# MATHEMATICS UNDERGRADUATE STUDY 2020/2021 - THE UNIVERSITY OF WARWICK

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WHY STUDY MATHEMATICS? 91% IN THE 2014 RESEARCH ONE OF ONLY FIVE EXCELLENCE FRAMEWORK, 90% 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 SAID THAT OUR DEGREE 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.” 86% would be possible without mathematics. £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 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 ANNIVERSARY UNDERGRADUATES WERE IN WORK OR FURTHER STUDY STUDENTS and education, they conduct research into (EPSRC) and Council for Mathematical PRIZE SIX MONTHS AFTER SIX MONTHS AFTER GRADUATION* machine learning, tomography, data systems and financial products. Sciences (CMS), 2012. GRADUATION* FOR HIGHER AND FURTHER EDUCATION * DERIVED FROM THE HESA DESTINATIONS OF LEAVERS FROM HIGHER EDUCATION SURVEY FOR 2016/17, CARRIED OUT APPROXIMATELY SIX 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 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. research. + STRONG PEER SUPPORT + FLEXIBILITY OF COURSE COMPOSITION he whole set-up of our T 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

YOUR WAY IN… 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 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 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* warwick.ac.uk/mathsstep 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 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 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 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 1 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 English language: All applicants must satisfy the 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 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, Analysis • 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. 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 • • 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 Analysis • 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

MATHS to greatly reduce the prevalence of sleeping sickness to manageable levels. THAT But to get from low cases to no cases is 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 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 OF MATHS 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 RESEARCH 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 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 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

ALUMNI 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. 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

ALUMNI 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 Applications are made through For more information about fees Open Days UCAS ucas.com and funding for both Home/EU and The university organise four open 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 visit the offer, and get the required grades academicofficefinance/fees university, including opportunities in your exams we will confirm your to visit the academic departments place and look forward to warmly We want to ensure that, wherever of your choice. welcoming you at the start of your possible, financial circumstances life here at Warwick. do not become a barrier to warwick.ac.uk/opendays 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 warwick.ac.uk/study/ income families. If you receive an offer from us, you undergraduate/apply will be invited to one of our Maths warwick.ac.uk/study/ 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 warwick.ac.uk/study/undergraduate/ 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 www.warwick.ac.uk/io for warwick.ac.uk/accommodation information on applying from your country. This course information was accurate at the time of printing. Our course and module content and schedule is continually reviewed and updated to reflect the latest warwick.ac.uk/mathematics research expertise at Warwick, so it is therefore very important that you check the relevant course website for mathadmissions@warwick.ac.uk the latest information before you apply and when you accept an offer. For full terms and conditions, please visit warwick.ac.uk/ugtermsandconditions

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