Studies

Revision and Relaxing

When the revision period starts, this is an opportunity for me to test my knowledge on everything I have learnt, and identify any gaps in my current understanding. In the past I may have dreaded the revision period due to the natural stresses that exams can cause, but now I am more relaxed which mainly comes down to giving myself regular breaks when revising and rewarding myself daily for hard work. A typical revision day for me involves treating my day as if I am going to university. I start revising around 9am until 6pm, taking regular breaks when needed. I first start with the most difficult module, as I feel mentally fresh at the start of the day, and continue with other modules later. In general, I find studying 2 modules a day to be optimum for myself although other people may find this to be different.

Image 1: This is an example of a study area at QMUL which gives a more relaxed environment for studying.

Image 1: This is an example of one of many study areas at QMUL which I use to study.

Once I have finished revising for the day, I always make sure to reward myself. Psychologically, this makes me feel much better about revising because I always know I will have time for myself if I work hard. Therefore, I am more likely to be focused entirely on revision when studying, and completely switch off from studying mode when having fun. Another reason why I always reward myself is that this gives my mind a chance to relax. I like to think of my mind as a funnel which I fill with information, but there is only so much information I can absorb and process. In this case, feeling overwhelmed would be equivalent to the funnel overflowing, while having time to relax would be the funnel emptying so that next time I am ready to absorb new information. If I could share my top 3 tips when it comes to revising I would say the following:
1) Always try to make your study notes easily accessible
2) Always try to keep your study area tidy – Think “Clear desk, clear mind”
3) As long as you tried your best there is nothing more you can do when it comes to revising.

Image 1: Don't forget to relax as well !

Image 2: Don’t forget to relax!

Revision is meant to challenge you and ensure you are well prepared for an exam. It is also completely normal to feel stressed at times.  Why not try rewarding yourself more next time? You may even be surprised to find you actually study better and more efficiently as well. Evidence has actually shown that having time for yourself especially when revising, could increase your ability to retain information!

Caffeine, Confidence and Careless Planning: A Personal Guide to Revision

Advice on how to get the most out of your revision, from information on visual aids to what foods you should be eating, is available everywhere.   As someone who is prone to stress, I often feel overwhelmed with everything that I am told I “should” be doing whilst revising.  After years of trial and error, I have found a few things that really work for me:

1.       Mathematics can be intense and overwhelming so I find it incredibly useful to take a few hours to remind myself why I’m doing the degree.  If I’m finding a module particularly wearing I’ll find an article, book or video loosely based on the subject to spark my interest again.  For example, after reading through my probability notes for a few hours yesterday and very almost losing the will to live, I decided to watch a video by Vsauce about the maths behind shuffling a deck of cards (which, by the way, is mind blowing).

2.       Finding a suitable place to revise was actually a bit issue for me.  At home I get too easily distracted but I can’t deal with the silence in the library.  Coffee shops were my saviour.   When I’m struggling to revise, I walk to a local coffee shop, order myself a drink and set out all my revision on a little table.  I enjoy working within a lightly bustling area; I can concentrate well but also when I need a break I can get some fresh air and take a stroll.  Obviously, the big upside to working in a café is the possibility of a constant supply of caffeine which is extremely alluring. 

3.       One major issue I used to have whilst studying for exams was confidence.  I would always compare my work and results to my friends’ and subsequently be far too hard on myself.  During exam season, I find it useful to remember that people work at different paces and revise in diverse ways.  It is for this reason I tend to steer clear of ‘group revision’ as I know I am more comfortable going through things at my own speed.

4.       Finally, I find it most useful to be ridiculously organised during exam season.  Revision timetables are my strength, however I must remind myself to be realistic.  If I had followed the first timetable I had made for myself this year I’d be clocking a solid ten hours of revision a day, and subsequently, probably would have died after about a week.  Setting myself unattainable goals is a bad habit; I am never going to be doing ten hours a day and that is completely fine.  I find it important to set myself reachable goals at the end of each week and if I was unable to finish everything one week I go back and assess what the issues are. 

There is roughly twenty-two days, one hour and 35 minutes until my first exam.  I am soon to be completely submerged in scrap notes, past papers and post-it notes.  My hands are decorated with black ink smudges.  I am simultaneously completely exhausted and also experiencing a caffeine-induced spark of motivation.  My brain seems to be completely incapable of completing any tasks that aren’t maths related; for instance, after making a cup of tea, I proceeded to put the milk in the cupboard, tea bags in the fridge and spoon in the bin. 

