IN THE 2014 RESEARCH
                              ONE OF ONLY FIVE
                                                                          EXCELLENCE FRAMEWORK,

                              UK MATHEMATICS                                     MORE THAN
                             DEPARTMENTS IN THE                                                              For beauty and pleasure.                      “The object of pure
                                                                                                             Mathematics is a monument of
                                  WORLD                                                                                                                    mathematics [is]...
   OF OUR STUDENTS                                                                                           human imagination and intuition
   IS INTELLECTUALLY               TOP                                                                       guided by precision. It is sometimes          unfolding the laws of...
  STIMULATING IN THE                                                          OF OUR RESEARCH
                                                                               WAS RATED AS
                                                                                                             challenging, but the challenge is             human intelligence.”
        NATIONAL                                                                                             like ascending a hill to admire an
     STUDENT SURVEY                                                      ‘WORLD LEADING’ OR
                                                                          ‘INTERNATIONALLY                   enchanting vista. It is often also just       James Joseph Sylvester 1880
          2018                                                                EXCELLENT’                     plain fun.
                                  *QS World Rankings 2019

                                                                                                             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.

                                                                                                                                                           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
                                                                                                             high demand and enjoy a huge choice of        for the Engineering

  QUEEN’S                       OF OUR 2017
                                                                         IS THE AVERAGE SALARY
                                                                             ACHIEVED BY OUR
                                                                                                             fulfilling and creative opportunities.
                                                                                                             Working in computing, finance, government
                                                                                                                                                           and Physical Sciences
                                                                                                                                                           Research Council
                            WORK OR FURTHER STUDY
                                                                                STUDENTS                     and education, they conduct research into
                                                                                                                                                           (EPSRC) and Council
                                                                                                                                                           for Mathematical
   PRIZE                          SIX MONTHS AFTER
                                                                                SIX MONTHS AFTER
                                                                                                             machine learning, tomography, data systems
                                                                                                             and financial products.
                                                                                                                                                           Sciences (CMS), 2012.
        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.”

                                                                                Adday, Mathematics with Intercalated Year BSc
                                                                                student 2015-2019 and Women in Maths representative

+ CHOICE AND DEPTH                        support you will receive will be
                                          equally as intense. We want
	We offer a huge number of               you to have a fulfilling university
  exciting modules allowing you           experience. Your personal
  to develop and pursue your              tutor facilitates your academic
  interests within mathematics.           progress and looks out for your
  Many 3rd and 4th year modules           well-being, and lectures are
  offer a glimpse of the latest           supported by supervisions with
  developments in mathematics             postgraduate students.
                                        + STRONG PEER SUPPORT
   COMPOSITION                             he whole set-up of our
                                          department - the breakout
	You are free to do 100% maths if        areas and common spaces -
  you prefer, but we also offer the       are all geared to you sharing,
  opportunity to choose options           collaborating and making
  from several other world-class          life-long friendships.
  departments at Warwick. This
  provides flexibility to tailor your   + OUR INTERNATIONAL
  degree to suit your interests,          REPUTATION
  and also your potential career.
                                        	As a centre of excellence we
+	STRONG SUPPORT FOR                     attract research mathematicians
	TEACHING AND                            from all over world. We offer
                                          an intellectually stimulating
   LEARNING                               atmosphere that few
	The timetable is full and the           institutions rival.
  topics challenging, but the

04                                                                                                                                    05
MAT, TMUA and STEP                                                   With A Levels
We encourage (but do not                                             Applicants for 2020 entry who
require) applicants to sit one of                                    take MAT or TMUA in November
the following admissions tests:     Here are some points you         2019 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 2020 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
                                      three STEP papers and we       (or do not do well in these tests)
                                                                     are likely to receive the following
  STEP - Sixth Term
•	                                   accept all three
  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 1 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*
                                                                           department, and meet staff

                                                                       or A* (Maths), A* (Further            and current students.
For further information and updates regarding our admissions           Maths), A, A
                                                                                                           • G
                                                                                                              eneral Studies and Critical
processes and entry requirements please check our website:                                                   Thinking do not count towards                                                                          A Level requirements.

