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MATHEMATICS UNDERGRADUATE STUDY 2021/2022
WHY STUDY
MATHEMATICS?
91%
IN THE 2014 RESEARCH
ONE OF ONLY FOUR
EXCELLENCE FRAMEWORK,
UK MATHEMATICS MORE THAN
DEPARTMENTS IN THE For beauty and pleasure.
90% Mathematics is a monument of "It is impossible to be a
OF OUR STUDENTS WORLD human imagination and intuition mathematician without
SAID THAT OUR DEGREE
TOP being a poet in soul."
20
IS INTELLECTUALLY guided by precision. It is sometimes
STIMULATING IN THE OF OUR RESEARCH
WAS RATED AS
challenging, but the challenge is
NATIONAL like ascending a hill to admire an
‘WORLD LEADING’ OR Sofia Kovalevskaya
STUDENT SURVEY
‘INTERNATIONALLY enchanting vista. It is often also just (1850-1891)
2020 EXCELLENT’ plain fun.
*QS World Rankings 2020
To make a difference to the world. “The quantified contribution of
Mathematical techniques and talent are mathematical science research to
employed to solve real-world problems the UK economy is estimated to
across industry, business and government. be approximately 2.8 million in
Take the internet, medical imaging, weather employment terms and
forecasting, encryption, the human genome £208 billion in terms of
project, data compression… none of these GVA contribution.”
would be possible without mathematics.
92% £28,200
Measuring the Economic
WARWICK MATHEMATICS To start the journey towards a rewarding Benefits of Mathematical
AND STATISTICS IS THE career. Our mathematics graduates are in Science Research, a report
RECIPIENT OF THE
high demand and enjoy a huge choice of for the Engineering
IS THE AVERAGE SALARY
QUEEN’S OF OUR 2018 ACHIEVED BY OUR
fulfilling and creative opportunities.
Working in computing, finance, government
and Physical Sciences
Research Council
ANNIVERSARY UNDERGRADUATES WERE IN
HIGH-SKILLED EMPLOYMENT
STUDENTS and education, they conduct research into
(EPSRC) and Council
for Mathematical
PRIZE 15 MONTHS AFTER
SIX MONTHS AFTER
GRADUATION*
machine learning, medical imaging, data
systems and financial products.
Sciences (CMS), 2012.
GRADUATION*
FOR HIGHER AND
FURTHER EDUCATION * DERIVED FROM THE HESA GRADUATE OUTCOMES SURVEY FOR 2017/18, CARRIED OUT
APPROXIMATELY 15 MONTHS AFTER SUCCESSFUL COMPLETION.
Awarded in 2015
02 03
“You have to be prepared to work hard
but once you’re OK with that it’s the
WHY MATHS most exciting place to study Maths.”
AT WARWICK?
Adday, Mathematics with Intercalated Year BSc
student 2015-2019 and Women in Maths representative
+ CHOICE AND DEPTH Your personal tutor facilitates your
academic progress and looks out
We offer a huge number of exciting for your well-being, and lectures
modules allowing you to develop are supported by supervisions
and pursue your interests within with postgraduate students.
mathematics. Many 3rd and 4th
year modules offer a glimpse of + STRONG PEER SUPPORT
the latest developments in
mathematics research. he whole set-up of our department
T
- the breakout areas and common
+ FLEXIBILITY OF COURSE spaces - are all geared to you
COMPOSITION sharing, collaborating and making
life-long friendships.
You are free to do 100% maths if
you prefer, but we also offer the During the COVID-19 pandemic,
opportunity to choose options every space on campus has been
from several other world-class checked to make sure it is safe to
departments at Warwick. This use. Our plans for teaching and
provides flexibility to tailor your congregating enable us to keep
degree to suit your interests, and a safe distance wherever possible.
also your potential career.
+ OUR INTERNATIONAL
+ STRONG SUPPORT FOR REPUTATION
TEACHING AND LEARNING
As a centre of excellence we
The timetable is full and the topics attract research mathematicians
challenging, but the support you from all over world. We offer
will receive will be equally as an intellectually stimulating
intense. We want you to have a atmosphere that few
fulfilling university experience. institutions rival.
04 05
YOUR WAY IN…
MAT, TMUA and STEP With A Levels
We encourage (but do not Applicants for 2021 entry who
require) applicants to sit one of take MAT or TMUA in November
the following admissions tests: Here are some points you 2020 and do well are likely to
should bear in mind: receive the following offer:
• MAT - Mathematics
A* (Maths), A* (Further Maths), A
Admissions Test • The
MAT and TMUA are
in November
Applicants for 2021 entry who do
TMUA - Test of Mathematics
•
not sit either of the MAT or TMUA
for University Admission • S
TEP is in July - there are
two STEP papers and we (or do not do well in these tests)
are likely to receive the following
STEP - Sixth Term
• accept all three
offer:
Examination Paper
•
See our MAT, TMUA and •
Either A* (Maths), A* (Further
Preparing for one of these STEP page for helpful Note:
Maths), A, plus grade 2 in any
tests will help you develop resources and links STEP paper • W
e don’t interview but we do
your problem solving skills and explaining how to register
invite you to attend an offer
deepen your understanding for these tests •
or A* (Maths), A* (Further
holder open day to see the
of mathematics. Maths), A*
warwick.ac.uk/mathsstep department, and meet staff
•
or A* (Maths), A* (Further and current students.
