© 1997-2004, Millennium Mathematics Project, University
of Cambridge.
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Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us.
Careers with maths
Rupa Patel reflects to Plus on her work as a financial engineer
A favourite from the archive...
When we finally meet the Martians, John Conway believes they are going to want to talk mathematics.
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A B C D E F G H I L M N O P Q R S T V W
- A differential story
Plus Online Maths Magazine: News Story
[ ABEL PRIZE ] [ DIFFERENTIAL EQUATION ] - Abel to iPod
Plus Online Maths Magazine: News Story
[ ABEL PRIZE ] [ DYNAMICAL SYSTEMS ] [ FOURIER ANALYSIS ]
- Career interview: Actuarial researcher
Shane Whelan likes a challenge, and his career path has been defined both by what he enjoyed and by a desire to keep learning. Becoming an actuary seemed like the perfect solution.
[ FUND MANAGEMENT ] [ INSURANCE ] [ PENSIONS ] [ STATISTICS ] [ STOCK MARKET ]
- Bang up a boomerang!
Here's how you can make your own cross-shaped boomerang - and it's safe enough to fly indoors! Hugh rolls up his sleeves and proves that theory isn't everything.
[ BOOMERANG ] - Unspinning the boomerang
In this article, we look at the physics behind the curved flight path of a returning boomerang, and explain that boomerangs are really a kind of gyroscope. We even show you how to bang up a boomerang yourself!
[ ANGULAR FORCE ] [ BOOMERANG ] [ CIRCULAR MOTION ] [ COUPLE ] [ FORCE ] [ GYROSCOPE ] [ MOMENT OF INERTIA ] [ PRECESSION ] - Career interview: Aerodynamicist
Plus talks to Christine Hogan, programmer, sysadmin and author, now studying aerodynamics and hoping to become a member of a Formula One team.
[ AIRCRAFT WAKE VORTEX ] [ COMPUTER PROGRAMMING ] [ DISTRIBUTED COMPUTING ] [ OBJECT-ORIENTED PROGRAMMING ] [ RACECAR DESIGN ] [ SYSTEMS ADMINISTRATION ] [ TURBULENCE ]
- Puzzle page
Plus Online Maths Magazine: Regular Item
[ ] - Puzzle page
Plus Online Maths Magazine: Regular Item
[ ] - Puzzle page
Plus Online Maths Magazine: Regular Item
[ ]
- Career interview: Architect
Wen Quek works for an award-winning architectural cooperative based in London. Recently, she worked on the new library at the University of Cambridge's Centre for Mathematical Sciences. As she tells Plus, Wen sees many parallels between mathematics and architecture.
[ ]
- In perfect harmony
The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
[ ARITHMETIC SERIES ] [ CONVERGENCE ] [ CONVERGENCE ] [ DIVERGENCE ] [ GEOMETRIC SERIES ] [ HARMONIC SERIES ] [ LOGARITHM ] - An infinite series of surprises
Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.
[ CONVERGENCE ] [ DIVERGENCE ] [ EULER'S SOLUTION TO THE BASEL PROBLEM ] [ GEOMETRIC SERIES ] [ HARMONIC SERIES ] [ INFINITE SERIES ] [ INTEGRAL TEST ] [ POWER SERIES ] [ SINE ] - Curious quaternions
Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the first of two articles, he talks about connections between algebra and geometry, and the importance of lateral thinking in mathematics.
[ COMPLEX NUMBER ] [ HAMILTON ] [ QUARTERNIONS ] - Ubiquitous octonions
Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the second of two articles, he talks about the characters of the different dimensions, beauty and utility in mathematics, and just why he likes dimension 8 so much.
[ COMPLEX NUMBER ] [ HAMILTON ] [ MATHEMATICAL THINKING ] [ OCTONIONS ] [ QUARTERNIONS ] - The death of the lightning calculator
Plus Online Maths Magazine: Feature Article
[ ARITHMETIC ] [ HISTORY OF MATHEMATICS ] [ MENTAL ARITHMETIC ]
- Practice makes perfect
In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.
