Overview
Mathematics has many faces Number crunching, and plenty of it. It can be challenging, powerful, fascinating and even mysterious - but above all it is useful. Mathematics makes essential contributions to the biological, information and physical sciences, economics, engineering and finance. Mathematics can also be applied to communications, linguistics and genetics. Wherever problems need to be solved, mathematics has a role to play.
One of the longest established of disciplines, and underpinning many others, mathematics is the language of science and engineering and an intellectual field in its own right. It speaks without barriers across time. It is a discipline that is forever opening up to us, revealing new and fascinating truths and ideas, and helping to expand upon our knowledge in all directions.
Maths is essentially the science of numbers, and all the wondrous things you can do with them. You’ve got the likes of (*deep breath*)… algebra, trigonometry, statistics, mechanics, calculus, differential equations, geometry… the list goes on. What it all *cough* adds up to is the theory and manipulation of numbers, and applying those numbers to real-world problems.
Mathematics is the foundation that underpins the sciences, and it is considered a universal subject in that it transcends language barriers and cultural beliefs. It is also one of the few subjects that can deliver exact, clear-cut answers, giving us a base of fact on which to operate.
What is mathematics?
The Oxford English Dictionary states that mathematics is an “abstract science which investigates deductively the conclusions implicit in the elementary concepts of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra”. The American Heritage Dictionary sums up the subject as the “study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols”.
What to expect from mathematics degrees
Most undergraduate mathematics degrees take three or four years to complete with full-time study, with both China and Australia offering the fourth year as an “honors” year. Some institutions offer a Masters in Mathematics (MMath) as a first degree, which allows students to enroll to study mathematics to a more advanced level straight after completing secondary education. Some institutions arrange placement years for students to work in industry, providing opportunities to apply mathematics skills and knowledge in a real-world setting.
Mathematics is typically taught through a combination of lectures and seminars, with students spending a lot of time working independently to solve problems sets. Assessments vary depending on the institution; you may be assessed based on examinations, practical coursework or a combination of both.
A typical mathematics degree program involves a combination of pure (theory and abstract) mathematics and applied (practical application to the world) mathematics. Some institutions also offer pure and applied mathematics as separate degrees, so you can choose to focus on just one. Mathematics is also often offered as a joint-honors degree, paired with subjects including business management, computer science, economics, finance, history, music, philosophy, physics, sports science and statistics
Why study mathematics?
Studying any mathematics course will expand your knowledge and understanding of the world, helping you to become a sought-after graduate wherever there is a call for logical thinking and statistical or strategic knowledge.
Maths can be a very satisfying subject to study in that there’s always a right answer (even if that answer isn’t always easy to come by). That’s one of the best things about maths: when you’re right, you’re right. If you’ve always had a good head for numbers and you like solving puzzles and working through problems in a logical manner, then a degree in maths could be your number one (sorry) option.
We weren’t lying when we said maths is a universal language, either. The skills you’ll learn on a maths degree will set you up for an incredibly wide range of different careers, so when you do graduate you’ll have all sorts of different options available to you.
“Studying Maths is about discovery: it explores centuries-old disciplines and problems that are still unanswered, as well as continually finding new connections and applications to other fields such as physics, biology and economics,” says Emma Goulding, Assistant Publications Officer at the University of Bristol. “Maths informs many diverse subjects – engineering, finance and science to name but a few – but is also a fascinating subject in its own right.”
What are your study options?
At uni, maths can be divided in to two main strands: applied mathematics and pure mathematics. The former involves applying maths to real-world problems, while the latter is concerned with theory. Most mathematics degrees will cover both of these, giving you the option to narrow your focus to the area you’re most interested in as you move into your second and then final years (although some unis will offer specific degrees in either applied or pure).
Most maths courses will be the standard three years in length, although some unis do offer MMath courses (which are four years long and will give you both an undergrad qualification and a masters), and others offer you the chance to combine maths with another subject (common options include maths and economics or maths and physics, although degrees in the likes of maths and biology or maths and psychology are also available).
What kind of skills will you learn on the course?
A Maths degree will equip you with a range of critical thinking methods using evidence and logical patterns, as well as the skills to design and analyse models. You’ll also develop your communication skills and the ability to assess risk and solve problems.
Areas of study
Stage I Mathematics courses provide you with a range of concepts, theoretical results and skills in analysis, computation and modelling. Stage II and III courses build on these and help you to acquire a broader base of skills and a deeper understanding of the concepts involved.