For further information and updates regarding our admissions
processes and entry requirements please check our website:
Maths), A, A
• G
eneral Studies and Critical
Thinking do not count towards
warwick.ac.uk/mathsadmissions/offer A Level requirements.
06 07
YOUR WAY IN…
with the International if you live outside
Baccalaureate the UK
Applicants for 2021 entry who take MAT or The University of Warwick is home to a vast number
TMUA in November 2020 and do well are likely of international students from over 140 countries,
to receive the following offer: and the Mathematics staff are recruited world-
wide and contribute to the Institute’s cosmopolitan
•
39 points overall, with 6,6,6 in Higher Level outlook. We warmly welcome applications from
(HL) subjects, including HL Maths international students who share our passion for
mathematics. Typical offers for 30 international
Applicants for 2021 entry who do not sit either qualifications can be found at
of the MAT or TMUA (or do not do well in these
warwick.ac.uk/maths/admissions/ug/otherquals
tests) are likely to receive the following offer:
•
either 39 points overall, with 6,6,6 in HL If your qualification is not listed, or if you have
subjects, including HL Maths, plus grade 2 in any queries about entrance requirements, please
any STEP paper contact us at mathsadmissions@warwick.ac.uk
•
or 39 points overall, with 7 in HL Maths, and Further help and advice can be found on our
6, 6 in two other HL subjects international study pages:
warwick.ac.uk/study/international
nglish language: All applicants must satisfy the
E
University’s Admissions Requirement, including
a minimum level of competence in the English
language.
warwick.ac.uk/study/undergraduate/apply/
language
08 09
MATHEMATICS
DEGREES Three or Four Years Maths?
The Maths BSc and MMath have
the same entrance requirements
We offer two single-subject The remaining modules and share the same core in the
Mathematics degrees: can be chosen from 1st year. It is easy to switch from
mathematics or one of the Maths BSc to the MMath
G100: Mathematics BSc many subjects. until the end of the 1st year, and
This is a 3-year maths from the MMath to the Maths
degree that is broad and Course Structure BSc until the end of the 3rd year.
highly flexible. for MMath: If you're struggling to decide
• Same core as BSc. pick either and you can change
G103: Master of your mind later.
Mathematics (MMath) •
Students must do at Teaching: Most of our teaching is
This 4-year degree is a natural least 75% maths through lectures. These are typically 3 Taking a gap year before study?
route for those contemplating each year. hours per week for each module, and
a mathematical career in We welcome applicants who
delivered by a member of academic wish to take a ‘gap year’ between
industry, business or academia. staff. Undergraduates usually take school and university. Just achieve
around five modules in each of Term your admissions offer and your
Course Structure for 1 and Term 2. Term 3 is mostly for
Maths BSc: place will be reserved.
revision and examinations.
• 1
st year: 8 core modules Can I study abroad or do a
(75% of typical workload). “Studying Maths at Warwick is
work placement?
challenging, but a nice challenge.
•
2nd year: 5 core modules You can choose to study abroad
When you put a lot of effort in and
plus essay (55% of or undertake a year-long work
typical workload).
manage to work out something
you’ve been stuck on for a while, placement as part of either the
•
3rd year: no core, but do at BSc or MMath degrees. More
that feeling is so rewarding.”
least 50% maths. information can be found
on page 18.
Helen, MMath student
2014-2018
10 11
Modules offered in 1st year + Modules offered in 2nd year +
2nd Year Core Maths Modules:
1st Year Core Maths Modules: Advanced Linear Algebra; Analysis III; Groups and Rings; Multivariable Calculus;
Foundations, Differential Equations, Introduction to Abstract Metrics, Norms and Topologies; Second Year Essay.
Algebra, Analysis I, Analysis II, Linear Algebra, Maths by Computer,
Geometry and Motion, Probability A. 2nd Year Optional Modules
• F
rom Mathematics and From Computer Science:
• • I nterdisciplinary Modules:
1st Year Optional Modules Statistics: Combinatorics, Algorithms, Logic and Applied Imagination,
Geometry, Introduction Verification, Algorithmic Challenges of Climate
• F
rom Mathematics and • F
rom Philosophy: Mind “One of my favourite to Partial Differential Graph Theory. Change, Genetics:
Statistics: Probability B, and Reality, Introduction to things about studying Equations, Combinatorial Science and Society.
Programming for Scientists, Symbolic Logic.
