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Master of Science, novice of life | stolenclay's rambly and sporadic journal

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AngelWings:
Really interesting journal and read thus far, StolenClay! Glad to see another journal up and running.

zofromuxo:
Yay someone doing postgrad studies, I always enjoy reading these journals due to the research project and just the mindset of a master's student.
I'm also digging the polandball reference, I hope to see more them from you :)

stolenclay:
Keeping true to the promise of sporadic updates… Here we are! The teaching period for 2018 Semester 1 has just come to an end, and I finally have [a bit more] breathing space (cough cough although I should really be studying for my exams at the moment).

For actuarial students, the first semester of second year would be the opportunistic moment to decide whether you wish to continue with the pathway or not… if only you had actually done more than two actuarial studies subjects by this point. But you haven't! So you'll have to take it from me.

If you're in your third year of actuarial studies, then I'm sure you're shitting your pants right now for your exams (as has historically occurred for actuarial studies students at this point), but you're probably also not sure if you want to go through with this, even with the (potential) single semester left.

Reflections on actuarial studies II: disillusionment

Picking up where we left off: Last time, I ended with two quotes that I felt became increasingly accurate (in some ways) as I progressed throughout the degree.

First, let me describe some of the (mathematical) content that I had anticipated would be in the curriculum coming into the degree. In a more qualitative sense, I had expected to study probabilistic tools and models to quantify the unknown. With my knowledge now, I can put names to those areas: risk theory (no, not the Honours-level subject), extreme value theory, martingales, stochastic calculus… This is basically probability theory (and is what I eventually ended up studying in my Master of Science). With the overarching tone of this series of posts, you can probably tell that this is precisely what you don't study until very, very late, if at all. I had expected to study some beautiful underlying theory of stochastic processes, which, if you've done VCE, includes things like Markov chains but to a much higher level of complexity. This brings us to validating a part of our two reference quotes:


--- Quote from: darlok on June 16, 2010, 09:02:27 pm ---There is none of the beauty of math in these subjects, if you "love math" then you wouldn't disrespect it by even calling actuarial studies math.

--- End quote ---

Now, whether you believe the mathematics in actuarial studies is a misnomer is entirely your subjective opinion. As I said in the thread opener, society needs people to study applications of mathematics (and not just dwell on abstract theories which may not see the light of an engineer's/physicist's/computer scientist's day for a couple of centuries) whether you agree or not. However, any applied mathematician knows that, for applications of increasingly high complexity, you are going to struggle without knowing what your fellow pure mathematicians studied in bygone times. For example, any modern education in applied mathematics is probably sorely inadequate if there is no study of complex analysis anywhere.

Herein lies much of my gripe about the undergraduate actuarial studies curriculum. Again, let me stress that this is not the common opinion among the cohort, since unfortunately most do not feel as strongly as I do about what they study. Without diving into the specific topics that are studied, let me comment on the nature of these topics. In the vast majority of undergraduate actuarial studies subjects, you learn tools to perform computations: valuing annuities, solving equations of values, finding optimal portfolio composition, performing hypothesis tests, finding probabilities of survival, etc. Great! You are learning things.

The crucial problem is that none of these computations

* are done under conditions that emulate real-life conditions; or
* produce results that are of real-life significance;
Notice how both points mention "real-life": If you are studying mathematical content that is not beautiful abstract theory, then you had better hope that what you are studying is the prelude to something that you would actually need to use. There is technically more credit to the tools that are studied than is evident, but the ways in which these tools are applied are severely limited in the undergraduate actuarial studies curriculum. I will mention later the few points in the curriculum where there is merit to how the material has been covered. If you are studying mathematical content, but not studying abstract theory and also not studying tools that you would eventually use, you need to ask yourself, "Why?" If you do not ask yourself this, then you are missing out on demonstrating that one key ability that every employer and their cat seems to list for desired attributes in a graduate: critical thinking.