What you will learn
By studying mathematics you will be stimulated and challenged by some of the greatest ideas in the history of human thought. Our stage I courses will provide you with a range of concepts, theoretical results and analytical, computational and modelling skills that may be applied in a wide variety of areas - in biological, information and physical sciences, economics, engineering and finance for example. As you advance to stage II and III you’ll understand more advanced topics, and will acquire a broader base of skills and a deeper understanding of the concepts involved.
What key modules can you expect to cover in your first year?
Linear algebra and geometry
Analysis (2 units)
Calculus
Mechanics
Computational mathematics
Number theory and group theory
Statistics
Probability
Specializations
You can expect to study a range of introductory courses in your first year, covering key mathematics topics such as abstract algebra, calculus, complex numbers, differential equations, geometry, number theory, probability and statistics. You’ll then move on to more advanced study, and will need to choose from a range of elective courses. Popular mathematics topics include:
Complex analysis
Complex analysis involves investigating the functions of complex numbers – numbers which can be expressed in a form which allows for the combination of real and imaginary numbers. Complex analysis is useful in many branches of mathematics, including algebraic geometry, number theory and applied mathematics, so it is an essential starting point for the further study of mathematics. You’ll learn about the analytic functions of complex variables, complex functions and differentiation of complex functions, how complex variables can be applied to the real world and cover the many theorems surrounding complex functions such as Cauchy’s theorem, Morera’s theorem, Rouché’s theorem, Cauchy-Riemann equations and the Riemann sphere to name a few.
Discrete mathematics
Discrete mathematics involves mathematical structures that are fundamentally discrete (with finite, distinct, separate values) rather than continuous. This includes topics such as integers, graphs, trees, sets, chromatic numbers, recurrence relations and mathematical logic. Discrete mathematics usually involves examining the interrelations between probability and combinatorics. You’ll also learn about the complexity of algorithms, how to use algorithmic thinking in problem solving, algorithmic applications of random processes, asymptotic analysis, finite calculus and partitions. You’ll learn how discrete mathematics is applied to other topics within mathematics, and you’ll also look into broader academic fields such as computer science.
Mechanics
Mechanics is concerned with the study of forces that act on bodies and any resultant motion that they experience. Advanced study of mechanics involves quantum mechanics and relativity, covering topics such as electromagnetism, the Schrödinger equation, the Dirac equation and its transformation properties, the Klein-Gordon equation, pair production, Gamma matrix algebra, equivalence transformations and negative energy states. You’ll also look at how relativistic quantum mechanics can be used to explain physical phenomena such as spin, the gyromagnetic ratios of the electron and the fine structures of the hydrogen atom. You could also study statistical mechanics, which covers topics such as inference, multivariate complex systems, state variables, fluctuations, equilibrium systems, transport models, dynamical ordering and phase transitions, and emergent behavior in non-equilibrium systems.
Measure theory
Measure theory originates from real analysis and is used in many areas of mathematics such as geometry, probability theory, dynamical systems and functional analysis. It is concerned with notions of length, area or volume, with a measure within a set being a systematic way to assign a number to a subset of that set. You’ll look at the definition of a measurable space, additive measures, construction of measures, measurable functions, integrals with respect to a measure, differentiability of monotone functions, k-dimensional measures in n-dimensional space, Lebesgue-Stieltjes measure and Lebesgue measure. Theorems you will cover include Lusin’s theorem, Egoroff’s theorem, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem, Fubini’s theorem, Radon-Nikodym theorem, Riesz representation theorem and divergence theorem.
Fractal geometry
The mathematical concept of ‘fractals’ is difficult to formally define, even for mathematicians! Fractals are geometric forms that display self-similar patterns on all scales of magnification, making them look the same when seen from near as from far. Fractal geometry looks at the mathematical theory behind fractals, the definition and properties of Hausdorff dimensioning and iterated function systems. You’ll gain intimacy with forms such as the middle third Cantor set, the Mandelbrot set and the von Koch snowflake curve.
Fluid dynamics
Useful for students interested in engineering and aerospace, fluid dynamics addresses fluid phenomena of various scales from a mathematical viewpoint. You’ll apply mathematics topics such as ordinary and partial differential equations, basic mechanics and multivariable calculus, and will learn about governing equations, how to deduce the equations of motion from conservation laws (mass, momentum, energy), vorticity, dimensional analysis, scale-invariant solutions, universal turbulence spectra, gravity and rotation in atmospheric and oceanic dynamics, equations of motion such as boundary layer equations, flow kinematics, classical and simple laminar flows and flow instabilities. You’ll cover Euler’s equation, Navier-Stokes equation, Bernoulli’s equation, Kelvin’s circulation theorem, Taylor-Proudman theorem, Reynold’s number, Rayleigh number, Ekman number and Prandtl’s boundary layer theory.