Optimization, Theory From Economics:
•
Maths at Warwick is
Statistical Laboratory. Mathematical Economics • E
ducation Studies:
• F
rom Economics: how flexible the degree of ODEs, Introduction
1A, Mathematical Introduction to Secondary
• F
rom Physics: Classical Introduction to Quantitative to Systems Biology,
has been. I was able to Introduction to Number Economics 1B. School Teaching.
Mechanics and Special Economics.
Relativity, Electricity and choose options from my Theory, Variational • F
rom Warwick Business The Language Centre at
•
• F
rom the Warwick Business very first day - and the Principles, Games
Magnetism, Introduction to School: Foundations Warwick offers academic
Astronomy, Introduction to School: Mathematical Decisions and Behaviour,
number of options has of Accounting, modules in Arabic,
Particle Physics, Quantum Programming I. Introduction to
only increased as I’ve gone Foundations of Finance, Chinese, French, German,
Phenomena. Mathematical Statistics,
• T
he Language Centre at along, allowing me to pick
Starting a Business, The Japanese, Russian and
Stochastic Processes. Practice of Operational Spanish at a wide range
• F
rom Computer Science: Warwick offers academic
modules to my interests.” Research, Mathematical of levels.
Design of Information modules in Arabic, Chinese, • F
rom Physics:
French, German, Japanese, Hamiltonian Mechanics, Programming II.
Structures, Discrete
Russian and Spanish at a Emily, Mathematics Computational Physics,
Mathematics and its • From Philosophy:
wide range of levels. Quantum Mechanics
Applications 2. BSc student 2015-2018 Logic II, History of
and its Applications, Modern Philosophy.
Electromagnetic Theory
and Optics, Physics of
Fluids, Stars, Methods of
Mathematical Physics.
+
The list of modules varies from year to year and is subject to changes in
curriculum and staff research interests. This list is accurate for the 2020—2021
academic year.
12 13
Modules offered in 3rd year + Other modules
The 3rd year has no core modules.
offered in 3rd year +
3rd Year Optional Modules from
3rd Year Optional Modules from Mathematics and Statistics
Other Subjects
Algebra and Discrete
• • Real-World Systems and
Mathematics Applied Mathematics • P
hysics: Statistical Physics, Weather and the
Galois Theory, Rings Topics in Mathematical Environment, Physics in Medicine, Quantum
and Modules, Groups Biology, Bifurcations Physics of Atoms, Electrodynamics, Scientific
and Representations, Catastrophes and Symmetry, Programming, Plasma Electrodynamics,
Commutative Algebra, Fluid Dynamics, Numerical Galaxies, Optoelectronics and Laser Physics,
Algebraic Number Theory, Analysis and PDEs, Control Cosmology, Nuclear Physics.
Set Theory, Combinatorics II. Theory, Variational Principles.
Computer Science: Complexity of Algorithms,
•
Computer Graphics, Compiler Design,
Analysis
• Probability and Statistics
•
Principles of Programming Languages,
Complex Analysis, Functional Bayesian Statistics and
Approximation and Randomised Algorithms,
Analysis I, Functional Analysis Decision Theory, Applied
Algorithmic Game Theory.
II, Manifolds, Measure Theory, Stochastic Processes, Monte
Markov Processes and Carlo Methods, Mathematical • Engineering: Systems Modelling and Control.
Percolation Theory. Finance, Designed
Experiments, Probability Warwick Business School: Business Studies I,
•
Geometry and Topology
• Theory, Multivariate Statistics, Operational Research for Strategic Planning,
Fractal Geometry, Geometry Topics in Statistics, Medical Business Studies II, Simulation, Mathematical
of Curves and Surfaces, Statistics, Topics in Data Programming III, The Practice of Operational
Introduction to Topology, Science, Bayesian Forecasting Research.
Algebraic Topology. and Intervention.
The Language Centre at Warwick offers
•
Other
• academic modules in Arabic, Chinese, French,
Problem Solving, Essay. German, Japanese, Russian and Spanish at a
wide range of levels.
+
The list of modules varies from year to year and is subject to changes in curriculum and staff research interests.
This list is accurate for the 2020—2021 academic year.
14 15
Modules offered in 4th year + SUPPORT FOR
4th Year Core Maths Module:
Research Project/Maths in Action Project.
LEARNING
Tutorials you how to solve a problem to the
4th Year Optional Modules from Mathematics and Statistics: Your Personal Tutor is a member of point where you develop your
academic staff. Tutors will advise on approach to problem solving.
Algebra and Discrete
• Atmospheric Dynamics, module choices, discuss mathematics
Mathematics Topics in Complexity Science, with you in detail, help you to overcome Support Classes
Lie Groups, Graph Theory, Mathematical Acoustics, minor and major problems, guide you Most 2nd, 3rd and 4th year
Analytic Number Theory, Structures of Complex through writing your 2nd year essay, modules have support classes
Elliptic Curves. Systems. and write reference letters for you. associated with them. These are run
by postgraduates who work through
Analysis
• Probability and Statistics
• Supervisions (1st & 2nd Year) examples, provide homework
Fourier Analysis, Stochastic Brownian Motion, Bayesian Your supervisor is a postgraduate or 4th feedback, answer questions,and
Analysis, Ergodic Theory, Forecasting and Intervention, year student. Being only a little older often offer an alternative point-
Advanced Real Analysis, Applied Stochastic Processes, than you, your supervisor remembers of-view from the lecturer.