Here is a bit more of a perspective on the mathematical content in the undergraduate actuarial curriculum. When I was in my first and second year of the undergraduate program, I would occasionally attend some of the Actuarial Students' Society's networking events. Now, the only reason students attend these events is to find out more about the industry and possibly try their hands at that fabled opportunity of networking events whereby you connect with a firm representative on LinkedIn and obtain some know-how (or even fast-tracking) for their recruitment process. It is a bit cynical to boil it down to this, but I will be surprised if anyone goes for reasons beyond these. With an undying interest in doing maths for a job, I frequently asked the firm representatives at those events whether they did any maths at work. Stripping away the formalities and the pleasantries, it was clear that the answer was a resolute no. Of course, most professionals would embellish their answer by saying they occasionally needed to get some mental estimate of an annuity's value, but, if I were a working actuary and a student asked me this question at a networking event, it would just be a reminder of how little an idea students actually have of the career at that point.

Now, before I continue my seemingly brutal attack on the undergraduate actuarial curriculum at UoM, let me highlight some of its redeeming points:

* ACTL30006 Financial Mathematics III: Despite my own bitter adventure with this subject, I have to admit that you do actually have a chance of using most of the tools that are covered here if you work in portfolio management. This would really only be a small minority of actuaries, as these opportunities are mostly on the asset management side of the financial industry.
* ACTL30001 Actuarial Modelling I: Excellent subject with a fantastic perspective on the use of probabilistic models in life insurance (perhaps specific to the lecturer). This is the second closest that an actuarial studies subject comes to being a maths subject (since there is actually some proof in the subject), but the flavour is still more on the computational side. If you look closely you can see that the techniques here (particularly on survival analysis and Markov jump processes) have enormous potential of being used outside of the specific life insurance applications on which you are examined.
* ACTL30005 Models for Insurance and Finance: The closest an undergraduate actuarial studies subject will get to a maths subject. It took until the very last semester of the undergraduate curriculum to even get a whiff of some of the terms talked about in the Black–Scholes–Merton model (which is essentially staple for any study of derivatives pricing). There is generally an emphasis on developing some parts of probability theory and stochastic processes in preparation for the Honours-level subjects, because you finally get to model interesting things there. This is not a practical subject, but, akin to complex analysis, if you actually want to do interesting things with stochastic models, you will need this.
* ACTL30002 Actuarial Modelling II and ACTL30004 Actuarial Statistics: These two are really statistics subjects, so let's compare apples to apples here (i.e. compare them to the statistics subjects offered by the School of Mathematics and Statistics). What is sorely missing here is the theoretical foundation of linear models (no, second-year MAST20005 Statistics does not count), which the School of Mathematics and Statistics does extremely well with MAST30025 Linear Statistical Models. If you actually understand the statistical theory that is present in these two subjects, however, you will find uses for them outside the actuarial industry. As much as I hate the term "data scientist", I would say every "data scientist" should really at least be aware of the statistical knowledge present here. Of course, I am not willing to call you a scientist if you don't understand the material here.
* Professor Mark Joshi (RIP): One of the most valuable lecturers that the Centre has had and will ever have. He was the personification of what "critical thinking" should actually be and was a stark contrast to the somewhat hollow computations that were being studied. Obviously I am a fan of his; many students are not.
If you're careful you will note that I've actually named all of the third-year actuarial studies subjects here, except ACTL30003 Contingencies, and for good reason: I didn't actually do this subject. If what I heard from my peers is correct, this subject is by far the worst perpetrator of being computational and (mathematically) useless, and I'm fairly sure I dodged an enormous bullet by deciding that the undergraduate actuarial pathway was not for me before embarking on this subject.

As I'm writing, after listing the above merits of actuarial subjects, I really do wonder where things went wrong. As described above, there are actually lots of subjects with a high potential of being interesting (to the point of deserving the name "maths", as darlok puts it), but even among these, most fall somewhat short. Funnily enough, as unbearable as the nature of the curriculum may be, end-of-semester exam papers sometimes contained the highlight of the semester in the form of actually needing critical reasoning before being able to devise the necessary computation. Like a true masochist, I sometimes enjoyed the challenge of the exams far more than the material in the 12 weeks of the subject itself.