[ CHESS ] [ CHINOOK ] [ COMPUTER CHESS ] [ DEEP BLUE ] [ DRAUGHTS ] [ GAME THEORY ] [ GARRY KASPAROV ] [ SHATURANGA ]
- Life as we don't know it
Physicist and cosmologist Paul Davies has made an unusual move into the infant discipline of astrobiology. He tells Plus about his interest in the big questions: what is life, how would we recognise aliens - and are they all around us?
[ ALIEN LIFE ] [ CHIRALITY ] [ EVOLUTION ] [ INFORMATION ] [ NATURAL SELECTION ] [ ORIGINS OF LIFE ] [ QUANTUM INFORMATION ] [ SEMANTIC INFORMATION ]
- Mathematical mysteries: the three body problem
Plus Online Maths Magazine: Regular Item
[ CELESTIAL MECHANICS ] [ LAGRANGE POINT ] [ SATELLITE ] [ SPACE EXPLORATION ] [ THREE BODY PROBLEM ] - Spiralling stars
Plus Online Maths Magazine: News Story
[ WOLF-RAYET STAR ] - Martian mayhem
Plus Online Maths Magazine: News Story
[ NASA ] [ SPACE EXPLORATION ] - Planets, planets everywhere
Plus Online Maths Magazine: News Story
[ ECLIPSE ] [ GRAVITY ] [ PLANETARY ORBIT ] - Lensing helps see in the dark
Plus Online Maths Magazine: News Story
[ COSMOLOGY ] [ DARK MATTER ] [ GRAVITY ] [ LENS ] - All about asteroids
Plus Online Maths Magazine: News Story
[ ASTEROID ] [ ASTEROID COLLISION ] [ METEORITE ] [ NEWTONIAN MECHANICS ] [ SPACE EXPLORATION ] - Heavenly choreography
Plus Online Maths Magazine: News Story
[ LAGRANGIAN SYSTEM ] [ NEWTONIAN MECHANICS ] [ PLANETARY ORBIT ] [ THREE BODY PROBLEM ] - Stellar heartbeats
Plus Online Maths Magazine: News Story
[ ACOUSTIC OSCILLATION ] [ ASTROSEISMOLOGY ] [ DOPPLER SHIFT ] [ FREQUENCY ] [ HELIOSEISMOLOGY ] [ SOUND WAVE ] [ STANDING WAVE ] - No place like home for Martin Rees
Astronomer Royal Sir Martin Rees gives Plus a whistlestop tour of some of the more extraordinary features of our cosmos, and explains how lucky we are that the universe is the way it is.
[ BIG BANG ] [ CURVATURE OF SPACE ] [ DARK MATTER ] [ ENERGY ] - X-otic X-ray visions
Plus Online Maths Magazine: News Story
[ BINARY STAR ] [ BLACK HOLE ] [ EQUATION OF STATE ] [ GRAVITATIONAL REDSHIFT ] [ NEUTRON STAR ] - Lagrange and the Interplanetary Superhighway
In the last issue Lewis Dartnell explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.
[ 3-BODY PROBLEM ] [ ANALYSIS ] [ ASTRONOMY ] [ CALCULUS ] [ CENTRIPETAL FORCE ] [ CHAOS ] [ COPERNICUS ] [ DYNAMICAL SYSTEM ] [ EULER ] [ GRAVITY ] [ INTERPLANETARY SUPERHIGHWAY ] [ LAGRANGE ] [ LAGRANGE POINT ] [ MANIFOLD ] [ NEWTON ] [ PHYSICS ] [ POINCARE ] [ SPACE EXPLORATION ] - The right spin: how to fly a broken space craft
On the 25th of May 1997 a dramatic collision tore a hole into the space station Mir and sent it hurtling through space. As NASA astronaut Michael Foale tells Plus, the fate of Mir and its crew hinged on a classical set of equations.