Advanced PDEs. Monte Carlo Methods, the challenges of being a 1st and
Multivariate Statistics. 2nd year maths undergraduate and Maths Society
Geometry and Topology
• will support you through these. The There is also a very active
Algebraic Geometry, Theoretical Physics
• supervisor marks your homework undergraduate Mathematics Society.
Differential Geometry, Relativistic Quantum I’ve always felt like I can go to a providing feedback, and endeavours They organise a weekly Maths Café,
Geometric Group Theory, Mechanics, High lecturer if I need help. The staff are to answer your questions. a student-led peer support group
Cohomology and Poincare Performance Computing always happy to answer emails and which offers informal problem-solving
Duality, Algebraic Curves. in Physics, Gauge Theories have office hours so you can speak Small Analysis Classes sessions and a listening ear, and
in Particle Physics, General to them in person. They encourage These help smooth the transition produce revision notes at exam time
• Real-World Systems and Relativity, Quantum you to ask questions during between school Calculus and as well as organising other academic
Applied Mathematics Mechanics Basic Principles lectures if you feel confused, or undergraduate Analysis. Working and social activities.
Dynamical Systems, and Probabilistic Methods, are happy for you to go to them in small groups, and supported
Applied Dynamical Systems, Statistical Mechanics. afterwards if you don't want to by a Teaching Assistant (TA) and
Population Dynamics, speak in front of the class. fellow students you will gradually be
encouraged to move on from
+
The list of modules varies from year to year and is subject to changes in the situation where the TA shows
curriculum and staff research interests. This list is accurate for the 2020—2021 Vicki, MMath student
academic year. 2014-2018
16 17
STUDY ABROAD & AT THE FRONTIERS
WORK PLACEMENTS OF KNOWLEDGE
Although we offer two main G106: Mathematics with Mathematics is constantly evolving. Mathematical Interdisciplinary
• “One of the best
degrees students may then elect Study in Europe MMath The Warwick Mathematics Research at Warwick, fosters things about studying
to follow further pathways on This option will not add a year to Institute is home to a number of mathematical research and Mathematics at Warwick’s
these degrees – typically when your degree duration but instead world-leading research groups training across 11 academic Mathematics Institute is
choosing to study abroad or you will spend the third year of your in pure and applied mathematics disciplines. that you can be taught by
undertake a year-long work degree at one of our European that keep our department and study under some
experience placement. If you’re partner universities in Belgium, at the forefront of research The Centre for Scientific
• of the most eminent and
interested in one of these France, Germany, Italy, The developments. Computing, driving high- leading Mathematicians
options you can apply during Netherlands, Spain and Switzerland. performance computational in their field. If you
your second year: After your year in Europe you will Active research areas include research. choose to do a third
return to Warwick for your final year. Algebraic Geometry, Number year essay or fourth
G101: Mathematics with Theory, Probability, Geometric The Centre for Discrete
• year research project
Intercalated Year BSc If you choose to study abroad we Analysis, Dynamical Systems, Mathematics and its you have the incredible
You will spend a year studying can prepare you with the necessary Mathematical Biology and Applications, brings together opportunity to be
abroad or on a work placement language skills through the Complexity Science. researchers in graph theory, supervised by an expert
typically between years 2 and 3 Warwick Language Centre. combinatorics and operational in your area of interest.”
of your degree, adding a year to Research initiatives involving research from Mathematics,
your degree duration. While we do not offer any formal mathematics at Warwick include: Computer Science and the
support with arranging work Business School. Alexandra,
G105: Mathematics with placements, our departmental • T
he Warwick Mathematics MMath student
Intercalated Year MMath careers advisor and the university- Research Centre. Founded in • T
he Alan Turing Institute. This 2011–2015
You will spend a year studying wide careers support services 1964, this was the first such is the national institute for
abroad or on a work placement are available to students and can centre in the UK. It runs many data science, founded by the
either between years 2 and 3 of provide support sourcing and workshops and conferences, Mathematics, Statistics and
your degree, adding a year to applying for placements to those and hosts hundreds of visiting Computer Science departments
your degree duration. who are interested. mathematicians every year from at Cambridge, Edinburgh,
all over the world. Oxford, UCL and Warwick.
18 19MATHS
to greatly reduce the prevalence of
sleeping sickness to manageable levels.
But to get from low cases to no cases is
THAT
much, much harder. My work looks at
the feasibility and value of that.”
