**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:**

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**