Okay, so we really have an important question to answer here: Why? Why do I feel so strongly about this? Why do these subjects fall short, even though they had potential? As I write this post, I seem to have quelled some of my own distaste for the curriculum, but there is still some regret left. I believe the rest of the explanation is more related to the second quote from darlok:


--- Quote from: darlok on June 17, 2010, 12:38:56 am ---Now what im saying is, that someone that decides to study actuarial puts 100% of the weight on 2. and 0% on 1.

--- End quote ---

I still am yet to comment on the accuracy of rumours of the dropout rate and job situation for graduates, but I think they will be more suited to the next post.

[To be continued in Reflections on actuarial studies III.]

stolenclay:
Reflections on actuarial studies III: wrap-up

I realised that I have too much to say about this topic. If you're a high school leaver contemplating studying actuarial studies at university, especially at UoM, please reach out by PM!

The several other points that I had hoped to cover were


* Some context on the process to becoming qualified as a professional actuary: In Australia you need to undertake three parts of assessment (Parts I, II, and III) in order to obtain Fellowship with the Actuaries Institute, which oversees the professional actuarial accreditation process in Australia. Once you obtain Fellowship, you are officially recognised (by the Institute, at least) as a professional actuary. Parts II and III are actually centred on business knowledge relevant to various business lines in which potential actuaries find themselves; in particular, the focus is not mathematics (and there is very little of it, anyway). The trend in Australia (at least for the past decade to 15 years) has been for aspiring actuaries to undertake Parts II and III after an undergraduate degree, either while working or during an Honours year or graduate course. Part I is usually taken as part of the undergraduate actuarial science degree; that is, the Institute has an agreement with most of the universities in Australia that completing certain sequences of subjects will allow students to become exempt from the Part I assessment.
* The Actuarial Studies major is recognised as a "mathematically-focussed business degree" by staff themselves (lifted verbatim from Mark Joshi's words in a video that used to be on the Faculty's YouTube channel). Importantly, it is not marketed as a maths degree even though it has such a reputation.
* The material in the curriculum answers "what" far more than it does "why". I am not even referring to economic questions like "How does the superannuation system need to evolve to keep up with the aging Australian demographic?" Rather, I'm referring to the trend (in the mathematical parts) of an emphasis on computational "rules" and not enough of inspecting the crucial assumptions under which those "rules" are valid or have been mathematically derived. In many cases, we almost get to studying some of the underlying theory and mechanics to answer "why", but alas there is always some sort of about-turn as we get close, presumably because it's not part of the professional actuarial requirements. This is why the actuarial studies major intrinsically fails to be a maths degree. You need the abstract theory.
* I believe there is a mismatch between the public perception of how much maths the major has, how much maths it actually has, and how much maths it needs to build the fundamental quantitative skills necessary to become a modern actuary in Australia. What is the role of the undergraduate curriculum for the actuarial profession? Is the current curriculum (at UoM) perhaps overly focussed on the technical side when there is so much else? I have heard that the Actuaries Institute is revising what they consider necessary as a technical foundation, so my opinions here may not be relevant in the future.
* Actuaries in Australia and actuaries in the UK and North America: The scene there is far more developed and the work is more diverse (as is usual for the financial industry) than it is in Australia. There is more "sexy" technical work that would be on offer in those countries in comparison to Australia.
I also had a few points to make about the culture.


