Hello, my name is Jeremy
I am new to the MAM1000W team of tutors – if you want to read more about my background you can take a look at my bio in the MAM1000W document on Vula. In short, I returned to UCT last year to do my second undergraduate degree, a BSc in Applied Maths and Computer Science, at 25 years old, after not doing any maths for seven years. In the beginning, I found MAM1000W really hard; the pace of the content and the tutorials made me anxious and when test one came around I scored 50%. More anxiety. Luckily I have a great support system (inside and outside the Math department) and with some good advice and determination, I was able to figure out a new, way of studying and managing my time that worked better for me. When it came time for test 2, despite being super stressed out, I scored 81%. A huge relief! With some small changes, I had completely shifted my academic trajectory – and the good marks kept rolling in, for just about all my subjects. So, I want to share some lessons from my experience with you, especially if you are feeling a bit anxious or if you have not done so well in the past tests. Hopefully, I will be able to give you some perspective as well as some practical tips for success in this course, and in all your other courses, too. Here goes –
[Part 1: Why Math?]
“Why are you studying Maths?”. This is the most important question you (and I) need to answer if you want to do well. If your answer is ‘I just want to pass’, then I think you are at risk of missing out on the value that studying mathematics can add to your ability to think, to solve problems; to your future career and to your life. It also means you will probably not enjoy the course or the work, and life is to short to do things you don’t enjoy doing. If you want to do well, you need motivation, and in order to stay motivated, you need to have a good reason.
You need to have your own ‘why’.
This is true for Mathematics, but it is true for everything you decide to pursue in your life. The difference is that the benefit of some skills is much more immediately apparent than others. For example, the benefit of studying law so that you can practice as a lawyer is fairly obvious (the same goes for medicine and doctors). But what about Mathematics? Most people who study math-heavy degrees don’t want to become researchers. And you will almost certainly never have to do an integral or a derivative by hand in any other industry profession (we have computers for that now). So, it’s no surprise that one of the most common questions you hear from high-school students who are made to do math is; “What’s the point?”. Fair question, and it’s not obvious why or how the skills you learn in MAM1000W are beneficial to you in the real world. Having worked out in the real world for some time before coming back to university, one thing which surprised me most about the types of careers people end up in after university in this modern time: most people never end up doing exactly what they studied to do. People in our generation typically change careers multiple times before settling on something (https://www.linkedin.com/pulse/millennials-job-hop-more-than-previous-generations-guy-berger-ph-d-).
So, what are you studying for if not to go into a specific job and stay there your whole life? The broad answer: to learn how to solve problems. In every single company, in every single industry in every country in the world, the most valuable and the most successful are the people who are best at solving problems. There are many books, articles and studies you can read on this topic, but one thing that I promise you is true is this: people who are excellent at solving mathematical problems have developed an area of their brain which makes them very good at solving other problems too, particularly problems they have often never encountered before. This skill is commonly referred to as abstract thinking, loosely defined as the ability to think and reason about things which do not have an obvious physical representation (for example, the idea of a limit, 4-dimensional space, or the notion of probability). The world is full of abstract problems, which require abstract thinkers to solve them. And the people who are best at this, 9 times out of 10, are people who have a background in mathematics.
Two surprising examples of this are:
- Engineers make great CEOs: https://www.linkedin.com/pulse/20141027165614-47746721-3-reasons-why-engineers-make-the-best-ceos.
According to recent research, of the top 100 companies globally, 24 of them have engineering degrees. Why? They are logical, systemic problem solvers able to think abstractly about problems. Whether a business problem, a financial problem, a systems or logistics problem makes no difference – engineers make the best problem solvers, and engineering is a discipline underpinned by mathematical principles (especially calculus).
- Hedge Funds and Investment Banks seek out physics graduates: https://www.cityjobs.com/cityblog/2015/05/06/banks-physics-maths-grads/.
“Peter Harrison, a former Goldman Sachs executive and founder of banking recruitment adviser Harrison Careers, said that for many City jobs these days, if you don’t have a physics or maths degree ‘you’re not going to get hired’.“
Physicists are excellent at mathematical modeling and (you guessed it) solving abstract problems related to the financial markets. And classical physics, like engineering, is founded firmly in mathematics (again, especially calculus).
These are just two very practical examples, but the general message (here and in many other industries) is the same: math-heavy graduates make good problem solvers, and every company has hard problems that need solving.
If you are yet to be convinced that Mathematics is worthwhile, it is definitely something you should spend time thinking about. Maybe talk to a lecturer who has worked in industry or do some research of your own. If you feel like you have a good reason for taking this course (a ‘why’), then you will find the motivation you need when you become tired or frustrated with the work. This was my first step to succeeding – it is the whole reason I came back to study.
So, now that you have a ‘why’, the next question is; ‘how?’
[Part 2: How do I win?]