06                                                                                                                                           07
     with the International                              if you live outside
     Baccalaureate                                       the UK
     Applicants for 2020 entry who take MAT or           The University of Warwick is home to a vast number
     TMUA in November 2019 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 2020 entry who do not sit either     qualifications can be found at
     of the MAT or TMUA (or do not do well in these
     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 1 in     any queries about entrance requirements, please
       any STEP paper                                    contact us at

       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:

                                                         English language: All applicants must satisfy the
                                                          University’s Admissions Requirement, including
                                                          a minimum level of competence in the English

08                                                                                                             09
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

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            Particle Physics, Methods    • I nterdisciplinary Modules:
1st Year Optional Modules                                                                                                   Statistics: Combinatorics,       of Mathematical Physics.        Applied Imagination,
                                                                                                                            Geometry, Introduction                                           Challenges of Climate
• F
   rom Mathematics and                       • F
                                                 rom Philosophy: Mind                      “One of my favourite            to Partial Differential          From Computer Science:
                                                                                                                                                           •	                               Change, The Science
  Statistics: Introduction to                   and Reality, Introduction to                things about studying                                            Algorithms, Logic and
                                                                                                                            Equations, Numerical                                             of Music and Genetics:
  Geometry, Experimental                        Symbolic Logic.                                                                                              Verification, Algorithmic
                                                                                            Maths at Warwick is             Analysis, Combinatorial                                          Science and Society.
  Maths, Probability B,                                                                                                                                      Graph Theory.
                                              • F
                                                 rom Economics:                            how flexible the degree         Optimization, Theory
  Programming for Scientists,                                                                                                                                                             • E
                                                                                                                                                                                             ducation Studies:
                                                Introduction to Quantitative                                                of ODEs, Introduction            From Economics:
  Statistical Laboratory.                                                                   has been. I was able to         to Systems Biology,                                             Introduction to Secondary
                                                Economics.                                                                                                   Mathematical Economics
                                                                                            choose options from my          Introduction to Number                                          School Teaching.
• From Physics: Classical                                                                                                                                   1A, Mathematical
   Mechanics and Relativity,                  • F
                                                 rom the Warwick Business                  very first day - and the        Theory, Variational              Economics 1B.                  The Language Centre at
   Electricity and Magnetism,                   School: Mathematical                                                        Principles, Games
                                                                                            number of options has                                                                           Warwick offers academic
   Introduction to Astronomy,                   Programming I.                                                              Decisions and Behaviour,       • F
                                                                                                                                                              rom Warwick Business
                                                                                            only increased as I’ve gone                                                                     modules in Arabic,
   Introduction to Particle                                                                                                 Introduction to                  School: Foundations            Chinese, French, German,
                                              • T
                                                 he Language Centre at                     along, allowing me to pick
   Physics, Quantum                                                                                                         Mathematical Statistics,         of Accounting,                 Japanese, Russian, Italian,
                                                Warwick offers academic
   Phenomena.                                                                               modules to my interests.”       Stochastic Processes.            Foundations of Finance,        Portuguese and Spanish
                                                modules in Arabic, Chinese,
                                                                                                                                                             Starting a Business, The       at a wide range of levels.
• F
   rom Computer Science:                       French, German, Japanese,                                                 • From Physics: Geophysics,       Practice of Operational
  Design of Information                         Russian, Italian, Portuguese                Emily, Mathematics               Hamiltonian Mechanics,          Research, Mathematical
  Structures, Discrete                          and Spanish at a wide range                 BSc student 2015-2018            Computational Physics,          Programming II.
  Mathematics and its                           of levels.                                                                   Quantum Mechanics
  Applications 2.                                                                                                            and its Applications,         • From Philosophy:
                                                                                                                             Electromagnetic Theory        	 Logic II, History of
                                                                                                                             and Optics, Physics of           Modern Philosophy.
                                                                                                                             Fluids, Stars, Experimental
     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 2018-2019
     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
•	                                                Biology, Bifurcations
  Mathematics                                      Catastrophes and Symmetry,                                             • P
                                                                                                                             hysics: Statistical Physics, Weather and the
	Galois Theory, Rings                             Fluid Dynamics, Numerical                                                Environment, Physics in Medicine, Quantum
  and Modules, Groups                              Analysis and PDEs, Control                                               Physics of Atoms, Electrodynamics, Scientific
  and Representations,                             Theory, Variational Principles,                                          Programming, Plasma Electrodynamics,
  Commutative Algebra,                             Approximation Theory and                                                 Galaxies, Optoelectronics and Laser Physics,
  Algebraic Number Theory,                         its Applications.                                                        Cosmology, Nuclear Physics.
  Set Theory, Combinatorics II.
                                                                                                                            Computer Science: Complexity of Algorithms,
                                                 Probability and Statistics
                                                                                                                            Computer Graphics, Compiler Design,
•	                                            	Bayesian Statistics and
                                                                                                                            Principles of Programming Languages,
	Complex Analysis, Functional                   Decision Theory, Applied
                                                                                                                            Approximation and Randomised Algorithms,
  Analysis I, Functional Analysis                Stochastic Processes, Monte
                                                                                                                            Algorithmic Game Theory.
  II, Manifolds, Measure Theory,                 Carlo Methods, Mathematical
  Markov Processes and                           Finance, Designed                                                        • Engineering: Systems Modelling and Control.
  Percolation Theory.                            Experiments, Probability
                                                 Theory, Multivariate Statistics,                                           Warwick Business School: Business Studies I,
  Geometry and Topology
•	                                              Topics in Statistics, Medical                                              Operational Research and Strategic Planning,
	Fractal Geometry, Geometry                     Statistics, Topics in Data                                                 Business Studies II, Simulation, Mathematical
  of Curves and Surfaces,                        Science, Bayesian Forecasting                                              Programming III, The Practice of Operational
  Introduction to Topology,                      and Intervention.                                                          Research.
  Knot Theory, Algebraic
  Topology.                                      Other
                                               •	                                                                          The Language Centre at Warwick offers
                                               	Problem Solving, Essay.                                                    academic modules in Arabic, Chinese, French,
•	 Real-World Systems and                                                                                                  German, Japanese, Russian, Italian, Portuguese
    Applied Mathematics                                                                                                     and Spanish at a wide range of levels.
	Topics in Mathematical