Other mathematics topics you can choose from include: algorithms, applied mathematics, calculus, commutative algebra, computational mathematics, computer game technology, cryptography, differential equations, financial mathematics, financial modelling, functional analysis, geometry, knot theory, linear algebra, linear equations, mathematical biology, mathematical modelling, matrix analysis, multivariable calculus, number theory, numerical analysis, probability, pure mathematics, qualitative theory, real analysis, set theory, statistics, theoretical physics, topology and vectors.
Mathematics skills
While you will build expertise in a range of specific mathematics skills, both technical and analytical, a mathematics degree should also equip you with a range of wider reaching skills applicable across many different sectors. Some transferable mathematics skills you may gain during your degree include:
Specialist knowledge of mathematical theories, methods, tools and practices
Knowledge of advanced numeracy and numerical concepts
Advanced understanding of mathematical and technical language and how to use it
Understanding of complex mathematical texts
Ability to analyze and interpret large quantities of data
Ability to interpret mathematical results in real-world terms
Ability to work with abstract ideas, theories and concepts with confidence
Ability to construct and test new theories
Ability to design and conduct observational and experimental studies
Ability to communicate mathematical ideas to others clearly and succinctly
Ability to construct logical mathematical arguments and conclusions with accuracy and clarity
Proficiency in relevant professional software
Ability to work on open-ended problems and tricky intellectual challenges
Logical, independent and critical thinking skills
Creative, imaginative and flexible thinking skills
Excellent problem-solving and analytical skills
Excellent skills in quantitative methods and analysis
Understanding of statistics
Good knowledge of IT and scientific computing
General research skills
Organizational skills, including time management and presentation skills
Team-working skills
Careers with a mathematics degree
Mathematics graduates go on to pursue many different career paths, often shaped by the mathematics topics they’ve chosen to focus on and the level of academic study they reach – as well as other interests with which they choose to combine their mathematics skills. The long list of possible careers with a mathematics degree includes roles in scientific research, engineering, business and finance, teaching, defense, computing and various types of analysis.
Mathematics graduates are highly sought-after by employers in many sectors as they are perceived as having proven intellectual rigor, strong analytical and problem-solving skills and an ability to tackle complex tasks. So, even if your decision to study mathematics at university is motivated solely by your love of the subject, it seems likely that your degree will nonetheless provide a strong foundation for future career options. Some popular careers with a mathematics degree include:
Accountancy careers
Accountancy careers involve providing professional advice on financial matters to clients. This might involve financial reporting, taxation, auditing, forensic accounting, corporate finance, businesses recovery, accounting systems and accounting processes. You’ll be relied on to manage financial systems and budgets, prepare accounts, budget plans and tax returns, administer payrolls, provide professional advice based on financial audits, and review your client’s systems and analyzing risks.
You’ll need to carry out tests to check your client’s financial information and systems and advise your clients on tax planning according to legislation, on business transactions, and on preventing fraud. You’ll also need to maintain accounting records and prepare reports and budget plans to present to your client. You may need to manage junior colleagues.
Engineering careers
A mathematics degree could also be the starting point for many different roles within engineering careers. Most engineers work as part of a multi-disciplinary project team, with a range of specialists. As such, you’re likely to need excellent team-working and communication skills – as well as the ability to apply your mathematics skills in a very practical environment.
Potential engineering careers with a mathematics degree include roles in mechanical and electrical engineering, within sectors including manufacturing, energy, construction, transport, healthcare, computing and technology. You may be involved in all stages of product development or focus on just one aspect – such as research, design, testing, manufacture, installation and maintenance.
Banking careers
There are a range of banking careers that may be suitable for mathematics graduates due to their strong focus on numbers and analytics. Two of the major pathways are investment banking and retail banking. Investment banking careers involve gathering, analyzing and interpreting complex numerical and financial information, then assessing and predicting financial risks and returns in order to provide investment advice and recommendations to clients. Retail banking careers involve providing financial services to customers, including assessing and reviewing the financial circumstances of individual customers, implementing new products, processes and services, maintaining statistical and financial records, meeting sales targets and managing budgets.
