This is a continuation of the previous post, essentially collecting thoughts for first year students. I am asking you, the reader to suggest what might be wrong, or missing from this, and anything else which will be helpful for a new first year who is just arriving at university to study maths…

The second part of the resource book is a “Meet the team” section, which includes photos and a short bio of the convenor (me), the lecturers, and the senior tutors for the course.

The next section is entitled “Why study mathematics”, and is in some ways the most controversial/important section in here.

For quite a few of you, the immediate answer you may have thought of to this question is not one that will make you happy, but I hope that this section will give you reasons to feel really positive about taking this course.

For some of you, the reason to study maths is because you have to study it as a prerequisite for your course. This is especially true for Actuarial Science students. It’s necessary to take MAM1000W and then MAM2000W in order to complete your degrees. There will be a lot of material in the course which you won’t see ever being applied within the actuarial science part of your studies, and this can be frustrating! This section is partly for you to see that despite it not being obviously relevant for becoming a good actuary, actually the skills it gives you are vital, although how that happens is not necessarily obvious.

It gives you a new perspective on the worldWe look around us at the world and by our very nature we try and understand it. In the past we wanted to understand the seasons, and the weather, the constellations and the way different crops grow, the flow of the river and the way fire burns. As we built up our understanding of our environment more and more we found that we got to the point where a pure description wasn’t enough. If we really want control over the world around us we need to understand it quantitatively not just qualitatively.

We discovered that mathematics was the right language to have a perfect description of the world where every detail can be captured. Of course, depending on the system you are dealing with, this is not necessarily easy, nor practical, but it turns out that the tools that we can develop through mathematics give us an amazing perspective on why the world works the way it does. If you want to understand why a population of rabbits and foxes changes over time as it does, write down the Lotka-Volterra equations and study them. If you want to know why a neuron in the brain fires off at one moment to lead to an avalanche of thoughts, then write down the Hodgkin-Huxley equations and solve them. If you want to know why the light from a distant galaxy is bent around another galaxy then write down Einstein’s equations for General Relativity and you will see why.

Mathematics is the best way we have of understanding the world in detail, and in theory everything can be understood through mathematics. It is a language, a tool for describing the whole Universe! What is amazing about it is that there are many areas of mathematics that we still haven’t discovered quite what it is in the universe that they describe, but over time we do understand more and more about how the most abstract areas of maths can be used for our advantage. Who, 100 years ago, would have guessed that prime numbers would be the most important element of all cryptographic systems today?

Learning mathematics gives you a new perspective on how to understand the world. This, for me, is one of the most important reasons there can be to study mathematics!

It’s a gym for the brainTo keep the body running well throughout our lives we have to move it. The more we move it and push it, the more situations we will find we can tackle which would otherwise be impossible. If you have to pick up a heavy weight, then it’s pretty easy to hurt yourself if you haven’t spent some time training your back, and your legs. If you need to run for class, then unless you’ve done some running before, you’re going to arrive in class with your heart pounding and your chest in pain.

The brain is just like another muscle. You have to use it in order for your ways of thinking to become more flexible. The harder you push it, the better you will get at being able to tackle new problems. Mathematics is a skill unlike almost any other in terms of the abstract thinking necessary to succeed in it, but as you practice more and more, you will become more comfortable each time you come across a new problem. In the same way that if you don’t push your body then you will never see it change, you need to push your brain into places which you might not find very comfortable at first in order to really build those thinking skills.

Coming across a problem which you don’t know how to solve is like picking up the next heavy weight which up until now you haven’t been able to lift. Spend time with it, and after a while you will be able to do it. In fact, after a while you will forget that you ever found it difficult! This is the most wonderful feeling, I can promise you!

Studying maths doesn’t just make you get better at maths, it will make you be able to think faster and more dynamically about everything! You will have trained your brain to see the world from so many different directions that you will have a huge advantage over anyone who has not had the luck to learn mathematics. Take advantage of this time, practice, make your brain sweat a little, learn to love that feeling of breaking through a problem, or even of being stuck on a problem and you will gain a skill which will stay with you for the rest of your life!

Maths is all around you!Maths is in the media, it’s in technology, it’s in the infrastructure of society, it’s in your phone, and it’s in your clothes, it’s in your food and it’s in your household products, it’s in every flower and every cloud you see around you. Learning to untangle the mathematical descriptions of these things gives you a way to both build a better world, but also simply to be more comfortable in the world that you live in. It can be as simple as understanding how the statistics in a medical study have been used correctly, or incorrectly in the media, to working out a new way to describe some system in society, from poverty to education to energy to transport, to cracking the stock market.

Take home points

- From this course you will gain a new understanding of the way the world works.
- You will train your mind to work in ways it has never been worked before.
- This will give you an amazing advantage in the workplace, not because you know how to integrate a particular function, but because you have confidence in tackling complex, abstract problems.
- Understanding mathematics gives you tools to navigate the world, both in terms of the media, and in terms of molding the environment as you would like to see it.

Aidan HornJanuary 26, 2016 at 6:46 pmThis is a difficult question to answer, but I think you have done it well. Reading Hardy’s ‘A Mathematician’s Apology’ gave me the sense that one argument for studying mathematics is that is does not harm anybody in the same way that other sciences have the capacity to do. I think the ‘take home’ points should be a bit shorter for this section. I think you shouldn’t introduce a new example when you say that maths gives one an advantage in the workplace. I think it is good to keep the conclusion short.

Jonathan ShockJanuary 27, 2016 at 9:22 amGreat, I’ve altered the take home points. Good idea.

J

LilithaJanuary 27, 2016 at 2:20 pmGreat post. I think you should include the main reason we study Pure Mathematics which is the elegance and beauty. It is the highest level of knowledge we can possibly wish to have. A theory can be falsified as more experiments are conducted but a theorem is eternal.

Jonathan ShockJanuary 27, 2016 at 7:09 pmI agree that it is enormously beautiful, and I try to instill in all students a bit of that sense of beauty. I think though that for anyone who doesn’t appreciate the beauty (which is something that takes some time to truly understand), it is more important to understand the short-term utility of taking a first year maths course. I will try and integrate your wise words into the document though

UCT MAM1000 lecture notes subject links – MathemafricaJanuary 17, 2018 at 9:33 am[…] Why study mathematics? […]