I used to hate mathematics at school. Math was a four letter word worse than any other F-word could ever be. It wasn’t because I didn’t understand the subject, it had a lot to do with having to sit through continuous assessment tests every 2 weeks. It just took me longer than two weeks to fully assimilate the new concepts and make them part of my knowledge base. I never preformed well at those short term tests. My hatred for the subject also had a lot to do with the fact that our teachers taught maths for the sake of maths. Never really relating things to the real world and what the terms meant.
It took a very practical approach to maths for me to fall in love with two rather complex concepts at university. The maths lecturer drew a simple RLC (resistor, inductor, capacitor) circuit on the black board and asked us to give the circuit’s output waveform equation based on a step input. My eyes glazed over at having to solve those differential equations. After a few minutes of all of us sweating over the problem at hand he stood-up in front of us and said:
“Right! Anyone have the answer?”
Only one lonely hand was raised. Our maths buff thought he had the solution…
“Why is such a simple circuit so difficult to analyse? Because you have the wrong tool for the job! You’re trying to put a nail in the wall not with a hammer but with a JCB! You’ll get there but it will take you a lot more effort than necessary.”
He then proceeded to solve the problem by changing the problem’s equation space. Instead of solving differential equations he just did some arithmetic. and about 30 seconds later he had the solution.
I loved the simplicity of it. I loved the fact that I didn’t need to solve a differential equation again when designing a filter or a control loop.
The Laplace transform became one of the most powerful tools in my design arsenal.
At the test that followed a number of weeks later I obtained my best score in Maths ever! 105% No this isn’t a typo I completed all of the questions and the bonus one. I had for the first time in my life fallen in love with a mathematical abstraction, not because of its inherent beauty, but because of its practical applications.
The same thing happened for Fourier transforms and to a much les
Smith chart. Used for circuit analysis and tuning.
ser degree Z-transforms.
I have long forgotten how to solve differential equations but I still use Laplace, Fourier and Z-transforms on a regular enough basis in my job as an embedded system designer.
I probably would have performed really well at school if the practical side of Mathematics had been taught to us rather than doing Maths for the sake of Maths.
Like any language, mathematics needs to be useful to be understood. It needs to be practised in the real world. Physics is such a domain. One can understand most basic physics concepts quite easily but mathematics helps in explaining why this has to be so. Even the the special theory of relativity can be explained in layman’s terms, but it rarely is!
I intend on teaching my children mathematics at the same time as they learn to read and write. Hopefully being familiar with the “alphabet” of mathematics early on they won’t be scared off by them when it comes to sitting learning at school. Hopefully they will be as fluent in mathematics as in any other foreign language that I’ll be passing on to them.
Do I love maths now? Not really, I’m still scared off by differential equations and integrals, but I know where to go to help me solve them…
I mathematics important for a career in science or engineering?
I would have to say it is. But I’d qualify that by saying that practical mathematics is important. Theory for the sake of theory only serves to scare off people.
Just think of every day life and how mathematics can help you solve problems more easily.
Are you a Casino goer? Learn statistics! You’ll realise that the odds are in favour of the casino, not by a huge proportion but just enough to ensure that you’ll always loose more than they do. Roughly they are ahead by 1.5% in the odds. Some statistical analysis of the table you’re at might improve that to 1% in their favour. That small bias of odds towards the casino is what makes them rich and you poor. If you think you have a system that will break their bank: learn statistics and you’ll realise that overall you’ll only end-up loosing your hard earned money. All you can do is maximise the time it takes for you to run out of money…
Buying a house? Maths can help you compare the market. List the features you are looking for in a house (price, number of rooms, size, garden, local amenities etc…) and give them a relative value based on how important the particular item is on your “shopping” list. This multiple variable equation will describe your market and you’ll be able to compare houses more efficiently.
Want to invest your hard-earn cash. Mathematics will help you maximise your return on investment by comparing the various investment options available.
And there are many more applications of calculus to every day life.
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