COUNTS
“When I started my Maths degree at
Warwick I had no idea what job I might
do afterwards, although my Dad was
keen for me to be an actuary. Some
of my friends went down that route
Kat Rock is an Associate Professor The project aims to inform decision- but I found the flexibility of the course
in the Mathematics Institute. making strategies for the elimination allowed me to develop my own path.
of the disease. Bringing together an I became drawn to the application of
A Warwick MMath graduate international, multidisciplinary team of maths to solve real-world problems.
herself, she is a mathematical mathematical modellers, researchers and Even though I only took Biology to
epidemiologist with a particular national programmes, the group assesses GCSE, by taking specialist modules
interest in vector-borne neglected local elimination strategies, provides cost- in the second and third years, as well
tropical diseases. effectiveness analyses and will deliver an as undertaking relevant projects I was
investment case for elimination. able to shape my degree to nurture
Kat investigates and develops models my growing interest in the dynamics of
Kat explains, “There are two options for infectious diseases.”
for human African trypanosomiasis (HAT,
disease control – you either treat current
or more commonly known as sleeping
infections or focus on preventing the “I frequently employ the skills I
sickness) and leads the Bill and Melinda
future spread of the disease. Prevention developed on my undergraduate course
Gates Foundation-funded research project
measures vary by disease but might include even now. Modules in programming,
‘HAT Modelling and Economic Predictions
vaccination and insect control. Smallpox differential equations, population
for Policy’. HAT is a parasitic infection,
remains the only human disease to have dynamics and systems biology are all
affecting large parts of Sub-Saharan Africa,
been completely eradicated from the globe directly relevant to my work.”
that’s transmitted by tsetse flies, causing
by our deliberate intervention. Through
debilitating symptoms and is often fatal
treatment and tsetse control it is possible
without treatment.
20 21GLIMPSES Three Colourings of Maps
You might have heard of the A list R,S,T,U of four regions in a In 2016 Steinberg’s conjecture
OF MATHS
Four Colour Theorem, proved map is called a cycle of length 4 was disproved by Warwick
in 1977 by Appel and Hanken. if R shares a border with S, and graph theorists Daniel Kral and
A map is n-colourable if we S shares a border with T, and Michael Hebdige, working with
RESEARCH
can colour it using n colours so T shares a border with U and colleagues in France and Chile.
that no two adjacent regions U shares a border with R. You In fact they constructed a map
share the same colour. The Four can define a cycle of length 5 with 123 regions that doesn’t
AT WARWICK
Colour Theorem simply says in the analogous way. A famous have cycles of length 4 or 5
that any map is four colourable. problem in graph theory (from and isn’t 3-colourable.
You should be able (with a little 1976) is known as Steinberg’s
experimentation) to draw a map conjecture. This claims that a Open problem: Is there a
that isn’t 3-colourable. map that doesn’t have cycles map that doesn’t have cycles
of length 4 or 5 is 3-colourable. of length 4, 5 or 6 and isn’t
You’re perhaps curious about the research-level Many graph theorists have tried 3-colourable?
to prove Steinberg’s conjecture.
mathematics that takes place at Warwick.
Here we present a few examples of theorems and
ideas due to Warwick mathematicians. These have Irrationality of Odd Values of the Riemann-Zeta Function
been chosen because their statements are accessible
We call a number rational if it This is the Riemann-Zeta time mathematicians have been
to A-level students, even though the methods and
can be written as a ratio of two function, one of the most trying to prove the irrationality
ideas behind some are very advanced. In perusing
whole numbers, and otherwise fascinating functions in of these odd values of the
these, you’ll notice that they’re not motivated by
we say it is irrational. In your mathematics, and intimately Riemann-Zeta function, with the
practical applications. Some of the maths research at
first week at university you’ll related to the distribution of only success being due to Roger
Warwick is aimed at solving real-world problems, but
probably see a proof that 2 primes. If n is even then (n) Apery who showed in 1978
most of it is driven by a burning desire to know. You’ll
is irrational. Another famous can be written in terms of π that (3) is irrational. Warwick
also notice that mathematicians in other countries are
irrational number is π. For a for example: mathematician Keith Ball, in
involved as collaborators, and this is typical: research
whole number n≥2 we let: collaboration with Tanguy Rivoal
is international.
(2)= π ’ (4)= π ’ (6)= π ’ ...
2 4 6
at Grenoble, showed that there
6 90 945 are infinitely many irrational
These examples also give rise to further natural 1 + 1 + 1 + ...
questions and new directions. Perhaps you might (n)=1+ odd values of the Riemann-Zeta
2n 3n 4n These expressions can be used function.
solve one of these some day?
to show that (n) is irrational for
even n. For odd n, it seems that Open problem: Is (5) irrational?
