical modelling has the potential to save lives, assist in policy and decision-making, and optimise economic growth. It can also be exploited to help understand the universe and the conditions needed to sustain life. The movement of all solid objects and fluids can be described with the unifying language of mathematics. Wind movement, turbulence in the oceans, the migration of butterflies in a big city; all these phenomena can be better comprehended using mathematics.
Mathematics in Daily Life
Everyone has a cell phone and it requires a basic knowledge of math, and with today's technology, you can do basically everything on your cell phone. Baking and cooking require some of this mathematical skill as well. Every ingredient has to be measured and sometimes need to be multiplied or divide to get the exact amount. Whatever one does in the kitchen requires math.
Doing something as mundane as gardening requires some knowledge of basic mathematics. If you need to plant or sow new seeds you need to make a row or count them out or even make holes accordingly. So even without thinking you are doing math.
Fuel, oil and water, while driving is required for a car, without which it may break down. You will be bankrupt within hours if you don’t know to manage your finances. Taking into account the past and the future, and keeping a record of what has been done is statistics. It helps us to find balance and structure.
Mathematics at Workplace
Whether you are a sculptor, a painter, a dancer or even just doing a collage for fun, you will need to measure, count and apply basic math to it. Every form of art is co-dependent upon mathematic skills.
Making appointments and scheduling time that works for you requires math. Some people even have to chart in their appointments to take a break from work. Whether they go to the beach or the zoo is irrelevant, but they will plan their way there and will use time wisely and math is their guide to assist and help.
Wider scope of mathematics comes under weather forecasting, global warming, flight simulation, hurricane forecasting, nuclear winter, nuclear arms race. Mathematical models are also used to describe traffic flow, stock market options, predator-prey relations, and techniques of search.
Mathematical Modelling and its Usefulness
The objectives of mathematical modelling are forecasting the future, preventing an unwanted mishap, and understanding various 'natural' and unnatural phenomena. These might all be put into the category of problem-solving with the use of mathematics to mirror an aspect of the world.
What is Mathematical Modelling?
In its broadest sense, mathematical modelling is the process of mathematically defining a nonmathematical situation, phenomenon or the relationships between the situations, and finding out mathematical patterns within these situations and phenomena. It is commonly regarded as the art of applying mathematics to a real-world problem with a view to better understand the problem. As such, mathematical modelling is directly related to problem-solving. Beginning with a real-life problem, the objective is to produce a real-life solution.
The first step in the mathematical modelling process is to understand the problem and describe it as a mathematical symbol to form an equation. In other words, mathematize the problem. In doing so, it is essential to be able to identify the variables in the problem and to form relationships between or amongst these variables. The next step is to manipulate the problem and constructing hypotheses. Interpreting the shared solution, making decisions, analysing the system and proposing new solutions is next. Linking the results or solutions of the model to the real-world problem may be the last step.
Challenges with Mathematical Modelling
There are also certain problems associated with Mathematical Modelling. The model does not address what you want to achieve and is very sensitive to the initial conditions or to the values of the parameters. The model is too simple to mirror adequately, and at the same time too complex to aid understanding. The results are too technical to communicate and are not in a form that can be implemented. However, it helps one to choose what to focus on and prioritize factors. The modelling process helps make thoughts more precise. A model helps one go beyond the superficial layer of a phenomenon to an understanding of inner mechanisms and deeper relationships.
To successfully implement the same in daily life, one can try out different scenarios, modifying assumptions, manipulate variables, initial values, and values of parameters, to see the resulting effects.