[ ASTRONOMY ] [ MOMENT OF INERTIA ] [ SPACE EXPLORATION ] [ SPIN ] - Untangling a magnetic mystery
Plus Online Maths Magazine: News Story
[ DYNAMO EFFECT ] [ FLUID MECHANICS ] [ MAGNETIC FIELD ] [ NEPTUNE ] [ VENUS ] - Brave young worlds
Plus Online Maths Magazine: News Story
[ DOPPLER SHIFT ] [ ESA ] [ GRAVITY ] [ NASA ] [ PLANET ] - John D Barrow wins Templeton Prize
Plus Online Maths Magazine: News Story
[ MATHEMATICSAND RELIGION ] [ MATHEMATICS IN THE MEDIA ] - A rare view of Venus
Plus Online Maths Magazine: News Story
[ PLANETARY MOTION ] [ TRANSIT ] [ VENUS ] - Flyby asteroid
Plus Online Maths Magazine: News Story
[ ASTEROID ] [ ASTEROID COLLISION ] [ ASTRONOMY ] [ DOPPLER SHIFT ] - Just a second
Plus Online Maths Magazine: News Story
[ ASTRONOMY ] [ TIME ]
- Fishy business
'Of the myriad strategems I employ to avoid useful work, the one I most enjoy is to envision how scientists of earlier eras would have made use of modern computers.' John L. Casti tells us how today's mathematicians are using computers to carry on the work of turn-of-the-century polymath d'Arcy Wentworth Thompson, who showed how mathematical functions could be applied to the shape of one organism to continuously transform it into other, physically similar organisms.
[ CATASTROPHE THEORY ] [ COMPUTER RECOGNITION ] [ INVARIANT POINT ] [ MATHEMATICS OF GROWTH ] - Modelling, step by step
Why can't human beings walk as fast as they run? And why do we prefer to break into a run rather than walk above a certain speed? Using mathematical modelling, R. McNeill Alexander finds some answers.
[ BIOMECHANICS ] [ KINETIC ENERGY ] [ MATHEMATICAL MODELLING ] [ POTENTIAL ENERGY ] [ WORK ] - Understanding the noise
Plus Online Maths Magazine: News Story
[ DNA ] [ GENETICS ] [ MARKOV PROCESS ] [ MATHEMATICAL MODELLING ] - Clever coiling
Plus Online Maths Magazine: News Story
[ DNA ] [ HELIX ] [ KNOT THEORY ] [ OPTIMAL SHAPE ] - Maths for the broken-hearted
Plus Online Maths Magazine: News Story
[ BIOLOGY ] [ CARDIAC ARREST ] [ MATHEMATICAL MODELLING ]
- Career interview: Business analyst
From Einstein to water power, Plus author Anita King explains where maths has got her.
[ ECONOMICS ] [ MANAGEMENT ]
- Pluschat
Plus Online Maths Magazine: Regular Item
[ MATHEMATICS EDUCATION ]
- Robots can't play tennis - yet
Plus Online Maths Magazine: News Story
[ ATTRACTOR ] [ LYAPUNOV STABILITY ANALYSIS ] [ ROBOTICS ] [ STABLE ATTRACTOR ] - Finding order in chaos
All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in chaos.
[ BUTTERFLY EFFECT ] [ DOUBLE PENDULUM ] [ GALILEO ] [ LAPLACE ] [ LORENZ ] [ NEWTONIAN MECHANICS ] [ PENDULUM ] [ PERIOD ] [ PLANETARY MOTION ] [ PREDICTION ] [ TOWN PLANNING ] [ WEATHER FORECASTING ] - Chaos in the brain
Saying that someone is a chaotic thinker might seems like an insult - but, according to Lewis Dartnell, it could be that the mathematical phenomenon of chaos is a crucial part of what makes our brains work.