(n) is unrelated to π. For a long
22 23Mathematical Art A Module in Focus: Galois Theory
Saul Schleimer is a Warwick directions, none of the gears can You might have wondered if there is a formula to solve a cubic
geometric topologist. He has a move. Saul and Henry had the equation, similar to the familiar quadratic formula. Such a formula was
particular talent for helping the idea of designing a model of discovered by Niccolo Tartaglia (1500-1557) but is usually attributed
public (and undergraduates) three interlocking gears that do to Gerolamo Cardano (1501-1576) who was the first to publish it.
appreciate advanced ideas in actually move, and even printed
geometry and topology through a functional model using a 3D
mathematical art and concrete printer. You might want to google To solve a x 3+ b x 2+ c x + d = 0
models. As an example we their article “Triple Gear” to see the
mention here one of Saul’s models, mathematics that went behind the 3ac–b 2 2b 3 – 9abc+27a 2 d
developed in collaboration with design or watch the YouTube video let p = and q = .
Henry Segerman at Oklahoma showing the gears in motion. 3a 2
27a 3
State University. A relatively
common sight in graphic designs Open problem: Can you design Then one of the solutions is given by
is of three gears in contact. a mechanism with four
However, since neighbouring interlocking gears? 3 3
gears must rotate in opposite q q2 p3 q q2 p3
x = - + + + - - +
2 4 27 2 4 27
Sums of Cubes
The French mathematician Joseph On the basis of this experiment than 454 is the sum of seven
Lagrange proved in 1770 that the German mathematician Carl cubes. Amazingly, besides with the other two solutions given by similar expressions. Shortly
every positive whole number Jacobi suggested in 1851 that ingenuity the last step did not afterwards Lodovico Ferrari (1522–1565) gave a formula for
can be written as the sum of four every whole number bigger than require very advanced solving quartic (i.e. degree 4) equations. For the next 250 years
squares of whole numbers. 454 is the sum of seven cubes. mathematics and the proof mathematicians searched in vain for a formula for solving quintic
This is now a theorem and many can be understood by a equations. Evariste Galois (1811-1832) finally showed that there is
Ever since, number theorists mathematicians have contributed first-year undergraduate. no such formula (shortly before getting himself killed in a duel).
have been trying to prove similar towards the proof with the first Galois studied the symmetries of the solutions, and realised that
theorems with squares replaced steps being taken in the 1940s Open problem: Jacobi also when the degree is at least 5 the symmetries are too complicated
by higher powers. In the 19th by Russian mathematician Linnik. thought that every number for there to be a formula. In the third year Galois Theory module
century a huge experiment was But the final breakthrough that bigger than 8,042 is the sum these symmetries are studied and measured using the modern
carried out by hand where all completed the proof came in 2016 of six cubes. Is he right? language of groups and fields.
numbers up to 12,000 were and is due to Warwick number
decomposed as sums of cubes theorist Samir Siksek; we now know The language is so powerful that along the way many seemingly
of non-negative whole numbers. indeed that every number bigger hopeless questions are resolved. For example, you probably
remember how to bisect an angle using a ruler and compass. In
this module it is shown by dimension counting that angles can’t
be trisected using a ruler and compass.
24 25ALUMNI EXPERIENCES
YOUR FUTURE When I started my undergraduate and the different challenges I face, be
STARTS HERE
degree in maths at Warwick I was it a difficult credit, negotiating legal
not entirely sure what I wanted to do documents or pitching to win business
afterwards and had never considered from new clients.
banking. In my second year I got a
summer internship in corporate banking The flexibility in the degree at Warwick
at a UK financial institution, which gave enabled me to choose some modules
As a Warwick graduate with a Deloitte; Department of me the opportunity to explore different outside of Maths which I have since
mathematics degree, you will Helath; eBay; Ford Motor areas of the bank and I went on to apply found useful in my chosen career: a
have excellent prospects for Company; Fore Consulting; for capital/debt markets graduate roles. Principles of Finance module gave me
a wide range of careers, the Goldman Sachs; Government Nilanthi Gajraj, a basic introduction into corporate
Mathematics BSc 2007-2010 I now work in the loans and acquisition finance, and an Advanced Spanish
most popular areas being the Actuaries; Investec; Jane
Now Vice President, Citi finance team at Citi. We raise loan module was particularly useful when
Financial Sector (Accountancy, Street Capital; KPMG; Lloyds; financings for multi-national working on a Spanish transaction.
Actuarial and Investment MBDA; Metaswitch; Met Office; corporations, financial institutions
Banking), Computing and Softwire; Solid Solutions; Sword and governments across Europe, I hope to continue to develop and gain
Education. Apak; Ten10; Xafinity. the Middle East and Africa. experience in my role with the short
term goal of progressing to a more
Recent graduate job titles have Our Careers Service works for I enjoy the diversity of the role, senior level. Within banking in London
included: Actuary, Business you, providing skills training, working on a leveraged buyout facility there are few women in senior roles
Intelligence Consultant, Chief careers advice and information, in Poland is very different to a high so I’d like to help re-balance this and
profile acquisition finance transaction inspire the next generation of women.