     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 2018—2019 academic year.

14                                                                                                                                                                       15
Modules offered in 4th year +                                                                                                      SUPPORT FOR
4th Year Core Maths Module:
Research Project/Maths in Action Project.
                                                                                                                                   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
•	                                            •	 Real-World Systems and                 Theoretical Physics
                                                                                        •	                                        module choices, discuss mathematics
  Mathematics                                      Applied Mathematics                  	Relativistic Quantum                     with you in detail, help you to overcome   Support Classes
	Lie Groups, Ring Theory,                     	Dynamical Systems,                     Mechanics, High                          minor and major problems, guide you        Most 2nd, 3rd and 4th year
  Graph Theory, Analytic                           Applied Dynamical Systems,             Performance Computing                    through writing your 2nd year essay,       modules have support classes
  Number Theory, Elliptic                          Population Dynamics,                   in Physics, Gauge Theories               and write reference letters for you.       associated with them. These are run
  Curves.                                          Atmospheric Dynamics,                  in Particle Physics, General                                                        by postgraduates who work through
                                                   Topics in Complexity Science,          Relativity, Quantum                      Supervisions (1st & 2nd Year)              examples, provide homework
•	                                                Mathematical Acoustics,                Mechanics Basic Principles               Your supervisor is a postgraduate or 4th   feedback, answer questions,and
	Fourier Analysis, Stochastic                     Structures of Complex                  and Probabilistic Methods,               year student. Being only a little older    often offer an alternative point-
  Analysis, Ergodic Theory,                        Systems, Mathematics and               Statistical Mechanics.                   than you, your supervisor remembers        of-view from the lecturer.
  Advanced Real Analysis,                          Biophysics of Cell Dynamics.                                                    the challenges of being a 1st and
  Advanced PDEs, Calculus                                                                                                          2nd year maths undergraduate and           Maths Society
  of Variations.                                 Probability and Statistics
                                               •	                                                                                 will support you through these. The        There is also a very active
                                               	Dynamic Stochastic Control,                                                       supervisor marks your homework             undergraduate Mathematics Society.
  Geometry and Topology
•	                                              Brownian Motion, Bayesian                I’ve always felt like I can go to a      providing feedback, and endeavours         They organise a weekly Maths Café,
	Algebraic Geometry,                            Forecasting and Intervention,            lecturer if I need help. The staff are   to answer your questions.                  a student-led peer support group
  Differential Geometry,                         Applied Stochastic Processes,            always happy to answer emails and                                                   which offers informal problem-solving
  Riemann Surfaces, Geometric                    Monte Carlo Methods,                     have office hours so you can speak       Small Analysis Classes                     sessions and a listening ear, and
  Group Theory, Cohomology                       Topics in Applied Probability,           to them in person. They encourage        These help smooth the transition           produce revision notes at exam time
  and Poincare Duality,                          Multivariate Statistics.                 you to ask questions during              between school Calculus and                as well as organising other academic
  Algebraic Curves, Hyperbolic                                                            lectures if you feel confused, or        undergraduate Analysis. Working            and social activities.
  Geometry.                                                                               are happy for you to go to them          in small groups, and supported
                                                                                          afterwards if you don't want to          by a Teaching Assistant (TA) and
                                                                                          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 2018—2019     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      in pure and applied mathematics         disciplines.                       that you can be taught by
undertake a year-long work         your degree at one of 23 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, Malta, The    developments.                           Computing, driving high-           leading Mathematicians
options you can apply during       Netherlands, Portugal, Spain and                                              performance computational          in their field. If you
your second year:                  Switzerland. After your year in       Active research areas include           research.                          choose to do a third
                                   Europe you will return to Warwick     Algebraic Geometry, Number                                                 year essay or fourth
G101: Mathematics with             for your final year.                  Theory, Probability, Geometric          The Centre for Discrete
                                                                                                               •	                                  year research project
Intercalated Year BSc                                                    Analysis, Dynamical Systems,            Mathematics and its                you have the incredible
You will spend a year studying     If you choose to study abroad we      Mathematical Biology and                Applications, brings together      opportunity to be
abroad or on a work placement      can prepare you with the necessary    Complexity Science.                     researchers in graph theory,       supervised by an expert
typically between years 2 and 3    language skills through the                                                   combinatorics and operational      in your area of interest.”
of your degree, adding a year to   Warwick Language Centre.              Research initiatives involving          research from Mathematics,
your degree duration.                                                    mathematics at Warwick include:         Computer Science and the
                                   While we do not offer any formal                                              Business School.                   Alexandra,
G105: Mathematics with             support with arranging work           • T
                                                                            he Warwick Mathematics                                                 MMath student
Intercalated Year MMath            placements, our departmental            Research Centre. Founded in         • T
                                                                                                                  he Alan Turing Institute. This   2011–2015
You will spend a year studying     careers advisor and the university-     1964, this was the first such         is the national institute for
abroad or on a work placement      wide careers support services           centre in the UK. It runs many        data science, founded by the
either between years 2 and 3, or   are available to students and can       workshops and conferences,            Mathematics, Statistics and
between years 3 and 4 of your      provide support sourcing and            and hosts hundreds of visiting        Computer Science departments
degree, adding a year to your      applying for placements to those        mathematicians every year from        at Cambridge, Edinburgh,
degree duration.                   who are interested.                     all over the world.                   Oxford, UCL and Warwick.