Actuarial careers
Actuarial careers involve using mathematical and statistical modelling to predict future events that will have a financial impact on the organization you are employed by. This involved high levels of mathematics skills, combined with an understanding of business and economics. You’ll use probability theory, investment theory, statistical concepts and mathematical modelling techniques to analyze statistical data in order to assess risks. You’ll prepare reports on your findings, give advice, ensure compliance with the requirements of relevant regulatory bodies and communicate with clients and external stakeholders.
Careers in mathematics research
Careers in mathematics research are available within both the private and public sectors, with employers including private or government research laboratories, commercial manufacturing companies and universities. A research mathematician is able to study, create and apply new mathematical methods to achieve solutions to problems, including deep and abstract theorems.
The role also involves keeping up to date with new mathematical developments, producing original mathematics research, using specialist mathematical software and sharing your research through regular reports and papers. Your job will vary depending on the sector you work in, but some tasks may involve developing mathematical descriptions and models to explain or predict real life phenomena, applying mathematical principles to identify trends in data sets or applying your research to develop a commercial product or predict business trends and market developments.
Statistician careers
A statistician collects, analyzes, interprets and presents quantitative information, obtained through the use of experiments and surveys on behalf of a client. You’ll probably work alongside professionals from other disciplines, so interpersonal and communication skills are important, as well as the ability to explain statistical information to non-statisticians.
Typical tasks include consulting with your client to agree on what data to collect and how, designing data acquisition trials such as surveys and experiments while taking into account ethical and legislative concerns, assessing results and analyzing predictable trends and advising your client on future strategy. You might also advise policymakers on key issues, collecting and analyzing data to monitor relevant issues and predicting demand for products and services. Statistician careers are available in a range of sectors including health, education, government, finance, transportation and market research, and you may also teach statistics in an academic setting.
Teaching careers with a mathematics degree
In many countries, governments are calling for more mathematics graduates to go into teaching. Often this requires completing a postgraduate qualification in teaching, though this depends on the level and type of institution you teach at. Duties will involve instructing students, creating lesson plans, assigning and correcting homework, managing students in the classroom, communicating with students and parents and helping student prepare for standardized testing.
Other careers for mathematics graduates
Operational research (the science of improving efficiency and making better decisions)
Statistical research (using advanced mathematical and statistical knowledge to improve the operations of organizations);
Intelligence analysis (analyzing data to provide useful, useable information to businesses and governments)
General areas of business and management such as logistics, financial analysis, market research, management consultancy;
Careers in IT such as systems analysis and development or research.
Careers in the public sector, as advisory scientists or statisticians.
Scientific research and development, in fields such as biotechnology, meteorology or oceanography.
Career opportunities
Mathematics develops advanced problem-solving skills and opens up career opportunities in industry or government, computer development, insurance, meteorology, traffic engineering, systems analysis, computer programming, statistics, biometrics or operations research. There is also a demand for mathematics teachers.
After your degree
All the big graduate employers (Ernst & Young, PWC, etc.) are often only too happy to take on well-qualified maths graduates, and you’ll be perfectly suited to big-money careers in the likes of accounting and banking.
On the other hand – if you find you don’t want to go down one of these routes – you’ll also have a wide range of other options. Maths graduates go on to find work in everything from marketing to law, so you shouldn’t feel at all limited in your quest for a job.
When you graduate from one of our mathematics programmes, you can expect to be able to pursue careers in any one of the major blue chip companies in sectors as diverse as finance and computing or in government, teaching. Many students continue their studies to graduate level, taking masters programmes or PhDs. Wherever the application of logical thinking and statistical or strategic knowledge is called for, being one of our graduates will give you a head start.
This degree will help you to develop key skills such as analytic thinking, problem solving, independent research, report writing and the use of technical language. These skills are all highly sought after by employers.
Maths degree is evidence of your ability to succeed in a demanding academic environment. Employers target students for their drive, diversity, communication and problem-solving skills, their team-working abilities and cultural awareness, and our graduate employment statistics have continued to climb at a rate well above national trends. graduates have gone on to careers in, for example, management, accountancy and finance, software development, statistics, teaching and the Civil Service, but there are many diverse options out there for Maths graduates.”
Examples of occupations
Actuarial Trainee
Actuarial Consultant
Actuary
Analyst
Associate Auditor
Consultant
Financial Analyst
Management Accountant
Secondary School Teacher
Software Tester
Further study-examples of courses
ACA - Accountancy
ACCA - Accountancy
MSc Accounting and Finance
MSc Actuarial Science
MSc Computing Systems
MSc Finance and Investment
MSc Operational Research
MSc Statistics
PGCE Mathematics
PhD Applied Mathematics