An A-Level to University guide on all things Maths

Have you looked at maths degree modules and had no idea what any of it means? Compared to A Levels, university modules can sound terrifyingly vague. What in the world will you study in Methods? But fear not, this guide will break down how the A Level Maths topics you enjoy link to the modules you can study at UCL, so you can tailor your UCL degree to what you like learning. Taking a look at the mandatory modules I studied in first year:

If you like… well all of A Level Maths, you’d enjoy Mathematical Methods!

Mathematical Methods (or the shortened name ‘Methods’) is a continuation of almost all your favourite A Level Maths and Further Maths topics like vectors, polar coordinates, integration, differentiation and more! By balancing new ideas with revision of familiar concepts, UCL structures this course to make studying undergraduate maths friendly and never monotonous. 

If you like sequences, series and proofs, you’d enjoy Analysis!

Analysis 1 and 2 dissect the reasoning behind classic maths topics such as calculus and functions. Building on A Level proof types like contradiction and induction, new notation is introduced to prove fundamental ideas around limits and differentiation. These concepts are standard in any undergraduate maths degree but UCL’s well-structured, supportive framework means that you’ll understand the reasoning every step of the way. This module is a favourite amongst most students as it uses clever reasoning to provide dimension to ideas you already know, making the content feel relatable. So if you’ve always asked why in class (why is the limit of 1/x = 0 as x tends to infinity? Why are we able to differentiate this curve?) and love the certainty of maths, Analysis at UCL is perfect for you!

If you like matrices, functions and set theory, you’d enjoy Algebra!

If Analysis focuses on the fine print, Algebra’s about the big picture. Algebra 1 and 2

discusses what links mathematical objects (such as matrices and vectors) together – what can we say about the way these groups behave? The first year centres around the underlying complexity of different linear equations like functions and matrices. This unlocks greater depth to the ‘simple’ A Level topics you know to create cohesion between Algebra and other mandatory modules. Algebra 1 and 2 are the modules I enjoy the most because its straightforward concepts are easy to conceptualise. This makes the ideas grounded and logical, enabling them to feel accessible and engaging.

UCL’s mandatory modules build a strong mathematical base which allows you to confidently explore any area you choose, inviting you to shape your own education so you study what you’re interested in. This personalisation is provided through the wide range of UCL maths degree programmes and modules you can pick. So, looking at the modules on offer:

If you like modelling, differential equations and conservation of energy, choose Applied Maths!

This mandatory module for Mathematics BSc students provides a great foundation on how maths is utilised in real life. Using ideas like second order differential equations and conservation of energy, this module applies pure maths concepts to build different population and oscillation models.

If you prefer statistics, why not pursue Mathematics and Statistical Science BSc?

This combined-studies degree allows you to take three Statistics modules in First Year:

•   Introduction to Probability and Statistics
•   Introduction to Practical Statistics
•   Further Probability and Statistics

With an emphasis on probability, distribution and coding in R, these modules incorporate data from a range of fields such as astronomy, medicine and finance to show theory in action!

And if you prefer less maths-focused topics, check out the other degree programmes you can take at UCL:

• Mathematics with Mathematical Physics BSc
• Mathematics with Economics BSc
• Mathematics with Modern Languages BSc
• Mathematics with Management Studies BSc
•  Mathematics and Physics BSc

With the cohesive structure and the flexibility to individualise, UCL is the perfect place for you to study maths depending on what you enjoyed at A Levels!

You can visit our module information page for more details on the syllabi of each module.

You can find more details on different degree programme structuresere. on the UCL Mathematics website.

Written by: Teren Lee, UCL Mathematics

Are you stuck trying to find a gift for the mathematicians in your life? As much as we love t-shirts with cheesy mathematical puns, it’s great to get something more intellectually satisfying for any mathematician you know this holiday season. Whether you’re passionate about numbers or know someone who loves solving problems, here are some of my favourite gifts that will make any prospective mathematician happy!

1) Maths Books

The Indisputable Existence of Santa Claus: The Mathematics of Christmas

These are great presents for anyone who wants to build their mathematical knowledge and venture into new areas of mathematics. Ever wanted to know how to use game theory to figure out who you should buy Christmas gifts for? Well, ‘The Indisputable Existence of Santa Claus’ written by UCL’s very own Dr Hannah Fry and Dr Thomas Oleron-Evans solves that exact question as well as all other mathematical Christmas conundrums (including the metabolic rate of Santa Claus!).

If these popular science topics pique your interest, definitely check out the rest of Dr Hannah Fry’s novels such as ‘The Mathematics of Love’ which finds patterns in romance and ‘Hello World: How to be Human in the Age of the Machine’ which tackles the good, bad and ugly of algorithms. If novels are too long for your liking, why not gift issues of Chalkdust magazine, a bi-annual magazine tackling all things mathematical? Founded by UCL Alumni Rafael Prieto Curie and published in UCL, each issue uses different areas of maths to solve real life problems so there’ll be something interesting for anyone who’s mathematically curious. Click here to check out some of their articles and order a copy!

2) Puzzles

Mathematicians are driven by a love of solving problems so gifting any sort of puzzle will definitely be fun. From chess sets and sudoku books, to mathematical board games like Decrypto and mechanical puzzles, the possibilities are endless. I’d particularly recommend puzzle books by Raymond Smullyman as they blend recreational maths problems with different fields of logic and set theory, the perfect brain teaser for on-the-go or a relaxed afternoon.

3) Klein Bottles

Klein bottles are key shapes in topology since the neck of the bottle twists into itself such that there’s no outside or inside to the shape. This topological surface isn’t actually possible to make in three dimensions, but 3D approximations are fun gifts as bottle openers, water bottles, lamps and decorative places!

4) Maths Pun utensils

No mathematician can deny the fun of mathematical puns, especially when they are in a practical application. Think ‘proof is in the pudding’ pudding bowls where mathematical proofs are written at the bottom, or a π pie plate. This will definitely put a smile on their face.

I hope this short list gave you some inspiration for the types of presents you can get to develop someone’s passion for maths. Regardless of what you give, what we value most is time with loved ones and a well-deserved break so I have no doubt that anything mathematical will be appreciated.

Happy Holidays!

Written by: Teren Lee, UCL Mathematics

Do you have math phobia? Well, you’re not alone! To celebrate the spooky season, UCL Mathematics student Teren asks UCL students to share their tricks to treat the fear of maths. Happy Halloween!