* (Warning: Possibly sensitive point. Certainly my own subjective opinion at the least.) The common motivations for becoming an actuary seem to characterise a (subjectively) accurate stereotype of the actuarial studies student cohort. People are good at computing things, look upon the idea of needing to learn abstract (mathematical) theory as a burden or "something they will have to memorise for the exam", and prioritise obtaining exemption from as much of the professional actuarial assessment as well as securing internships (and whatever necessary extra-curricular activities and leadership positions) over actually learning much at all. People are risk averse (an Optiver recruiter actually told me that this was their impression of UoM actuarial studies students) and want to qualify for Fellowship to settle as soon as possible into the famed stage of low-stress work and unparalleled job security that qualified actuaries enjoy. This probably accounted for the rest of my disappointment in my undergraduate experience.
* I absolutely respect the professional body of actuaries in Australia. A lot of their work has great social significance, particularly for those working in superannuation and social welfare. If you look at the Actuaries Institute website, you will see that there are many professional actuaries who volunteer their time to develop and move forward the profession as a whole (look at their online magazine). There are various conferences held throughout the year and different committees and working groups that make it all possible. They also hold themselves to a high degree of accountability and professionalism (see this story from a retiring actuary for a short anecdote regarding highly respected actuary Greg Taylor). Sadly, I find it difficult to identify confidently any of my peers who would have this level of dedication.
* Relating to the point earlier about the technical foundation for an actuary, please take a look at this document which is a review of the ways in which the modern actuarial education in Australia may need to evolve. I haven't read it all, but there is a common theme that a focus on the business side of the profession is increasingly necessary. This means, relatively, less of a focus on the technical side (which I support).
Now to address two of the more common points of concern about the actuarial studies major.

Dropout rate

It is high for reasons that may surprise you (unless you've been reading this series of posts). In the second semester of my first year, there were about 170 people enrolled in the introductory subject ACTL10001 Introduction to Actuarial Studies. By the time we progressed to the second semester of my third year, enrolment numbers were in the 80s.

Contrary to popular belief, failing subjects (in the sense of scoring below 50 or failing hurdle requirements) is not the primary reason behind why people depart the major. Most leave simply because the material isn't that interesting. Some leave because the people aren't interesting. For example, if you want to become an investment banker or management consultant (both of which are business careers with a reputation for attracting extremely high achievers), there is little chance you'd appreciate the people or the curriculum.

Then there are those that leave because they fail to obtain the scores necessary to become exempt from Part I (but still pass the subject for the purpose of credit points) and then decide that it's not worth their time to go back and pursue exemption. In this case, there is probably a mix of the other aforementioned reasons at play also.

Bottom line: If you do find yourself needing to consider the exit option, chances are it would not purely be because you found the subjects too hard and are verging on scoring below 50 or failing hurdle requirements. Rather, it would more likely be that you've identified something else as more worthwhile to study at university.

Graduate job situation

If you are a high school leaver, it is going to take you some years to grasp the following sentiment. I believe the situation will persist for at least a few years (3+ maybe); however, feel free to message me if/when it changes.

As much as you may read that there is good job security for actuaries, this only applies for qualified actuaries, i.e. those who have passed all their professional assessment. The situation for new graduates is tougher (and tougher still for internships). If you are thinking of entry-level roles in traditional actuarial lines such as life insurance, general insurance, and superannuation that are in Melbourne and which actually stipulate the need for an actuarial degree, the vacancies are hopelessly low in comparison to the number of fresh graduates.

This page lists many of the actuarial consulting firms in Victoria. This page lists many of the insurers in Australia (but most would have headquarters in Sydney).

In a good year, there might be about 10 firms in Victoria that would actively seek and take on actuarial graduates, assuming they haven't extended graduate offers to past interns (which is extremely common). Most firms would only be looking to take on one graduate in any year. Keep in mind I am referring specifically to roles that require/respect actuarial qualification progress and actually have a preference for those with an actuarial science degree over those who don't. For internship programs, the situation is even tougher: You can probably count on one hand the number of internship opportunities (that specifically require actuarial knowledge) in Melbourne in any given year.

If you've never experienced the trials and tribulations of a internship or graduate program application season (i.e. never been rejected), you may think that, since an actuarial studies degree is renowned to be so hard, your university grades must be the major decider between who gets an offer and who doesn't. This is completely false; the major decider is by far your critical thinking skills, how you communicate ideas in a corporate, team setting, and how well you fit the culture of the specific firm. I would say that the job situation for actuarial graduates is heavily tipped in your favour if you are a strong public speaker with decent grades (say, 70+ average at UoM).

As it turns out, at UoM there is usually a handful of people who have decent soft skills and rather good grades (say, 80+ average at UoM), and the internship/graduate offers usually gravitate towards them. For internships specifically, some will even do multiple in a given summer. Also, as much as you may want to, don't forget that Monash also offers an undergraduate actuarial science degree.

