Mathematical Sciences

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*

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.

 

Building Kingdoms, Chasing Dreams

Happy new year to all of you! 2016 has been a rather interesting year for all of us, but I believe 2017 would be a better year for all of us if we act upon our dreams and our goals, and be motivated and passionate about our ambitions. I too, have personal dreams and goals – both short term and long term – and by living each day driven by the will to become better, we experience circumstances that acts as stepping-stones that bring us closer to our aspirations. In my own opinion, our education is one of these stepping-stones. There are in fact numerous simple things that you can do now that will contribute achieving greatly in university or even after. Here are some things that I personally do:

 

  • 1. Manage my time, by having a calendar beside my study table and on it are upcoming events or deadlines.

 

  • 2. Keeping my room always organised, and not only when I feel like cleaning up!

 

  • 3. Set up a ‘goals and to-do’ list, as if making SMART goals, but less strict with the time limit, for example, ‘Go to Bermondsey and eat Padang food’ and ‘patch my jeans,’ as you can see in the picture below!

 

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Above all these, I believe that there is one thing that will motivate you, drive you, keep you fuelled up and burning with passion – your purpose. Finding your purpose liberates you from work that you may see as burdens now. Finding your purpose is not at all easy and can be time-consuming. It is a slow process, but it is an investment. I am also still in the process of discovering myself. I wouldn’t say that I have found my purpose, but it seems to me that I would love to become an inspiration to others, and this idea of becoming an inspiration has encouraged me more than ever before. Other than that, pushing yourself beyond your own limits and being a life-long learner are just as vital.

At Queen Mary, how are you doing? Are you pushing yourself in understanding the materials in the lectures, or do you have a more apathetic attitude towards learning? Remember, again, education plays a major role in achieving your dreams. Most importantly, keep in mind that “your mind has to arrive at the destination before your life does.” Let us all not just create new year’s resolutions, but act on it! #hustle2k17

Sunsets, Science and Sunflowers

Exploring London is without a doubt one of the most enjoyable elements of living in this city.  From scouting out hidden treasures; obscure coffee shops and underground bars; to being able to weave through the crowds of tourists and relax with a book on parliament square with Big Ben in view, the quote “When a man is tired of London; he is tired of life” has never felt more true.  Here are 3 of my best-loved outings at the moment:

 

Columbia Road Flower Market
Between the hours of 8:00 and 15:00 every Sunday, Columbia Road transforms into a vibrant floral paradise.  After popping to The Hackney Coffee Company for my early Sunday morning caffeine fix, a stroll through the bustling flower market is the ideal way to begin my day.  The incredible aroma of the plants intertwined with hint of coffee coming from one of the many independent shops along the street, as well as the hundreds of people socialising whilst boasting their large bunches of sunflowers and attempting to balance their over-sized orchids on under-sized coffee tables makes Columbia Road Flower Market my happiest place in the city.

columbiaroad

The Science Museum
London boasts an impressive range of Museums and Galleries, however the most significant one for me is, of course, the Science Museum.  I could spend hours meandering through the Space section, gawking at the rockets suspended from the ceiling.  Every so often the museum opens its doors after hours and hosts a range of unique workshops and interactive experiences, as well as a silent disco.  An evening spent talking to astronaut impersonators and dancing to Beyoncé below a suspended United States Scout was undoubtedly one of the most memorable evenings I’ve ever had.

scimuseum

Primrose Hill
After 15 minutes attempting to navigate the streets encompassing Regents Park in what felt like arctic conditions following a rather temperamental phone which occasionally told me to “make a legal U-turn”, I finally noticed a rather large hill poking out from behind some houses.   Honestly, the difficult journey and slight dizziness just made the view from the top even more satisfying.  Roughly 65 metres tall, Primrose Hill offers panoramic views of the entire city and on a wintery evening at sunset, it is one of the most spectacular things I have ever laid eyes on.  At the top very top is a stone with a William Blake inscription, reading “I have conversed with the spiritual sun. I saw him on Primrose Hill.”

primhill

I have an ever-growing list of favourite places; and an ever-growing list of places I want to visit.  I am so thrilled that I have another 2 and a half years in this city; although I highly doubt that this is an adequate amount of time experience everything London has to offer.

 

Breathing the London Air

Hal: Palace of Westminster Moving in to London, a bustling metropolitan city saturated with cultural differences and varied social backgrounds is to me an exciting challenge. During the first few weeks I moved in, I was busy with opening my student bank account, sorting out all the books that I need to purchase and decorating my room. Mingling with people here at first is difficult, especially when the kind of humour is different from where I come from – Indonesia! (If any of you wonder what and where on earth Indonesia is, it’s a tropical country home to Bali located in the Maritime of Southeast Asia.) The weather to me is a shock, perhaps more shocking than the cultural differences as the chilling wind stung my skin and made me shiver constantly. I underestimated the cold…I really did.

As a slightly socially awkward person, making friends and breaking the ice was tough. It took me time to find people I became comfortable with, and eventually spend time studying and playing around with.img_5232 Transitioning from school to university isn’t too rough if you keep this in mind – be open-minded! I’m glad to say, some first year modules supported the process of this transition, simultaneously refreshing your knowledge of the course that you are taking. Moreover, studies isn’t everything – you need your fun. I have joined the rowing club amongst the other hundreds of societies that the institution offer and I have been enjoying it to its fullest extent. Overall, eventually things get better over time and as the days and nights go by, Queen Mary and London feels more and more like home. Now I wonder what will London surprise me with next!

Awkward Hugs and Problematic Ovens

After pacing up and down the corridor a few more times, I looked down at my trembling hand to check my watch. I had been stood outside my flat mate’s door for roughly 4 and a half minutes. I lifted my arm once again, hoping that this time, I would have the courage to knock. Just before I could finally tap the door, it opened. I was now eye to eye with a stranger that I was going to have to live with for an entire year. Standing in his doorway, slightly perplexed as to why I was loitering directly outside his room, he introduced himself. Not thinking, I went straight for a hug. We’re now good friends.

The first week of university was a complete whirlwind of excitement intertwined with a little anxiety and a dash of homesickness. Moving from a small town in South Wales to the capital city was a shock to the system to say the least. Leaving a home with a supportive family and wonderful friends is always going to be difficult; especially when you realize after 3 days of living in halls that you have absolutely no idea how to work your own oven or iron your clothes. However, I’m so happy to be able to say that after 3 months I am well and truly settled and completely content with every aspect of my new life; and, after an hour on Facetime with my mother, I was able to resolve all my oven related issues.

After the craziness that was Freshers Week, I came face to face with an overwhelming realization. I know absolutely nothing. Or at least, very little.. As a Maths student I attend roughly 15 to 17 hours of lectures and tutorials a week, and in each of those hours, I would learn completely new concepts that I couldn’t have even imagined existed whilst sitting my A-levels. The jump is big, but I learnt to view it as an exciting challenge, rather than an impossible task. From learning the exam content to being introduced to some of Maths’ greatest problems; The Goldbach Conjecture, Fermat’s Last Theorem, The Riemann Hypothesis; I am more engrossed in Mathematics now than I have ever been.

Now that first semester is almost over, I am thrilled to be taking a well-earned break. As enjoyable and fascinating as it is, university can be difficult. Sometimes I think it’s important to remind myself that not long ago I was in a small school close to my house, which contained teachers who knew me well, friends who had known me my whole life and I was learning material that I was very comfortable with. I am very ready to unwind somewhere homely and familiar over the Christmas break but am happy to say I am thoroughly enjoying my first taste of the university experience.

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