[ DIFFERENTIAL EQUATION ] [ LORENZ ATTRACTOR ] [ PHASE SPACE ] [ STRANGE ATTRACTOR ] [ TRANSITION TO CHAOS ] - Chaotic crochet
Plus Online Maths Magazine: News Story
[ BUTTERFLY EFFECT ] [ LORENZ ] [ LORENZ EQUATIONS ] [ WEATHER ]
- Puzzle page
Plus Online Maths Magazine: Regular Item
[ CHESS ]
- Take a break
There are many errors that can occur when numbers are written, printed or transferred in any manner. Luckily, there are schemes in place to detect, and in some cases even correct, such errors almost immediately. Emily Dixon takes a break and discovers that codes are not just for sleuths.
[ BARCODE ] [ ERROR-CORRECTING CODE ] [ ISBN ] [ MODULAR ARITHMETIC ] [ NONCOMMUTATIVITY ] [ PERMUTATION ] - Calling all code crackers
Plus Online Maths Magazine: News Story
[ CRYPTOGRAPHY ]
- Mathematical mysteries: The Solitaire Advance
Plus Online Maths Magazine: Regular Item
[ ARITHMETIC ] [ ARITHMETICO-GEOMETRIC SERIES ] [ GEOMETRY ] [ STRATEGY ] - Mathematical mysteries: Painting the Plane
Plus Online Maths Magazine: Regular Item
[ PLANE COLOURING ] [ RAMSEY THEORY ] - Friends and strangers
Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. Imre Leader looks at the colourful world of Ramsey Theory.
[ COLOURING ] [ GRAPH THEORY ] [ RAMSEY NUMBER ] [ RAMSEY THEORY ] - Mathematical mysteries: What colour is my hat?
Plus Online Maths Magazine: Regular Item
[ ERROR-CORRECTING CODE ] [ GAME THEORY ] [ HAMMING CODE ] [ STRATEGY ] - Anything but square: from magic squares to Sudoku
Get on a commuter train these days and you can virtually see people's brains crunching away at filling the numbers from 1 to 9 into a square grid. As the Sudoku craze shows no sign of slowing, Hardeep Aiden investigates its relatives and predecessors.
[ LATIN SQUARE ] [ MAGIC SQUARE ] [ SUDOKU ]
- Kasparov defeated!
Plus Online Maths Magazine: News Story
[ CHESS ] [ COMPUTER CHESS ] [ DEEP BLUE ] - Using Java to enhance the WWW
Plus Online Maths Magazine: News Story
[ JAVA APPLET ] [ ONLINE MATHEMATICS RESOURCES ] - Cosmos launch
Plus Online Maths Magazine: News Story
[ COSMOLOGY ] [ SUPERCOMPUTER ] - What computers can't do
Mike Yates looks at the life and work of wartime code-breaker Alan Turing. Find out what types of numbers we can't count and why there are limits on what can be achieved with Turing machines.
[ ARTIFICIAL INTELLIGENCE ] [ CANTOR'S THEOREM ] [ DIAGONALISATION ARGUMENT ] [ HALTING PROBLEM ] [ THEORETICAL COMPUTING ] [ TURING MACHINE ] [ TURING TEST ] [ UNSOLVABILITY ] - Career interview: Games developer
Andrew Wensley works at Eidos Interactive, the company who publish the mega-successful computer game Tomb Raider, featuring 90s icon Lara Croft. Andrew is a long-term computer game fan with an academic background in maths. PASS Maths caught up with him at Eidos's Wimbledon offices.
[ COMPUTER GAMING ] [ GAME DESIGN ] - Prehistoric printer
Plus Online Maths Magazine: News Story
[ BABBAGE'S ENGINES ] [ HISTORY OF MATHEMATICS ] - Prize specimens
Last October, two mathematicians won £1m when it was revealed that they were the first to solve the Eternity jigsaw puzzle. It had taken them six months and a generous helping of mathematical analysis. Mark Wainwright meets the pair and finds out how they did it.
[ BAYES THEOREM ] [ COMPUTER SEARCH ] [ ETERNITY GAME ] [ PLANE GEOMETRY ] [ PROBABILITY ] [ TILING ] - Career interview: Systems administrator
Steve Traylen tells Plus about life as a Systems Administrator.