Revision sucks.  There is no point in sugar coating it.  However now that I have found my own little preferences, it sucks just a little bit less.

A Delicious Slice of Pie. Wait – I Meant π!

Happy belated π day! To start up, here are some amazing facts about and around π that you definitely need to know RIGHT NOW:

  • Chinese man Chao Lu memorised 67,890 digits of π in 2005. Seems like somebody’s got so much time in life!
  • Calculating π is used as a stress test in computers – I’d say it’s a stress test for all beings in the world don’t you agree with me?
  • “Wolf in the Fold”, the Star Trek episode, Spock spoils the evil computer by commanding it to, compute the last digit of π value. The geekiest way to defeat a bot.
  • π is defined as the ratio between a circle’s circumference and its diameter.
  • You can type π (like me!) in a Macintosh simply by pressing the alt button simultaneously (yes, simultaneously because…maths.) with p. Now let the πππππ roll in!
  • π is considered to be the most significant and intriguing constant, as mentioned by numerous scholars.

However, why do we even care about the existence of pi, then? In simple words, not everything in this world, both stationary or moving, are geometrically straight. Any form of curvature, to be measured more accurately, needs this irrational number π. Even if we are unable to get the true value of anything that is related to π as it is an irrational number, we are able to get the closest value and calculation of things almost perfectly despite this inexact constant.

I personally found Archimedes’ way of calculating π as the most interesting of them all as it invokes to me so many thoughts. He calculated π but drawing a hexagon inside of a unit circle, and calculated the ratio of the perimeter of the hexagon to the diameter of the unit circle. Then, he did this until he got up to 96 sides – meaning that the number of sides for the polygons he used were the numbers in the sequence an= 2an-1 where a0 is 6, and 0 ≤ n ≤ ∞. This makes me think – is a circle really a shape with no sides, or perhaps a shape with infinite number of sides?

π is delicious useful in our daily lives even though it may seem totally irrelevant in such a capitalistic society. Nevertheless, underestimate not the power of such a simple constant and the beauty it brings to the world! Once again, have a belated happy pie π day everyone! *stomach grumbles*

Fixing bones and finding new solutions

Last week I submitted a group project report for a module called “Implants Design”. This module includes designing implants for the human body and understanding the way broken bones heal. During the project we had to design a new bone fracture implant device. We were given a case study of an elderly patient who had broken their leg bone and was suffering a number of medicals conditions. Below you can see a CT scan (a special type of imaging technique) of the broken bones of the patient (image 1).

Image 1: CT scan of the patient with a broken leg.

Image 1: CT scan of the patient with a broken leg. The lettering identifies where the bone fractures were found.

Once we identified the issues with the patient, we researched the current ways bone fractures are fixed. We found many ways such as a cage like contraption called the ilizarov frame (image 2), which holds bone together using wires and a metal frame.

Image 2: An example of the ilizarov fracture fixation device currently used in industry.

Image 2: An example of the ilizarov fracture fixation device currently used in industry.

After countless meetings and sessions generating ideas, which included drawing sketches and models (Image 3 and 4), the group came up with a final design for solving the bone fracture (Image 5). The design was produced using special software known as Computer Aided Design (CAD) to create a computer model of the implant. The final design was also discussed in a final report which included describing how the implant works and how surgeons could implant the device during surgery.

Image 3: An example of an initial sketch of an implant, produced during an idea generation meeting.

Image 3: An example of an initial sketch of an implant, produced during an idea generation meeting.

Image 4: An initial CAD design for a possible implant.

Image 4: An initial CAD design for a possible implant.

 

 

 

Image 5: A side view of the final CAD design of the implant.

Image 5: A side view of the final CAD design of the implant.

This was a very enjoyable coursework overall and is definitely one of my favourite group projects to date. Perhaps one day I could make my implant design a reality!

Women and Space

“Science” is the term encompassing the study of our natural and physical world; its structures and behaviours.  A “scientist” is an intellectual with expert knowledge of a particular branch of science.  From the intense study of the human body we gain knowledge of disease and are then able to construct medicines.  By observing the nature of the stars in the sky we are able to assemble a broader perception of the universe in which we live.   Science is the foundation of our society; the knowledge, health, sources of entertainment and standard of living we have today has been built upon centuries of scientific study and discovery.  It is for this reason, I find it incredibly perplexing that science and scientists have not been immune to discrimination.   