As such, you can probably see why it is that many actuarial graduates don't actually end up in a role which supports and develops them in pursuing the Fellowship qualification. That is, many graduates who persevere all the way through the three-year undergraduate curriculum do not become actuaries. Instead, many will end up in the financial services industry somewhere or in the public sector, and the technical skills they learned from their bygone actuarial degree mostly rust away. As is the trend now, many will try to pursue some career in data analytics. In any case, your actuarial education is no longer as valuable and the pool of applicants for those positions is undoubtedly a magnitude larger. If you do end up securing a graduate position at all, it is likely that the only things you will actively need from your degree are the Excel skills and possibly the statistical knowledge (in particular, the terminology and the statistical computing skills).

There is also the possibility of further study. I have seen some peers continue at UoM for an Honours year or the Master of Commerce (Actuarial Science) degree, which gives them extra shots at graduate applications as well as the chance to obtain exemption from Part II assessment. I have also seen a couple continue with Master of Finance or Master of Business Analytics degrees at UoM. Of course, no one is crazy enough to convert to maths…

[This brings us to the end of the Reflections on actuarial studies series. If you have any further questions, please feel free to PM!]

stolenclay:
Hardly a master I: What is maths?

Baby don't hurt me
Don't hurt me
No more

For many people, perhaps the answer is something I want to stay away from. Of course, I can't invalidate opinions, and, realistically speaking, maths is something people can manage to avoid for most of their lives after finishing their high school education.

For the scientifically-minded, maths is about understanding the world, just like any field of science is. For the layman, maths is an extreme form of risk management — it tells us how things [are expected to] behave or not behave, without needing constant testing, monitoring, or scrutiny. For this reason, maths is about models or theorems (which may mean the same thing to you).

Spend enough time studying/on the internet/"both", and you will eventually run into this comic:

Okay, not trying to stroke my own ego here, but, going from right to left, the fields appearing in the comic are bound to feel more and more accessible, in the sense that you probably have a better and better idea of what the field is about (perhaps insert economics and finance on the very left and overlay engineering over the middle or something). You may have heard maths enthusiasts yell out maths is all around us as they desperately try to convince you that their field of interest is a serious academic area as well as the source of various party tricks, the latter of which is more likely to make an impression.

In recent [Australian] times, we have seen some blips of maths appearing on the media radar. Issues like falling STEM standards, shortage of STEM teachers, gender representation in STEM, as well as the superstar teacher Eddie Woo… Unfortunately maths still needs a far better [long-term] marketing department until the situation in Australia will improve.

For now, let's hope you're convinced that maths is something useful, despite it having been processed by developments in all the other fields appearing in the comic above before actually reaching you.

...what is the point of this post?

Well, lest something terrible happen, I will be graduating from my masters degree in maths at the University of Melbourne at the end of this year. The last 4 semesters have been more or less ferociously intense, so it would be good to reflect somewhat (yes, again, instead of studying for my exams, as usual).

I hope to spend some posts introducing what studying maths as a university major/degree is like [in Australia/Melbourne] as well as various related issues, e.g. a sustainable student mindset and career prospects. I'm also fairly sure that I'll expose along the way some of my own opinions on the state of maths/science in Australia (spoiler: mostly negative). Please remain sceptical of them when they appear.

Why maths?

Let's say you have just finished high school somewhere in Australia or are in the early years of your undergraduate degree. I would say there are two reasons why you should choose maths for a university major/degree in Australia:


* You enjoy maths. This is a no-brainer. As is the case for many (but not all) fields of tertiary study, dedicating yourself to something that you don't particularly enjoy is usually a recipe for mediocrity or, even worse, disaster. For doing maths as a major/degree, I would say disaster is imminent if you don't enjoy maths. Most importantly, your idea of what maths is will change as you do more maths at university, and if at any point you no longer enjoy it then you should seriously reconsider.
* You are in it for the long haul. You believe in lifelong learning. Most importantly, you have the resources to sustain an education in maths (money, time, dedication). This is a bit of a strange reason, but not as important as the previous one.
Now, some serious qualification of these two reasons needs to happen, because different people will have their own interpretations, and unfortunately some of those may be slightly misleading. Let's debunk some myths (I'm sure that there may be some ATAR Notes post doing roughly the same thing already… but I didn't search hard enough). Just to be on the safe side, each point will start off with the [more] appropriate view rather than the statement of the myth.