[ DYSLEXIA ] [ FOURIER ANALYSIS ] [ NUMERICAL ANALYSIS ] [ SIGNAL PROCESSING ] [ SYSTEMS ADMINISTRATION ] - Of prime importance
Plus Online Maths Magazine: News Story
[ GIMPS ] [ MERSENNE PRIME ] [ PRIME NUMBER ] - Why Was The Computer Invented When It Was?
Clearly the modern electronic computer couldn't have been built before electronics existed, but it's not clear why computers powered by steam or clockwork weren't invented earlier. Tom Körner speculates on the historical reasons why computers were invented when they were.
[ ALGORITHM ] [ ANALOGUE COMPUTER ] [ BABBAGE'S ENGINES ] [ MECHANICAL CALCULATOR ] [ TURING MACHINE ] - Charity begins @home
Plus Online Maths Magazine: News Story
[ DISTRIBUTED COMPUTING ] [ GIMPS ] - Career interview: Games developer
In the real world, balls bounce and water splashes because of the laws of physics. In computer games, a physics engine ensures the virtual world behaves realistically. Mathematician and computer programmer Nick Gray tells us about playing God in a virtual world.
[ COMPUTER ANIMATION ] [ COMPUTER GAMING ] [ COMPUTER GRAPHICS ] [ PHYSICS ENGINE ] - CAPTCHA if they can
Plus Online Maths Magazine: News Story
[ ALGORITHM ] [ ARTIFICIAL INTELLIGENCE ] [ THEORETICAL COMPUTING ] [ TURING TEST ] - Is now a good time?
Plus Online Maths Magazine: News Story
[ ATTENTIVE USER INTERFACES ] [ BAYESIAN MODEL ] [ POSTERIOR PROBABILITY DISTRIBUTION ] [ PRIOR PROBABILITY DISTRIBUTION ] - Open wide...
Plus Online Maths Magazine: News Story
[ CLOSED-SOURCE ] [ MATHEMATICAL MODELLING ] [ NETWORK ] [ NODE ] [ OPEN-SOURCE ] [ SCALE FREE NETWORK ] [ SOFTWARE DEVELOPMENT ] - Ada Lovelace - visions of today
Rachel Thomas looks at the life and work of pioneering woman mathematician Ada Lovelace, who foresaw computer-generated music and graphics, despite living long before the computer era.
[ ANALYTICAL ENGINE ] [ BERNOULLI NUMBER ] [ CHARLES BABBAGE ] [ DIFFERENCE ENGINE ] [ WOMEN IN MATHEMATICS ] - Matrix: Simulating the world
Plus Online Maths Magazine: Feature Article
[ COMPUTER ANIMATION ] [ COMPUTER PROGRAMMING ] [ COMPUTER SCIENCE ] [ COMPUTER SIMULATION ] [ EMERGENT BEHAVIOUR ] [ MATHEMATICAL MODELLING ] [ MATHEMATICAL MODELS ] - Perfect buildings: the maths of modern architecture
Plus Online Maths Magazine: Feature Article
[ ARCHITECTURE ] [ COMPUTER GRAPHICS ] [ COMPUTER PROGRAMMING ] [ COMPUTER SCIENCE ] [ COMPUTER SIMULATION ] [ GEOMETRY ] - Forever rich
Plus Online Maths Magazine: News Story
[ COMPUTER SCIENCE ] [ COMPUTER SEARCH ] [ ETERNITY GAME ] [ PROBABILITY ] [ PUZZLE ] - Machine prose
Plus Online Maths Magazine: News Story
[ COMPUTER SCIENCE ] [ GRAPH ] [ GRAPH THEORY ] [ LANGUAGE ]
- Cracking codes
In the first of two articles, Artur Ekert takes a tour through the history of codes and the prospects for truly unbreakable quantum cryptography.