So, once you have your ‘why’, you have your motivation. Once you have your motivation, the recipe for success in this course is fairly simple (not necessarily easy, but simple):
- Attend lectures: there’s no substitute for being in the lecture every day, being able to hear clearly and ask your own questions. If you don’t feel like you can ask questions at the time, write them down and take them to a tutor or mail the lecturer.
- Never move on from a concept without understanding it: I know you will never – realistically – be able to read notes before every lecture (even though you are encouraged to do so), sometimes there is just not enough time. But, if you do not have a firm understanding of a topic after the lecture, you must go and read up on it yourself – if you move on from a section without understanding it – you will struggle with the next section and so on – a cascading problem. Start with the Stewart textbook, and then search YouTube or Khan Academy for visual explanations which will help with intuition. If you still don’t understand, ask for help; mail your lecturer, come to the MLC (every weekday at 1 pm and 4 pm) and ask a tutor, ask older students or friends. There is tons of help available to you – and everyone wants you to do well.
- Attempt every question in the tutorial: This is your single most important task (it guarantees point 2). If you never leave a tutorial unfinished, you are guaranteed to pass and you will probably do really, really well. You will probably not be able to solve every question, but *you must attempt every question*. If you come across a question you can’t solve, make a note of it and move on, come back to it later (even the next day after some sleep). If you still can’t do it, (again) ask for help! Then, when you get the answer – even if you only see it in the tutorial solutions – make sure you do not move on unless you understand it.
- Less note-making, more understanding: A big mistake I made in preparing for the first test was that I essentially re-wrote my own version of the lectures notes for two days, doing very few practical examples. You should make sure you only have notes on the essential things you need to memorise (e.g. a list of derivative identities, the essential formulae that would take too long to work out in the test). Other than that, most of your time preparing for tests should be focused on understanding concepts and applying them to tutorial problems. The more you understand, the less you will need to memorise, and the more comfortable you will be when confronted with problems you have never seen before.
- Write down every proof: This is the first thing I do before every test. Get a list of the proofs you need to learn, write down the statement, then the proof. As you are writing it, make sure you understand what each line means. Once you have written all the proofs down, staple them together and carry the booklet around with you. Read through them when you have a spare moment, and try to prove them scrap paper and in your head. Most students will only read the proofs before a test, and end up losing incredibly easy marks because they are too lazy to put in a little extra work.
- Do past papers: Tests are stressful. Doing past papers will prepare your brain for the format (usually, the structure of each test will be similar to that of the past tests), and you will have one less thing to worry about on the day. Find somewhere quiet where you can focus, put your books away, time yourself and attempt a past test. Keep track of what you didn’t know, review the concepts and try again with another test. Do this as many times as you can.
- Make the most of your time: If you are motivated and focused you will be able to find gaps and spaces to work on math problems during your day – before you leave for varsity, in between lectures, on the bus, just before you go to bed. Get creative; keep the problems in your mind during the day and you will become better at solving them faster, with more confidence. Math is not confined to a desk. (Also, work consistently, don’t cram or overload by trying to do maths for 5 hours without a break. Your brain works best in 45 minutes bursts.)
- Take care of yourself: The importance of this cannot be overstated. If you do not manage your physical and mental health, you will find points 1-7 to be too hard to manage consistently and effectively (especially along with all your other courses). Here are some essential rules for maintaining your health and keeping anxiety and stress at bay:
- Exercise – every day or as often as you can manage: Whenever I feel overwhelmed or I hit a wall and I feel like I cannot solve a problem or understand a concept – I put my pen down, put on my running shoes and go for a jog. You will increase blood flow to your brain and the rest of your body, you will generate endorphins making you less anxious and clearing your head of negative thoughts, allowing your sub-conscious brain to focus on the problem, instead of spending your energy on stress. As soon as you get frustrated or over-tired, it is often better to stop and recover, and exercise is the best medicine.
- Sleep (at least 8 hours per night): Nothing, I repeat, nothing is a substitute for good sleep. Especially the night before a test. There is nothing romantic about staying up until 3 am cramming – your brain will literally stop working properly if you are over-tired, you will become anxious and you will make stupid, elementary mistakes (adding, multiplying, division etc.). Good sleep decreases anxiety and improves your average cognitive performance in the short and long term. (Also, exercise helps with good sleep).
- Drink water – all day, every day: If you have not got a water bottle, get one and carry it around with you. Your body is more than 80% water, you cannot function or maintain a healthy state of mind if you are dehydrated. You should be aiming to drink about 8 glasses each day.
One last bit of general advice I would give would be this; be aware of what you are spending your time and energy thinking about. If you are a person experiences anxiety or high levels of stress; Instead of spending time worrying about the course or the test, about passing or failing. Rather, shift your focus and energy toward solving specific problems. If you dedicate more of your energy toward solving problems, you will find tests become just another few problems you need to solve, and all your worries about passing will take care of themselves. And you may even do better than you expect.
Finally, remember to always ask for help if you are feeling unsure. It’s very likely that if you had a problem, someone has had it before, and we can help you solve it. We want you to do well!