In school, we discuss Newton, Einstein and Pythagoras.  At university, I have considered Fermat, Euler and Euclid.  With this education, it wouldn’t be outrageous to believe that female scientists accomplished very little.  However, this is definitely not the case.  The list of influential women within science is, actually, a rather extensive one; but I would like to focus on one in particular. 

Katherine Johnson, an African American physicist and mathematician, made substantial contributions to the US’ aeronautics and space programmes at NASA in the 1950s and 60s.  From a young age, Katherine was a gifted mathematician with a passion to succeed.  Her early career consisted of teaching jobs; as work within mathematics for an African American woman were few and far between.  In 1953, Katherine was offered a job at the Langley Memorial Aeronautical Laboratory, which she accepted and so started her career within the early NASA team. 

For five years, Katherine worked in an office labelled “Coloured Computers”.   The women who worked within that office were required to do all of their daily activities completely segregated from the white men.  Regardless of how important their work was, these women were unable to put their names on reports they had contributed to.  Katherine herself said that women needed to be “assertive and aggressive” in order to be recognised; which, she was.

When NASA disbanded the “computing pool” in 1958, Katherine worked as an Aerospace Technologist until her retirement.  A women, who was once unable to use the same bathroom as her scientist colleagues, was now a vital part of an important team.  She calculated the trajectory for the first American man in space, she calculated the launch window for the 1961 Mercury Mission, she plotted back up navigational charts and was asked personally to verify the numbers for John Glen’s orbit around the Earth.  Katherine helped calculate trajectories for the 1969 Apollo mission; as well as helping to establish confidence in new technologies with her work with digital computers.

Katherine Johnson is just one example of many under-appreciated women working in NASA at the time; and is just one of thousands of under-appreciated women contributors to science.  Despite increasing rates of women studying mathematics and science at universities; the percentage of women within STEM careers is still extremely low.  It is vital to celebrate and learn about women who were not only major contributors to science; but had to overcome all kinds of social barriers to do so.  

A Personal View of Mathematics

Mathematics is a scientific language whose nature is theorised by people like us to produce a system made from mathematical elements that act as useful items that describe everyday objects that bring the idea of this language to reality. Many of its components are correlated to the universe and can explain its constituents, such as the idea of finite quantities, and some that cannot be fully understood, such as the idea of infinity. It is, I believe, independent of human logic and intuition, but through them it is defined and further developed into enterprises that may be beneficial in helping us to understand the universe.

Findings that arise from mathematical elements may sometimes be judged as invalid if proof is absent (as one of my lecturers said!), but majority of them have in fact displayed validity and illustrate more thoroughly the universe, such as transverse waves having similar shape as the sine or cosine graph, potential wells of planets similar to the function of x2, and even projectile motions. Equations created as a consequence of mathematical notations and numbers have even made researches easier, for example, the equation found in chi-square tests and the equation of the normal distribution graph in order to find to find approximate probabilities of large-sized populations. Some other simpler instances include Fibonacci’s rabbits, parabolic movement of a basketball shoot, snowflakes having six-fold radial symmetry, and numerous more. Imagine what else we can find if we continue to immerse ourselves in the world of maths and further develop it – who knows you might be the Nobel Prize winner one day!

Mathematics grants us access to universal truth despite its man-made essence because of its theories being backed by powerful evidence that is so persuading that minor contradictions may be abandoned. Mathematics is indeed a scientific language that plays a significant role not only in sciences and businesses and other developing areas of study, but also in other aspects of our lives.

The Ultimate Goal

After two years of decision making, months of revising, weeks of planning, hours of driving and lugging the far too many suitcases I brought up five flights of stairs; I had finally made it.  For me, university always felt like the ultimate goal; a route out of a small town; a way to learn things that genuinely interest me rather than being dictated an enforced curriculum.   However, within a week this euphoric independence already began to wear off.  I was not as prepared for University as I initially thought.

 

Before attending university, I was a little unsure of how exactly I would be taught.  I was so used to my school timetable; I had a good relationship with all my teachers, knew all my classmates well and was completely comfortable with the course.   However, with a little time I got used to the new university system I found myself in.  I use lectures to soak up as much information as possible; each one of my lecturers offers invaluable insight into Mathematics and, even if I don’t understand all of it yet, I write as much down as I can.  During my tutorials, which usually only contain 20 to 30 students, I ask any questions I need to and discuss any topic I feel necessary in order to get myself as comfortable with the material as possible.