[ BLETCHLEY PARK ] [ CAESAR CIPHER ] [ ENIGMA ] [ FREQUENCY ANALYSIS ] [ ONE-TIME PAD ] [ POLYALPHABETIC CIPHER ] [ SCYTALE ] [ SUBSTITUTION CIPHER ] [ VERNAM CIPHER ] - Exploring the Enigma
During the Second World War, the Allies' codebreakers worked at Bletchley Park to decipher the supposedly unbreakable Enigma code. Claire Ellis tells us about their heroic efforts, which historians believe shortened the war by two years.
[ ALAN TURING ] [ BLETCHLEY PARK ] [ ENIGMA ] - Cracking codes, part II
In the second of two articles, Artur Ekert visits the strange subatomic world and investigates the possibility of unbreakable quantum cryptography.
[ ACTION AT A DISTANCE ] [ CIPHER ] [ LOCAL REALISM ] [ QUANTUM CRYPTOGRAPHY ] [ QUANTUM ENTANGLEMENT ] - The dangers of cracking hash
Plus Online Maths Magazine: News Story
[ HASH ALGORITHM ] [ INTERNET SECURITY ]
- How the leopard got its spots
How does the uniform ball of cells that make up an embryo differentiate to create the dramatic patterns of a zebra or leopard? How come there are spotty animals with stripy tails, but no stripy animals with spotty tails? Lewis Dartnell solves these, and other, puzzles of animal patterning.
[ ANIMAL PATTERNING ] [ DIFFUSION ] [ MORPHOGENESIS ] [ PARTIAL DIFFERENTIATION ] [ PERTURBATION ] [ REACTION-DIFFUSION EQUATIONS ] [ SATURATION ] [ THRESHOLD ]
- Vaccination works
Plus Online Maths Magazine: News Story
[ DYNAMICAL SYSTEM ] [ FRACTAL ] [ JULIA SET ] [ MANDELBROT SET ] - A fat chance of chaos?
Plus Online Maths Magazine: News Story
[ DYNAMICAL SYSTEM ] [ FRACTAL ] [ JULIA SET ] [ MANDELBROT SET ]
- How to measure a million
Plus Online Maths Magazine: News Story
[ ECONOMICS ] [ MATHEMATICAL MODELS ] [ RISK ANALYSIS ]
- Decoding a war time diary
An account of how a prisoner of war's diary was recently decoded. Donald Hill wrote his diary in a numerical code, disguised as a set of mathematical tables, while in Hong Kong during and after the Japanese invasion of 1941.
[ FREQUENCY ] [ SUBSTITUTION CIPHER ] [ TRANSPOSITION CIPHER ] - Oops!
Plus Online Maths Magazine: News Story
[ COMPUTER PROGRAMMING ] [ SETI ] - Safety in numbers
Today's digital world with its free flow of information, would not exist without cryptography to guarantee our privacy. Plus meets mathematician, author and broadcaster Simon Singh to find out about the science of secrecy.
[ CAESAR SHIFT CIPHER ] [ CRYPTOGRAPHY ] [ DES ] [ KEY DISTRIBUTION PROBLEM ] [ RSA ] [ STEGANOGRAPHY ]
- Career interview - Electronic engineer
Geraldine Paxton, an electronics engineer, is a member of the Ford Motor Company Limited's graduate trainee scheme. Geraldine tells us about her work there, from driving cars on the German autobahns to ensuring production lines keep working. There's also salary information and a careers contact point.
[ ELECTRONICS ] [ STATISTICS ] - Pilgrims, planes and postage stamps
Practical problems often have no exact mathematical solution, and we have to resort to using unusual techniques to solve them. From navigation in the 17th century to postage stamps, see how this principle applies to a variety of real-life problems - and also learn how to use a piece of string to locate a German bomber!
