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1st Class, Ba Economics and Philosophy, University College London (UCL)



This is a bespoke 1:1 tuition-based Mathematics course, which could be tailored as much as desired to suit the interests and abilities of the student.


The course is aimed at Mathematics university applicants who want to go beyond the school syllabus, gain a deeper understanding of their subject and get a feel for how Maths is approached at the undergraduate level.​

A different student might want a different programme, but this is informative of the possible topics that they might want to cover.

Introductory module

(2 hours) 

This module will help you map out a plan that will help you stand out from the crowd, giving you the tools to demonstrate initiative and enthusiasm reaching well-beyond the school curriculum.  

You will have the opportunity to discuss your university preferences and academic interests with your tutor.

Vector Spaces and Algebra

(3 hrs)


Vector spaces and algebras are used ubiquitously in mathematics, but are not discussed at this level at the pre-university stage. This module will give you a deep understanding of what a vector really is, and what the complex numbers really are.

We will begin by reviewing vectors' algebraic properties -such as the idea of addition and multiplication by a scalar.


We will then study abstract vector spaces, and vector spaces with a closed multiplication rule.

Generalisation of Complex Numbers
(2 hours)  


This module will give you an explicit picture of the types of structures studied in abstract algebra.


Starting with and introduction on complex numbers, this session will look at how they may be generalised to larger algebras.


The multiplication rules of the quaternions and octonions will be introduced and their algebraic properties discussed.

Group Theory

(3 hrs)


Group theory is used throughout mathematics, and can be seen as tool or as a subject in its own right.


This session will begin by looking at symmetry and how it may be described in terms of groups.


We will go over the definition of a group, and review multiple examples. We will then delve into the idea of an isomorphism between groups, and see that many basic examples of groups are isomorphic to one another.

After this module you will be able to demonstrate good knowledge of this fundamental topic.

Groups within the Complex Numbers and Quaternions

(3.5 hrs)

This will tie together notions studied in all the previous modules, and show how the complex numbers and quaternions relate to rotations of objects in 2,3 and 4 dimensions.

This will include an introduction to rotation groups, and how they may be represented within the complex numbers and quaternions.

Personal Statement 

(1.5 hours)

Personal statements provide students with an important opportunity to demonstrate their achievements, academic potential and interest in the course. Every sentence in the personal statement needs to pull its weight.


In this course you will be guided through the process of writing your personal statements, from its initial drafting to its final proof-reading, with the opportunity for considered and constructive feedback at every stage. We will review what has been learnt and channel your enthusiasm into a personal statement that reflects you talents.

You will also be able to discuss possible interview questions. Advice will be given on how to prepare for entrance exams such as the MAT (Oxford, Cambridge, Imperial).

All of our programmes​ are entirely bespoke: what you saw above was just an example. 


Our tutors will speak to you to understand your precise needs, and build a programme that feels right and is exciting.

Please enquire to find out more.

the hours you need

Built around
your degree choice

Studying topics 
you love



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