Analytics Officer, Computer and will continue to support
for a FTSE 100 corporate for example,
Games Designer, Consultant you after your graduation. See
During a Warwick Mathematics
Software Engineer, Financial warwick.ac.uk/careersandskills
degree you will develop many
Consultant and Adviser,
of the qualities of intellect and The Mathematics degree at Warwick is I applied for the graduate scheme in
Financial Software Developer, Why is a Warwick Maths temperament needed to meet challenging but as a result it is extremely my final year of university, and have
Investment Banking Analyst,
Market Risk Manager, and Degree an Excellent new challenges, including: rewarding. As soon as you have since progressed within the company.
Mathematics Teacher. Career Move? • Analytical skills
understood one topic/module, the next
one is never too far away. The flexibility
I wanted to work in an industry where I
could use some of the skills that I had
to pursue the areas of Mathematics that developed throughout my Mathematics
Firms that have employed In today’s workplace, the ability • Logical thought processes
you most enjoy is extremely helpful – degree, and Investment Consulting
recent Warwick graduates from to adapt to change and to learn • Problem-solving ability being able to tailor your degree to what looked like the right choice.
Mathematics and Statistics new things is as important as you are most interested in allows you to
• Investigative skills
include: Adder Technology; having a particular range of get the most from it. My main motivation is to keep learning
Merril Lynch; Brainlabs; Civil knowledge. • Communication skills Benjamin Li, and to keep challenging myself. Where
• Effective working habits Mathematics BSc 2011-2014 I now model pension fund assets and that will take me only time will tell, but
Service; Conduent; Darktrace;
liabilities, helping to advise trustees on I’m looking forward to finding out.
Now Associate Consultant
(Investment Consulting), Aon potential investment strategies to best
meet benefits payable to members.
26 27ALUMNI EXPERIENCES Dr Rachel Player
MMath 2009-2013
Now Postdoctoral
My first job out of university was doing user’s behaviour (through how they
Researcher, Information
fraud analytics on social networks for handle their smart phone for example) Security Group, Royal
banks and insurance companies. The to provide authentication. Holloway
‘Programming for Scientists’ module gave
me the minimum amount of programming The way the degree encouraged me
knowledge I needed for this role, and in to think deeply and logically about One of the best things about the MMath course at
my interview I gave a presentation based abstractions helps me to think about Warwick is the opportunity to study a wide range
on my fourth year project. systems; imagining how things are going of modules. During my first two years, I followed
to work without knowing every detail and courses in maths and physics. I discovered that my
Within this role I was always interested before they’ve been built. interest was in number theory and algebra, and I
Matthew Marshall, in the machine learning side of analytics was able to develop this interest by following many
MMath 2007 – 2011 as it involved more maths, so I moved to My degree also gave me the self-belief that advanced courses in these areas. In my final year I
working at a start-up where this is core to even if something seems as complicated was fortunate to work with Prof. Samir Siksek, who
Now Data Scientist
their business. I now work on prototyping as algebraic topology then if I apply myself supervised my MMath research project in number
and implementing models that take into to it then I'll crack it eventually. theory. This was a real turning point: Samir was
account location, device profiling and a extremely enthusiastic and helpful, and I enjoyed
this project so much I began to think seriously
about a career in research.
My work involves looking at the validation their Applications. These modules gave After graduating from Warwick, I began studying
of risk models, particularly those used for me an in-depth and diverse understanding for a PhD at Royal Holloway. My background
risk management; from setting risk limits on how to construct and test mathematical in number theory and algebra gave me a solid
on individual trading desks to ensuring models observable phenomena which foundation for my specialism, cryptography.
the firm has sufficient capital so that the definitely influenced my career. The highlight of my PhD was an internship in
bank can adequately mitigate its potential the Cryptography group at Microsoft Research,
Maths Quiz
exposures during severely adverse After my undergraduate degree I wanted Redmond, USA. I went on to a postdoctoral For her MMath Research
market conditions. to continue studying maths but with more position at Sorbonne Université in Paris, before Project Rachel investigated
of a focus on “real world” applications returning to Royal Holloway. factorials that can be written
Prior to my undergraduate degree I leading to my Masters and PhD, and as sums of three Fibonacci
was fascinated by unique applications after these I decided to join the “real My current role is varied and involves conducting numbers, for example
Thomas Rafferty,
Mathematics BSc 2008-2011,
of maths, from Differential Equations to world” and see how maths is used in the research, writing papers, giving talks, teaching, 6! = F8 + F11 + F15
Brownian Motion. I therefore always tried financial industry. organising workshops, and peer-reviewing others’
Complexity Science MSc
to choose modules with a more applied work. Research is a dream job for me: not only Rachel found all such
2012-2013, Mathematics and
Complexity Science PhD. focus, such as Topics in Mathematical I really enjoy that I am continually learning being paid to work on interesting problems, but examples, and proved that
2013-2016 Biology, Dynamical Systems, Probability, new features and applications of maths for also the opportunity to travel and discuss ideas there aren’t any others.
Now Associate in Model Risk, Statistics and Stochastic Processes and modelling real world behaviour. with colleagues around the world. I regularly How many can you find?
JP Morgan present my work at national and international
conferences – my next trip will be to New Zealand!
