Crossing the Bridge into University Mathematics
Even ten years afterwards, I still remember the uncertainty that shadowed me for a summer, as I was choosing my university course. It seemed that everyone else had been focused on their careers in Mesapotamian Anthropology or Veterinary Neuroscience since they were 5 years old, while I felt that anything in the STEM umbrella of subjects could be perfect if I devoted my attention to it. Maybe I should become a Computer Scientist? Or an Engineer?
My indecision wasn’t helped by my lack of understanding about how individual subjects changed once they reached university-level. I read the syllabuses for so many courses and they were full of terms that were still completely alien to my high-school brain. Maxwell’s equations? Manifolds? Surjections? Where were the familiar topics that I knew I enjoyed, like integration and projectiles?
So I took a moment to remember my experience with Mathematics until that point. When I was 10 years old and learned how to do long division, it was the most impressive and complicated Mathematics I had ever seen, and couldn’t imagine what they could possibly teach us in senior school that would be any harder! Of course, we soon learned algebra and trigonometry and a whole new world of Mathematics opened up for me, and I was glad to still be studying it. Later, when I felt that I’d discovered everything possible in Mathematics, my teacher gave me a worksheet on differentiation, and the world of calculus opened up to me, with the myriad possibilities it enables.
When I thought that probability might just simply descend into increasingly complicated coin-tossing scenarios, my textbook introduced distributions and hypothesis testing. No sooner had I grown tired of solving simultaneous equations, I discovered the power of matrices for the same task.
Reflecting on all of this, I realized that at every stage of my Mathematics education when I was losing faith in it, it had revealed to me even more valuable secrets than I could ever have imagined – and so decided to trust it again as my chosen career subject.
12 months later, I found myself at Cambridge University, sitting with 246 other fresh students as the next layers of Mathematics were slowly revealed to us. Simple calculation systems were extended into the concepts of groups and rings. Calculus gained new power tools in the form of differential equations to explain the movements of pendulums and freefalling objects.
Most notably, the focus changed to understanding WHY different parts of Mathematics worked the way they did. Do power series always work? Why does sin(x) differentiate to cos(x)? Why is differentiation the opposite of inegration anyway?
Mathematics all started in primary school when you learned WHAT the results of calculations should be. Later, you learn HOW to solve problems using the skills you learned earlier. At university, as well as seeing practical applications that can only be solved using more advanced tools, you learn to see WHY Mathematics works the way it does, so you can create your own tools independently and confidently.
The other good news – and this applies to most courses at University – is that as the subject gets more advanced it also gets more broad. During your first year at university you will have the opportunity to experience a wide selection of material, and will have the option later to choose your direction and journey through the remainder of your academic career.
So maybe you are unsure of what lies ahead when you begin your studies in Mathematics – just as I was ten years ago! But hopefully this article has given you some idea of the experience available to you, and some reassurance that if you’ve enjoyed Mathematics until this point, then it still has so much more to offer you.
Daniel Timms, BA in Mathematics, Churchill College, University of Cambridge