Study Mathematics: A Comprehensive Subject Guide

“In a world where numbers govern much of our daily lives, the study of mathematics stands as a cornerstone of knowledge. Welcome to our comprehensive subject guide, where we embark on a journey through the diverse realms of mathematics. From the elegant simplicity of basic arithmetic to the intricate depths of advanced calculus, this guide will be your compass in navigating the captivating world of numbers, equations, and mathematical concepts. Whether you’re a curious beginner or a seasoned mathematician, join us as we unlock the doors to understanding and appreciating this vital discipline.


Table of Contents

What is Mathematics?

Mathematics is the cornerstone of the universe’s hidden language, the ultimate puzzle-solving tool, and the foundation of countless scientific discoveries. At its core, mathematics is the art of understanding and manipulating numbers, quantities, shapes, and patterns. It provides a structured way to make sense of the world and describe the relationships between different phenomena. Here’s a closer look at what mathematics truly entails:

The Language of Numbers: Mathematics is often described as the language of numbers. Just as spoken languages allow us to communicate thoughts and ideas, mathematics enables us to communicate, analyse, and model complex situations with precision.

Problem Solving: Mathematics is like a grand adventure in problem-solving. It equips you with the skills to tackle a wide range of puzzles, from simple arithmetic calculations to solving complex equations, all the way to unraveling the mysteries of the universe through advanced mathematical theories.

Abstraction: Mathematics excels at abstraction. It starts with real-world problems but abstracts them into general concepts and symbols. This abstraction allows mathematicians to create powerful tools that apply to a vast array of situations.

Diversity of Fields: Mathematics is not a monolithic subject. It’s a diverse landscape with various branches. These include algebra, calculus, geometry, statistics, and more. Each branch serves a unique purpose and can be applied to different real-world scenarios.

Why Study Mathematics?

Now that we’ve explored what mathematics is, let’s delve into why studying mathematics is not just academically rewarding but also practically beneficial.

Universal Applicability: Mathematics is the universal language that transcends cultural and linguistic barriers. It’s used in various fields, from physics and engineering to economics and computer science. A mathematics degree is like a passport that allows you to enter multiple career domains.

Problem-Solving Superpower: Mathematics equips you with exceptional problem-solving skills. It teaches you to break down complex issues into manageable components and find creative solutions. These skills are highly sought after by employers in nearly every industry.

High Demand: The demand for professionals with strong mathematical skills is ever-growing. In a data-driven world, industries rely on data analysts, statisticians, and mathematicians to extract valuable insights from vast datasets.

Career Versatility: With a mathematics degree, your career options are diverse. You can become an actuary, data scientist, software engineer, financial analyst, or even a researcher exploring the frontiers of mathematics itself.

Intellectual Fulfilment: Beyond its practical applications, mathematics offers intellectual fulfilment. It’s a field where you can continually challenge yourself, solve complex problems, and make contributions to human knowledge.


Best Universities for Mathematics in the UK

Here is a list of the top UK universities in this field according to the latest QS World University Rankings:

RankUniversity Name
2University of Cambridge
3University of Oxford
10Imperial College London
19The University of Warwick
36The University of Edinburgh
41UCL (University College London)
57The University of Manchester
71King's College London
74University of Bristol
92The London School of Economics and Political Science
108University of Bath
110Queen Mary University of London
113University of Leeds
137University of Birmingham
151-200University of Glasgow
151-200University of Southampton
201-250Durham University
201-250Heriot-Watt University
201-250Lancaster University
201-250Swansea University
201-250University of Exeter
201-250University of Nottingham
201-250University of St Andrews
251-300Cardiff University
251-300Loughborough University
251-300Newcastle University
251-300The University of Sheffield
251-300University of Strathclyde
301-350University of Liverpool
301-350University of York

Entry Requirements for a Mathematics Degree

Entry requirements for a mathematics degree in the UK can vary depending on the university and the specific mathematics programme you are interested in. Here’s a general overview:

1. Academic Qualifications:

  • A-levels: Many universities require A-level qualifications (or equivalent) in mathematics and sometimes further mathematics. The specific grades needed can vary but are often in the A* to B range.

  • International Baccalaureate (IB): For IB students, universities typically ask for a minimum of 36-38 points overall, including higher-level mathematics at a specified grade.

  • Highers/Advanced Highers (Scotland): In Scotland, the Highers or Advanced Highers are commonly accepted. Specific grade requirements may vary.

  • Access to Higher Education Diploma: Some universities accept Access courses in mathematics for mature students who may not have traditional qualifications.

2. GCSEs or Equivalent:

  • Universities may require a minimum of five GCSEs (or equivalent) at grade C/4 or above, including mathematics and often English.

3. Specific Programme Requirements:

  • Some mathematics programmes may have additional requirements or recommendations, such as prior study of particular mathematics topics.

Jobs for Mathematics Graduates

A mathematics degree opens the door to a wide range of career opportunities across various industries. Here are some jobs that individuals with a mathematics degree can pursue:

  1. Actuary: Actuaries assess and manage financial risks for insurance companies, pensions, and investment firms. They use mathematics and statistics to analyse data and make predictions about future events.

  2. Data Scientist: Data scientists collect, analyse, and interpret large datasets to help organisations make data-driven decisions. They use mathematical and statistical techniques to extract insights and patterns from data.