Not just about using formulaeMaths is not just about using formulae, which may be hard to believe if you've just come out of the Australian high school education. An even more appropriate statement would be that maths is about the journey that people took to come up with those formulae. Equally, this means that maths is absolutely not meant to be some mechanical procedure of doing calculations — at university, either the calculation is done by computers or the calculation is in fact not very mechanical at all. This leads me to say that the flavour of maths at university is very different from what it is at Australian high schools.

Different approach to mastery at university compared to at high schoolYour maths grades in high school aren't great predictors of how well you may do in maths at university. This is naturally a hard pill to swallow, but the reasoning is similar to the point above. At least from a Victorian point of view, past a certain point of understanding, extreme peak performance in maths at high school revolves around completing ludicrous amounts of practice questions to achieve a desirable speed as well as knowing some small library of shortcuts.

Now I can't make blanket statements about all the maths subjects at Australian universities, since I only studied at UoM and even then only around a third of the maths subjects on offer, but generally peak performance in maths at university is about attaining a level of intuition about the material to a point where you almost couldn't explain your own perspective to someone else if you tried.

Okay, but then do you really understand it? This sort of response annoys me to no end. Think about someone who's just finished a painting. They start trying to explain to you the different choices of texture and technique used in different parts. You don't understand. Okay, so they didn't explain very well. Sure. Are you going to claim they don't understand the structure of their own painting? On a side note, this is also roughly why great mathematical thinkers don't necessarily make great teachers.

The crucial point is that doing well in maths at university is about letting the ideas you've come across incubate in your head for so damn long that the mechanics behind them start to feel second-nature. In this sense, the flavour of maths at university is more creative than it is mechanical.

Lack of jobs needing the precise technical skillsVery few office jobs use the maths taught at universities, especially in Australia. This is related to the second reason behind why you should study maths and is somewhat of a lesson I learned the hard way. If you believe that you will sit down at a desk at your office job and start using and analysing complicated mathematical models that you saw at university then I have some bad news for you... These office jobs exist but are few and far between, and, more often than not, will require extensive academic research experience (read: PhD or higher).

Using complicated mathematical models would be far more likely in a research lab (but probably not a lab for maths research since Australia doesn't have those). If you are using and analysing models (not just running empirical tests but actually developing theoretical results) then I daresay you must be part of some maths faculty somewhere.

As a result, if you're not aiming to become an academic, you need to have a strong sense of career direction, because it's unlikely that the precise technical skills you gain doing maths for a major/degree will lead you anywhere obvious for an office job. University marketing departments may try to convince you otherwise by giving you cherry-picked fairytale examples, but, compared to the number of obvious career options for, say, accounting graduates, there is almost nothing out there specifically for maths graduates in Australia that makes use of the technical expertise.

What about statistics? Well... there are certainly jobs out there where you'd be handling data, but the technical side, which may not be present in a lot of the work, would mostly be limited to statistical computing. Whether you would call this a use of the maths taught at universities is an individual judgment call.

My personal view is that [in-house] software development often provides similar challenges to those in maths, in the sense that you really need a holistic understanding of the underlying systems (which includes, in software development, the programming language syntax) in order to produce an efficient solution. However, I have limited experience with software development, and I would not be surprised if frontend development was totally void of what I'm thinking of.

Even if you are not aiming for pure software development as a career option, programming skills are undoubtedly one of the most useful skills that a technically-minded graduate could have. In the off chance that you're offered a job that deals with mathematical models, you would definitely need to be familiar with programming.