 

Despite all of the academic support available, a substantial amount of independent learning and self-discipline is often required in order to do well.  Surprisingly, I thoroughly enjoy this part of university.  As well as attending everything that is required, there are often extra lectures and events put on by the university that explore different aspects of the subject and offer an insight you won’t obtain anywhere else.   In addition, even though there isn’t usually specific ‘required reading’ for a first-year mathematician, there are so many resources available to deepen your knowledge in general.  If a particular theorem, idea or field of mathematics sparks an interest during a lecture or whilst completing a piece of work I can research that specific item at the library and possibly use it to further my studies.  Mathematics can be a rather intense degree, but I personally find that the more engaged with it I become, the easier the work load is to manage.

 

When deciding what course to apply for I read a brief overview of module options and a snippet of their content.  In reality, the courses are much more in depth and detailed than I could ever imagine.  In the first semester, we pushed our A Level knowledge further in Calculus 1, we tackled Mathematical Structures where number systems and proofs were discussed, we were introduced to the world of Probability where we built on our knowledge of expected values and random variables, and we were exposed to procedures and plots in Computing.   Within the first week I found myself researching Fermat’s Last Theorem for an assignment and getting far too carried away with what was supposed to be a “small summary.”   After five months at QMUL, I can positively say that I have not “made it.”  Being here isn’t in fact the ultimate goal, but it is assisting me in discovering what my “ultimate goal” actually is; whether its working in finance or scientific research or something completely different and unexpected; I am excited to keep studying and find out.

 

Why my second year is better than the first

You usually hear people tell you how much harder second year of university is compared to first. Your first year “practically doesn’t count” so “don’t take it too seriously”. There’s no lie; workload is heavier this year and counts for more towards your final grade. But overall, my second year is going way better than my first. Why?

 

Firstly, I’ve familiarised myself with workload. I know how much to expect, when to expect it, and how to deal with it. Though my work is harder this year, I know not to neglect it too long and how to get it all done. This way, I do well in school and also have time to enjoy my life.

 

Secondly, I love my degree subject more. Maybe because I’m living in the era of Brexit and Trump-onomics where Economics is in the heart of every hot topic right now, I’ve really learned to appreciate my studies and everything that it will have to offer me in the future. My goals are more clear, I know what I love and don’t enjoy as much, and I get more involved in Economics events.
Lastly and most importantly, I’m settled. When you first move to a new place, especially as one as daunting as London, every day can be nerve-wracking and you can even find yourself quite lonely for a while. Don’t worry – this is completely normal and you WILL find your place. You will find who your friends are, your favourite hangout spots, places to eat, a good balance between work and social life, etc. It’s a natural way the universe works. You can’t force it and you can’t resist it – you will eventually become a citizen of London.

Second year – a devil in disguise ?

Yes, yes it is. I am not sure exactly how it happened or what it even is that happened, but my uni life is not as together as it seemed to be. One month ago everything was a bright pink, with some shades of red from my lipstick. Lectures were worthwhile, classes did the trick and the coursework went smooth – it didn’t exist. Now- a completely different story. With midterm season at its peak, opening the actual textbooks made me realize I didn’t know why Marx thought that there is a tendency of the profit to fall, I couldn’t figure out what makes a random sample random and I most certainly couldn’t tell you the relationship between Phillips Curve and the Aggregate Supply (the dark side of economics). Oh, did I mention the utter madness caused by desperately seeking an internship for the summer ?
What had happened to my inner peace being…well, so peaceful ? I jumped from red on my lips to grey on my soul, without even a warning. We are expected to know everything and we are questioned on everything; this everything I’m talking about is about 4 times bigger than it was last year. Don’t get me wrong, it’s a lot more interesting, but I miss the days when reading the slides and going to classes were an almost guaranteed first. They tell you first year is to adjust, they don’t tell you that second year is to survive.

It may be that I am overreacting, since I am writing this at a high point on my stress scale, but I think you could do with a warning: don’t underestimate the workload and don’t assume you can cram 3 months worth of lectures in one night- you will be proven very wrong. It’s better to be safe than sorry.

With Christmas break just around the corner and 2 more midterms to go, I am determined to start fresh next term, put on my red lipstick and make sure I study constantly, thoroughly, to avoid midnight breakdowns…Who am I kidding ? It’s university, if you don’t have a meltdown, it will definitely find a way to give it to you. But that’s what makes it the ‘uni life’ we all crave for, doesn’t it?

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