[ ALGORITHM ] [ COMPUTER PROGRAMMING ] [ NUMERICAL ANALYSIS ] - Millennial wobbles
Plus Online Maths Magazine: News Story
[ BIOFEEDBACK LOOP ] [ OSCILLATION ] [ PHASE SYNCHRONISATION ] - Shaped by the wind
Plus Online Maths Magazine: News Story
[ TORQUE ] [ WIND RESISTANCE ] - Fuzzy pizza
Plus Online Maths Magazine: News Story
[ FOOD ENGINEERING ] [ FUZZY LOGIC ] [ QUALITY CONTROL ] - Career interview: Biomechanical engineer
Jose Munoz explains how engineering can allow you to explore the unknown, from understanding how mechanical structures bend to investigating the way genes affect the shape of embryos.
[ BIOMECHANICAL ENGINEERING ] [ GENES ] [ MATHEMATICAL MODELLING ] [ STRUCTURAL ENGINEERING ] - Outer space: Bridging that gap
Plus Online Maths Magazine: Regular Item
[ ENGINEERING ] [ QUADRATIC EQUATIONS ]
- Another proof for Fermat's last theorem
Plus Online Maths Magazine: News Story
[ FERMAT'S LAST THEOREM ]
- The Fields Medals 2006
Plus Online Maths Magazine: News Story
[ FIELDS MEDAL ] [ POINCARE CONJECTURE ]
- Career interview - Accountant
We talk to Tim Pilkington, a keen basketball player, who has a joint honours BSc in Maths, Physical Education and Sports Science from Loughborough University. Tim has worked as a mathematics teacher and is now working as an accountant.
[ ACCOUNTANCY ] [ MATHEMATICS EDUCATION ] [ TAX ] - Career interview - Actuarial Student
Find out about what it is like to work as an actuary with Watson Wyatt Partners Worldwide. There's also salary information and a careers contact point.
[ ACTUARIAL MATHEMATICS ] [ INSURANCE ] [ STATISTICS ] - Career interview: Financial modelling
David Spaughton and Anton Merlushkin work for Credit Suisse First Boston, where they provide traders in the hectic dealing room with software based on complicated mathematical models of the financial markets. PASS Maths interviewed them at their offices in Canary Wharf in London.
[ BLACK-SCHOLES EQUATION ] [ COMPUTER PROGRAMMING ] [ DERIVATIVE INSTRUMENT ] [ FUTURE ] [ MATHEMATICAL MODELLING ] [ OPTION ] - Ye banks and Bayes
Plus Online Maths Magazine: News Story
[ BAYES THEOREM ] [ CONDITIONAL PROBABILITY ] [ PROBABILITY ] - Have we caught your interest?
Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it - or so says a well-known source of financial advice. But what is compound interest, and why is it so important? John H. Webb explains.
[ COMPOUND INTEREST ] [ FUTURE VALUE ] [ GEOMETRIC SERIES ] [ LOGARITHM ] [ MACLAURIN SERIES ] [ PRESENT VALUE ] [ RULE OF 70 ] - Death and statistics
Actuarial science began as the place where two branches of mathematics meet: compound interest and observed mortality statistics. Financial planning for the future is therefore rooted firmly in the past. John Webb takes us through some of the mathematics involved, introducing us to some of the colourful characters who led the way.
[ ACTUARIAL MATHEMATICS ] [ ANNUITY ] [ ARITHMETICO-GEOMETRIC SERIES ] [ COMPOUND INTEREST ] [ MORTALITY TABLE ] [ PENSION ] [ PROBABILITY ] - Adam Smith and the invisible hand
Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.
[ ADAM SMITH ] [ ARROW'S THEOREM ] [ FREE MARKET ] [ GAME THEORY ] [ INVISIBLE HAND ] [ PRISONERS' DILEMMA ] [ SOCIAL CHOICE ] - Career Interview: Actuary
Actuaries use mathematics to model the real world, finding business solutions to the perennial problems thrown up by life's uncertainties. Kathy Byrne tells Plus about life as Actuarial Director of an Insurance Company.
[ ACTUARIAL MATHEMATICS ] [ GENERAL INSURANCE ] [ LIFE INSURANCE ] [ PENSION ] [ PRICING ] [ TRANSFER VALUE ] [ VALUATION ] - Rogue trading?