Words are used in mathematical workWhen you complete assignment work for maths subjects at university, you are going to need to use words to explain the thought process and reasoning throughout. Well, technically this should already be happening at the high-school level, but it is far easier there to get away with wordless responses. This is especially important when you are writing a mathematical proof, which you will familiarise yourself with as you study more maths subjects. Mathematical proof is the core format of communication in formal mathematical work, and every step in a proof needs to be sufficiently well reasoned. In particular, it's pretty much impossible for a mathematical proof to have no words.

There are different types of mathsAt the high-school level, there is more or less a single sequence of maths subjects. At any given school, everyone does the same sequence, and some take it further than others. (Okay, not strictly accurate, even for VCE…)

At university, a similar thing happens for the first year. Maths subjects in the first year set you up with the foundational knowledge that every single field of maths eventually uses, and after the first year you begin to choose subjects from different areas of maths. In high-school level maths subjects, there would probably have been different topics in the syllabus. At university, some of these topics will constitute entire subjects themselves (and possibly more than one).

It is pretty much impossible to study all the maths subjects at, say, any Go8 university in Australia, simply because you have a limit on how many [maths] subjects you are allowed to take for a bachelors degree. Most students in a maths major/degree usually take all the maths subjects offered in one or two fields.

In the same vein, at university, there is usually no concept of "good at maths", simply because you don't get to find out how good you are at all the different maths areas. The reality is that you will have an affinity for some areas and be weaker at others. You may even find inconsistency between how well you understand different subtopics within the same subject.

An appropriate mindset

I will finish off this post with some thoughts on what a suitable mindset to approaching maths at university is like. This will be more philosophical and perhaps somewhat more generally related to studying any field of science at university. Most of these are views I've developed from my own experience as a maths student so far as well as from seeing the journeys of my peers.

Let's not sweep it under the rug: maths is hard. Maths is not something that you ever finish learning, and the hot milestones that appear in international media or cool applications that you've heard of in computer science or engineering can sometimes be the culmination of decades of collaborative research.

Learning maths (and doing research in maths) takes immense patience and has many ups and downs. If you are only motivated to learn maths by the prospect of being able to discover cool things (in the sense of a research discovery) then, at the risk of sounding a bit cruel, unless you mean cool things in a decade or two, I would say your view is a bit short-sighted. Throughout my high school education, my bachelors degree, and now my masters degree, I have seen my peers' interest in maths wax and wane. I would say my UoM classmates whose interest in maths has been sustained until the end of a masters degree have been those who've maintained a deep respect for understanding the mechanics in maths, sometimes in how it's applied to other fields, but mostly in an intrinsic sense.

This brings me to the issue of maths haters (bit of a hyperbole; read on). No, I don't mean the people who have hated maths since high school and never studied it at university. I mean the university students in a maths major/degree who vehemently avoid the maths outside of their own area of study or, worse, even treat with disdain the people studying those areas.

This concept was first planted in my head during an orientation session held at the beginning of my current masters degree. A professor gave an analogy with coffee. (Forgive me if what follows makes no sense; I don't drink coffee.) The professor said that most self-proclaimed coffee enthusiasts probably have in their mind very specific ways in which the coffee they consume is to be made, probably due to certain preferences in where the beans are sourced or other things like timing, milk, temperature, and whatever else that might affect the taste or texture. What ends up happening is that, for these self-proclaimed coffee enthusiasts, there exist far more ways in which they would hate a coffee than ways in which they would like one. So then… "coffee haters" doesn't sound so far off? (Forgive the specific example of coffee; I'm sure the same could apply to other hobbies or indulgences.)

Applying the same reasoning to studying maths, it would seem sensible that anyone seriously involved in studying maths should reconsider how serious they are exactly if they seem to close themselves off (either in fear or in contempt) from areas of maths outside their own focus. Whether an area of maths is applied, theoretical, old, new, rigorous, heuristic, the theme of Fields medal research, or secretly the mechanics behind party tricks, there will always be valuable insight within and researchers with an advanced understanding. It is important to remain observant and respectful of all areas of mathematics. Maths has the privilege of being a science which can avoid almost all the political roadblocks prohibiting progress in other sciences — it would be counterproductive to introduce any friction into the scene ourselves.

[Well, okay, that was characteristically rambly. To be continued in Hardly a master II.]

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