University

If you are questioning whether a maths (or related) university course might be suitable for you then consider the following questions:

1) Are you good at Maths?

For the next three years, you are (generally) going to be studying just one subject, and if you aren't particularly good at it then it will be a difficult three years, and it might be worth considering a course in a subject that is more suited to your abilities. Don't be put off if you haven't studied further maths A level; if your enjoyment of the subject has increased in the lower 6th then there are lots of universities that don't require you to study further maths, although you may wish to watch a few of the videos to get an understanding before you go to university. Additionally, each university will have a different definition of "good"; some will require an A or A* in Further Maths, and others will require a B at A Level Maths (along with good grades in other subjects) so do you research on university websites.

2) Do you enjoy solving hard problems?

Studying maths at university is hard. Mr Fletcher remembers coming home from university during the holidays and when relatives asked if he was enjoying himself at university he would reply "yes, its great fun, hard work, but great fun". Mr Fernando would also agree that a maths degree requires students to think hard for long periods of time, to be able to try certain problem solving strategies and to not be phased if that problem solving strategy doesn't work, to have a little spark of imagination and to try again until you find an approach that leads to success, enjoying the process for its ups and downs (not just the ability to answer 50 questions in an hour). Developing the ability to collaborate on hard problems whilst at Adams will put you in a great position heading to university, where team work and discussions can often get you through university assignments quicker AND with more understanding. There are plenty of difficult problems suitable for lower 6th students on the Extension Problems page, or you may wish to start going through the assignments at the Cambridge STEP foundation programme here.

3) Do you enjoy learning maths outside the syllabus?

Have you watched a few of these videos on the enrichment material page and thought "wow, that's really interesting"? Or at a minimum, have you caught yourself with a smile on your face whilst watching them, or learning about other mathematics? This might be a clue that you will enjoy learning more about maths. Although, please bear in mind that these videos are made for entertainment, you can certainly find some dry and drab lecturers at any university who feel like they suck all the fun out of the subject ... so how would you feel if this happened? Would you still find the content interesting for its own merit?

4) Are you stuck between a couple of different subjects?

Often, if you do your research, you can find joint honour degrees that strike the balance between two of your favourite subjects, and often in your third year you can choose to study one subject more than the other if your passion develops in a certain direction, or you find that the other subject wasn't quite what you had in mind. These courses can range from the obvious, Maths and Statistics, Maths and Economics, Maths and Physics, to the less obvious, Maths with French, and Maths with History, for example. Additionally, some universities allow you to study modules from outside the maths department for course credit, whilst maintaining the title of a pure "Maths Degree", but you will have to do your research on the university websites.

5) Do you have time to go to an open day?

Experiencing a maths open day at a university may help you make your mind whether maths is for you. University tutors and professors will be on hand to answer the questions you have, and be in a position to full describe the difference between university level maths and A level maths. Visits will allow you to see if the subject and/or university "feels right", and whether you can see yourself learning maths for the next three years. There will of course be a little bit of a "sales pitch" for their university, so try and see past this.

6) Still not sure?

Read the book Why Study Mathematics by Vicky Neale (link) available in the school library. Vicky is a lecturer at the university of Oxford, and you can read some details about the book here. You don't have to read it all, just the sections that answer your questions, but it is very informative to read it all. The aim of the book (and your wider research in general) is not to convince you to do mathematics at university, but to ensure you have correct information available when making this important decision.

This is a decision that you are unlikely to get wrong. Universities are such large places that there is usually something for everyone at every university. However, it would be sensible to do some research on making such an important decision; UCAS allows you to apply to 5 universities, so researching 10 would be a sensible suggestion. Here are some of the ways in which you can compare universities:

• Geographical Location - would you rather be close to home (an hour or less on the train), or far away (to avoid a quick catch up visit from parents)?

• Campus or City universities - Some universities are based on their own campus out in the countryside where all the university buildings are closely packed together. You are likely to live and socialise on campus in your first year, making everything available within an easy walk; the university will be referred to by the name of a nearby town/city/area that you may live in during your 2nd/3rd year. Other universities are based in the middle or on the outskirts of cities; university buildings will generally be clustered together with accommodation close by. It is a personal choice of what you prefer - visiting some for open days will help you make your mind.

• Entry requirements - It is sensible to apply to a range of universities with different grade offers, so if you unfortunately don't get what you were predicted, then you have a back up at a lower offer. Remember also that you can apply to universities above your predicted grade, but that is for the university to decide on whether to accept you, and you must still reach their grade requirements (it is a risky strategy so have a back up).

• Type of mathematics course - looking at the course description and the modules you will be taking is a good start, but you may not understand what the words mean yet, for example, "Analysis", "Linear Algebra", "Topology", so it would be difficult to make a decision on these words. But you might be able to decipher whether there is a statistics or mechanics leaning to the course based on some key words you have seen before. Something else you can keep an eye out for is the amount of compulsory modules and optional modules you can take in each year (typically more optional modules in 2nd and 3rd year). You might also want to find out how easy it would be to change courses midway through, for examples from a "Maths and Computing" to pure "Maths" or pure "Computing".

• Interested in studying for a Masters? - The advice on this is clear; if you MAY wish to study for a masters, then apply for the four year masters course, and then if you change your mind then you can drop to a three year course easily. However if you only apply for a three year course, the funding options for a masters are way more complicated and you sometimes can't just go through the student finance route, making it much harder to make this happen.

