I chose to study chemistry as part of a of a science degree with mathematics being my major area of study. Knowledge of basic maths is essential for understanding chemical processes and solving chemical problems. Stoichiometry is a great example of this as every step involves some level of maths, from balancing chemical equations to unit conversions. A strong parallel between chemistry and maths is the ability to use logic as part of the decision-making process when working through problems.
Mathematical modelling is what I’m most interested in and the chemistry concept that has the strongest link to this is matter. Everything that exists in the world is made from matter in some shape or form. Chemistry gives us a way of classifying matter through both physical and chemical properties. Mathematical modelling involves using maths to model real world events. These models can predict outcomes, explain processes occurring in various systems and describe interactions between things. To create such a model, an understanding of what is to be modelled is essential in addition to understanding what the outcome means in a real-world sense. Matter really matters in this respect, as previously mentioned it allows us to classify everything from objects to processes which occur in our world.
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Being able to understand a system with this level of depth enables a significantly more accurate mathematical model to be formulated as all possible variables, their interactions and processes can be accounted for. The more a system can be explained by a model, the more accurate it will be. The outcome of such a model will be incredibly useful for its intended purpose and an understanding of matter enables this result to be easily and correctly interpreted.
So essentially matter provides the framework that these mathematical models can be constructed from.
An example is as follows: You want to determine how time it would take ice to melt completely at a given temperature. To do so you would need to solve a differential equation so that time is by itself with all other variables on the other side of the equation. A basic model may look something like this: Time = (size of ice) – (temperature)
It makes sense from a theoretical point of view as a larger piece of ice will take longer to melt and with an increase in temperature the melting time will be faster. However, the outcome of such a model will be incredibly inaccurate for anything other than a large block of ice and a ‘normal’ temperature.
An understanding of the physical and chemical properties of ice is needed to enable a more accurate model to be developed. By understanding the reaction that takes place between ice and water the model can be modified to account for the fact that at and below zero degrees Celsius, ice will not melt in normal conditions. This is one of many factors that influence the outcome and need to be accounted for. If this was to be ignored, then the model would still produce a melting time for ice at negative temperatures which doesn’t make sense in the real world.
Summarising, we cannot understand and accurately model the real world without the knowledge of the chemistry involved.
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