18                                                                                                                                                                               19
                                                                                                   to greatly reduce the prevalence of
                                                                                                   sleeping sickness to manageable levels.

                                                                                                   But to get from low cases to no cases is
                                                                                                   much, much harder. My work looks at
                                                                                                   the feasibility and value of that.”

                                                                                                   “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 Assistant 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                                                                                                                                             21
GLIMPSES                                                   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
                                                                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
                                                                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

                                                                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
     These examples also give rise to further natural                     1 + 1 + 1 + ...                6        90      945              are infinitely many irrational
     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                                                                                                                                                                         23
Mathematical 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                                                                                                                                                                                                   25
YOUR FUTURE                                                                                                                              When I started my undergraduate               and the different challenges I face, be

                                                                                                                                         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
                                                                      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.
                                                                                                                                         understood one topic/module, the next         I wanted to work in an industry where I
Mathematics Teacher.              Career Move?                        • Analytical skills                                                one is never too far away. The flexibility    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                                                                                                                                                                                                                             27
ALUMNI 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,               of maths, from Differential Equations to      world” and see how maths is used in the
Mathematics BSc 2008-2011,
                                                                                                                             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                                                                                                                                                                                                                  29
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                                                                                                                                                                                                          31
How to apply                          Student fees and funding                   Visit Us

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                                      studying at Warwick and therefore
For more information about how we     we provide extra financial support         Maths Offer Holder Days
process applications please visit:    for qualifying students from lower                  income families.                           If you receive an offer from us, you
undergraduate/apply                                                              will be invited to one of our Maths
                                                   Offer Holder Days between January
                                      undergraduate/studentfunding               and March 2020. These give you a
Overseas Applicants                                                              chance to meet members of staff,
                                                                                 talk to current students and to get a
With a student population from over   Accommodation                              feel for and ask questions about the
145 countries, you’ll be part of an                                              course, campus life and the style of
international community here          Warwick Accommodation manages              mathematics we teach.
at Warwick. We have a dedicated       over 6,700 rooms on campus across
team available to advise, as well     a range of self-catered residences.        apply/offerholders/ohod
as a global network of Agents and     There is an excellent network of
Representatives.                      support staff in the Residential Life
                                      Team, and wider University.
See for
information on applying from your

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