• University Visits - A university might be perfect on paper, your desired location, your preference for campus or city, the right mix of courses, the right entrance requirements, but a visit to your top 5 universities will open up other aspects of the university that are difficult to consider without seeing it in person, such as the type and specification of accommodation for 1st year students or whether the city/campus feels safe and friendly, for example. Sometimes universities offer visits before you apply, and some offer visits after you have applied before deciding your 1st and 2nd choices, so do your research on university websites and visit a few in person to see if it has that indescribable "feel".

So you have decided that a maths degree course (or related) is suitable for you, and now you need to write your UCAS personal statement and tell someone you haven't met how interested in maths you are. This is a difficult task and something you may never have been asked to do before. Here is a bit of advice (and shall be topped up from time to time):

Unofficial: before I start, students, please do not let your parents write this for you. And parents, do not write this for your children. Students, if you really enjoy mathematics, then you should be able to find the energy, motivation and time to write this personal statement. If not, then don't apply to university, and parents, don't waste your money.

Introduction

Introduce yourself, why you enjoy mathematics, and why you would be a good fit at university to study mathematics. Some tutors over emphasise the first paragraph, they will say things like "make it memorable". What they really mean is, don't be boring. Be interesting, interested in mathematics, and honest. (Strictly not cheesy-ness and no quotes!)

Advice: sometimes it is easier to write this section after writing everything else, so if you are struggling, come back to it at the end.

Main Text

This is where you will really go into detail about what aspects of mathematics you enjoy, what topics you find interesting and what part of the problem solving process you enjoy. Start by answering these questions in relation to your A level Maths/Further Maths, and then move on to your wider reading.

Wider reading for mathematics can be generally be divided into two categories (1) general public/recreational reading and (2) mathematically rich/textbook style books. You want to aim for about two books in each category, more in the mathematically rich/textbook style if you are applying for an academically rigorous university. A good idea would be to group together with some friends and all purchase one book, and then swap and discuss the books you have read to get used to talking and listening about complex mathematics.

You don't need to read all of the book, but enough to take something away from them; for example an understanding of what "Analysis" is in mathematics, or an understanding for the story behind how a mathematician came to discover new mathematics, and how mathematicians regularly collaborate when discovering new theorems. Be prepared to talk about these books in interview, it is likely your interviewee will have just read your personal statement before calling you in, and they will want to talk about your wider reading with you. Some good suggestion are below (but not limited to):

Wider Reading - General Public / Recreational

The Calculus Story: A Mathematical Adventure - David Acheson

Infinite Powers: The Story of Calculus - Steven Strogatz

Closing the Gap: The Quest to Understand Prime Numbers - Vicki Neale

The Art of Statistics - David Spiegelhalter

Things to make and do in the Fourth Dimension - Matt Parker

Classical Mechanics: The Theoretical Minimum - Leonard Susskind

The Music of Primes - Marcus du Sautoy

Wider Reading - Mathematical Rich / Textbook Style

How to think about Analysis - Lara Alcock

How to think about Abstract Algebra - Lara Alcock

Excursions in Number Theory - C. Stanley Ogilvy

The Foundations of Mathematics - Ian Stewart

A Concise Introduction to Pure Mathematics - Martin Liebeck

Number Theory - George E. Andrews

Introduction to Topology - Bert Mendelson

Advice: Once you have read a book, write yourself a summary that you can read later before your interview. How would you answer the question "so what did you learn from this book?"

When you write about these books in your personal statements, then consider detailing what you have learned and why you have found it interesting. If you have struggled reading some of the mathematically rich texts, then it might be difficult at first, sometimes you will need to re-read sections for them to make sense, and sometimes they just won't make sense at all. Try the exercises as you go along to really develop your understanding. What will be interesting to put into your personal statement is how you overcame not understanding this content; did you leave your subconscious brain to puzzle it out for a couple of days, did you ask a friend or ask a teacher - showing that you can persevere through difficulties is a great skill that will be required of a university level mathematician.

You can pick up additional mathematical experiences through other means as well, through attending lectures (when COVID permits) or watching them on youtube, as well as other mathematically related videos, mathematical courses through 3Blue1Brown or other online providers, doing well in maths challenge and/or team maths challenges, school maths or academic clubs, maths mentoring etc. Universities often have taster days for lower 6th; book yourself onto one as soon as possible before they reach capacity. When writing about these, mention what you have learned through these experiences and (subtly) how this might link in to the skills of study maths at university.

In this section as well you might want to make a link to your other A levels and how they have expanded your mathematical understanding, or how your other subject has allowed you to use your mathematics in a way you hadn't previously thought of.

This section that focusses on mathematics should take up approximately 60 - 80% of your word limit; the more academically demanding the university, the higher the proportion of maths it should contain.

Extra Curricular

It is important for universities to see that you are a well rounded character; someone who would survive and thrive living away from home, someone who would get involved in new activities, make friends and contribute back to the university you attend. In order to show this, detailing some of your current commitments shows the university the type of student they are accepting. But choose carefully which of your extra curricular activities you mention; choose activities that show off a particular skill and personality trait that you think a university admissions tutor would admire. Have you:

• Been committed to be part of a team?

• Taken leadership opportunities?

• Developed a skill over a period of time to achieve a high level?

Detail your extra curricular activity, and in the next sentence, detail how this demonstrates a desired trait that universities wish to see at their university, and how it might support you in doing well on their course.

This section should take approximately 20 - 40% of your word limit; the more academically demanding the university, the lower this proportion. Try to put all the same detail in with fewer words (be efficient).

Ending

The end of your personal statement should emphasise why all of the above would make you a successful student at the university you have applied to. Don't repeat yourself, but be explicit about the themes of your personal statement; that you enjoy mathematics, you are keen to extend your understanding (and have done so independently), and you have the personal qualities to succeed studying away at university.