28 29ALUMNI
EXPERIENCES Natasha Agarwal
Mathematics BSc 2014-2017
Now MA in Vocal
Performance, Royal Academy
of Music in London
I am training to be a classical opera singer wide range of topics such as abstract algebra,
Emma Cooke which seems like quite a change from Maths! geometry and partial differential equations,
Mathematics BSc 2007-2010
However I always say that both music and maths and it was fascinating to see the connections
Now Key Stage 5 Coordinator are universal languages – they’re both built on to my other maths modules. I also had the
for Maths and 16+ Assistant, very simple foundations but have the power to opportunity to study language modules and
Sidney Stringer Academy communicate complex ideas and emotions no interdisciplinary modules such as “The Science
matter what language you speak. of Music”, which have proved extremely useful
I’m currently a Maths teacher with least 80% of every working day doing now as I have to sing in a variety of languages
a leadership role that involves maths. But even better than that, I also I’ve been singing and performing since the and understand the mechanics of vocal
planning the A Level Maths, Further spend that time spreading my love of age of four, and at Warwick I had so many production and resonance.
Maths and Core Maths curriculum, maths to others. The school I work in opportunities to pursue music and performance
monitoring student progress and is situated in a very deprived area, and alongside my studies. I now study a wide I think one of the key messages from my story
raising achievement. I am also in my many of my students have significant range of repertoires, including contemporary is that everybody has their own unique path
dissertation phase of a masters in socio-economic barriers to their music which is often very complex so my maths in life. My path from maths to music may seem
Professional Education part-time learning. Smashing these barriers and degree certainly comes in handy for that. To strange or unusual, but it was the right path
at Warwick. seeing students succeed against all support my studies I also work as a private for me. It is okay to go to university without
odds is what motivates me to wake up maths tutor for school pupils which is knowing what you want to do when you leave
In my second year at Warwick I each morning with renewed passion. very rewarding. – in fact this can often make you more open-
completed the Student Associate minded when it comes to career possibilities. It
Scheme*, which involved a term-long *Although this particular scheme is no longer One of the best things about the mathematics is important to work hard at your degree, but it
placement in a secondary school and
available there are numerous other opportunities degree at Warwick, apart from the world-class is just as important to pursue your hobbies and
for Maths students interested in teaching. For teaching and facilities, is the flexibility of the interests so that you develop as a well-rounded
a two-week teaching experience example, our optional module 'Introduction
and convinced me that I wanted to to Secondary Teaching in Mathematics' which course. In second year, we had to do an essay individual. Doing a Mathematics degree at
go into education. includes a ten-day placement in a local school, or on a mathematical topic of our choice, and I Warwick is challenging in many ways, but once
the Warwick In Africa programme. decided to research the relationship between you’ve accomplished that you will seriously feel
I am and always will be a maths and music. This research covered a like you can achieve anything in life!
mathematician at heart so it’s great
that in my current job, I get to spend at
30 31How to apply Student fees and funding Visit Us
Applications are made through For more information about fees Open Days
UCAS ucas.com and funding for both Home/EU
The university organise four open
and Overseas students see:
days in early summer and in autumn
If you are made and accept an warwick.ac.uk/services/
for students wishing to find out
offer, and meet all conditions we will academicoffice/finance/fees
more about the university, including
confirm your place and look forward
opportunities to find out more about
to warmly welcoming you at the start We want to ensure that, wherever
the academic departments of your
of your life here at Warwick. possible, financial circumstances
choice.
do not become a barrier to
For more information about how we studying at Warwick and therefore warwick.ac.uk/opendays
process applications please visit: we provide extra financial support
warwick.ac.uk/study/ for qualifying students from lower If you receive an offer from us, you
undergraduate/apply income families. will be invited to one of our Maths
Offer Holder Days between January
warwick.ac.uk/study/ and March 2021. These give you a
Overseas Applicants undergraduate/studentfunding chance to meet members of staff,
talk to current students and to get a
With a student population from over feel for and ask questions about the
145 countries, you’ll be part of an Accommodation course, campus life and the style of
international community here at mathematics we teach.
Warwick. We have a dedicated Warwick Accommodation manages warwick.ac.uk/study/undergraduate/
team available to advise, as well over 6,900 rooms on campus across apply/offerholders/ohod
as a global network of Agents and a range of self-catered residences.
Representatives. We also have an excellent network
of support staff in the Residential Life
See www.warwick.ac.uk/io for Team, and wider University.
information on applying from
warwick.ac.uk/accommodation
your country.
This course information was accurate at the time of
publication (September 2020). Our course and module
content and schedule is continually reviewed and updated
warwick.ac.uk/mathematics to reflect the latest research expertise at Warwick, so it is
therefore very important that you check the relevant course
mathadmissions@warwick.ac.uk website for the latest information before you apply and when
you accept an offer. For full terms and conditions, please visit
warwick.ac.uk/ugtermsandconditionsYou can also read