  3. Statistician: Statisticians design surveys and experiments, collect and analyse data, and interpret the results to inform decision-making in fields like healthcare, government, and research.

  4. Financial Analyst: Financial analysts evaluate investment opportunities, assess the financial health of companies, and provide recommendations for investment decisions. They use mathematical models to analyse financial data.

  5. Software Developer: Software developers create computer programmes and applications. A strong mathematical background can be valuable in developing algorithms and solving complex coding challenges.

  6. Quantitative Analyst (Quant): Quants work in finance, using mathematical models and statistical techniques to develop trading strategies, risk management tools, and financial products.

  7. Cryptographer: Cryptographers use mathematical principles to design secure communication systems and encryption methods, working in cybersecurity and data protection.

  8. Economist: Economists study economic trends, analyse data, and provide insights into economic policies and market dynamics.

These are just a few examples, and the versatility of a mathematics degree means you can find opportunities in various sectors, including finance, technology, healthcare, research, education, and more. The specific career path you choose may depend on your interests, additional qualifications, and specialisation within mathematics.

Salary for Mathematics Graduates

Check out the average salary for graduates in this field: 

Low skilled: £19,890

Medium-skilled: £21,500

High-skilled: £28,500

Topics for Mathematics Dissertation

Below, we present a diverse array of research areas, each offering an opportunity to delve into the complexities of Mathematics and make a significant contribution to its advancement:

1. Number Theory:

  • Investigating prime number patterns and conjectures.
  • Exploring Diophantine equations and Fermat’s Last Theorem.
  • Analysing modular forms and their applications.

2. Graph Theory:

  • Studying graph algorithms and their efficiency.
  • Investigating the theory of network flows.
  • Analysing properties of specific graph families, like planar graphs or Hamiltonian graphs.

3. Algebra:

  • Exploring group theory and its applications in cryptography.
  • Studying ring theory and its relevance in algebraic geometry.
  • Investigating abstract algebraic structures like Lie algebras or semigroups.

4. Geometry and Topology:

  • Researching the geometry of surfaces and their classification.
  • Exploring knot theory and its applications in DNA research.
  • Analysing topological invariants and their role in distinguishing spaces.

5. Differential Equations:

  • Investigating partial differential equations and boundary value problems.
  • Studying the stability and existence of solutions for specific differential equations.
  • Exploring applications of differential equations in physics or engineering.

6. Combinatorics:

  • Researching combinatorial designs and their applications in coding theory.
  • Analysing enumeration problems, such as counting permutations or combinations.
  • Studying Ramsey theory and its connections to graph theory.

Remember that the choice of your dissertation topic should align with your interests and career goals. It’s essential to consult with your advisor or professors for guidance and to ensure that your chosen topic is suitable for a dissertation at your academic level. Additionally, consider the availability of resources and data for your chosen topic, as this can significantly impact your research.

Mathematics Students in UK Growth Trend

Around 7000 students progress from schools and colleges in England to undergraduate studies in mathematics each year. Interestingly, this number has remained fairly constant despite the growth in A-level entries.

How Much Does it Cost to Study in the UK

One of the most important things to consider is how much the degree is going to cost. Here is a general guide for 2023/2024:

  • For home students in England, universities can charge up to a maximum of £9,250 per year for an undergraduate degree.
  • In Wales, institutions can charge up to £9,000 for home students. However, Welsh students can apply for a fee grant to cover some of the cost of their tuition fees. This grant is currently not repayable or income-assessed.
  • Northern Irish universities will charge up to £4,275 for home students and may charge up to £9,250 for students from elsewhere in the UK.
  • Scotland does not charge home students fees at the undergraduate level; however, students from England, Wales, or Northern Ireland are expected to pay up to £9,250 per year. International students from outside of the UK will pay significantly more to study in Scotland.
  • International students can expect to pay between £10,000 and £26,000 annually for lecture-based undergraduate degrees at universities across the UK. An undergraduate medical degree can cost overseas students up to £58,600 per year. As for postgraduate degrees, the average cost is estimated to be around £17,109 per year.
Besides the tuition fees, there are also several other cost considerations such as food, accommodation, phone bills, books, social life, memberships, and others. Remember to check out our free student budget calculator

Other Subjects to Consider

Given that you are interested in this subject area, you might also want to consider the following options: 

  • Physics
  • Engineering
  • Computer Science
  • Statistics
  • Economics
  • Actuarial Science
  • Operations Research
  • Data Science
  • Mathematical Finance
  • Mathematical Biology
  • Environmental Science
  • Teaching
  • Astronomy

Frequently Asked Questions

Consider your interests, passions, and career goals. Research various degree programmes and their content to see which aligns best with your aspirations.

While earning potential is important, it’s also crucial to select a degree that you’re passionate about and suits your skills. A balance between your interests and potential career prospects is ideal.

Location can impact your overall university experience. Consider factors like cost of living, proximity to industry hubs, and personal preferences.

Evaluate tuition fees, available scholarships, and potential for part-time work. Create a budget to ensure you can manage your finances during your studies.

Consider combining your passions with practical skills. For example, if you love art but want job security, explore fields like graphic design or digital marketing.

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