The dangers of trading derivatives have been well-known ever since they were catapulted into the public eye by the spectacular losses of Nick Leeson and Barings Bank. John Dickson explains what derivatives are, and how they can be both risky, and used to reduce risk.
[ ARBITRAGE ] [ CALL OPTION ] [ DERIVATIVE INSTRUMENT ] [ FORWARD CONTRACT ] [ HEDGING ] [ OPTION ] [ PREMIUM ] [ PUT OPTION ] [ STRIKE PRICE ] - Opinion
Plus Online Maths Magazine: Regular Item
[ BUDGET ] [ ECONOMIC PREDICTION ] [ PERCENTAGE ] [ TAX ] - The crystal ball
If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.
[ ACTUARIAL MATHEMATICS ] [ FORECASTING ] [ INSURANCE ] [ LIFE INSURANCE ] [ MATHEMATICAL MODELLING ] [ MATHEMATICS IN THE MEDIA ] [ MULTISTATE MODELLING ] [ PENSION ] [ STATISTICAL PREDICTION ] [ STOCHASTIC PROCESS ] - Career interview: Project finance consultant
Nick Crawley had recently set up his own financial consultancy firm in Sydney, Australia, offering advice on large-scale financing deals. He tells Plus about the challenges and rewards of working in an incentive-driven environment.
[ BLACK SCHOLES ] [ HEAT DIFFUSION EQUATION ] [ PARTIAL DIFFERENTIAL EQUATION ] [ PROJECT FINANCE ] - Career interview: Financial maths course director
Riaz Ahmad's mathematical career has led him from the complexities of blood flow to the risks of the financial markets via underwater acoustics. Plus found out how maths can explain all this and more.
[ DIFFERENTIAL EQUATIONS ] [ ECONOMICS ] [ FINANCIAL MATHEMATICS ] [ TEACHING ]
- Daniel Bernoulli and the making of the fluid equation
Daniel Bernoulli (1700-1782) discovered the relationship between the density of a fluid in a pipe, the speed it is travelling in the pipe and the pressure exerted by the fluid against the walls of the pipe. This is the story of what happened.
[ BERNOULLI EQUATION ] [ HISTORY OF MATHEMATICS ] - Understanding turbulence
Have you ever been in an aeroplane on a smooth flight when suddenly the plane bumps up and down for a short time as it goes through turbulent air? The study of turbulence is used to understand a range of phenomena from the simple squirting of a jet of water to the activity of the sun.
[ AERODYNAMICS ] [ BERNOULLI EQUATION ] [ COMPUTER SIMULATION ] [ LIFT ] [ NAVIER-STOKES EQUATIONS ] [ TURBULENCE ] [ VECTOR ] - Testing Bernoulli: a simple experiment
Here is an experiment that you can easily do yourself to test Bernoulli's equation. There are also 2 questions and answers.
[ BERNOULLI EQUATION ] [ BOTTLE EXPERIMENT ] [ CALCULUS ] [ LEAST SQUARES ] [ TURBULENCE ] - Long range forecast
Plus Online Maths Magazine: News Story
[ CHAOS ] [ FORECASTING ] [ METEOROLOGY ] [ STATISTICS ] - Career interview - Meteorologist
Read about what it is like to work at the Meteorological Office in this interview with Helen Hewson. There's also a contact point for careers information.
[ COMPUTER SIMULATION ] [ DIFFERENTIAL EQUATION ] [ METEOROLOGY ] [ NAVIER-STOKES EQUATIONS ] - Doing the twist
Plus Online Maths Magazine: News Story
[ BUTTERFLY EFFECT ] [ CHAOS ] [ METEOROLOGY ] [ TORNADOS ] - Probing the pint
Plus Online Maths Magazine: News Story
[ BUBBLE ] [ DRAG ] [ HYDROSTATICS ] - Career interview: Avalanche researcher
Jim McElwaine tells Plus how he combines his two loves - mathematics and mountaineering - in avalanche research.
[ AVALANCHE ] [ GRANULAR FLOW ] [ MATHEMATICAL MODELLING ] [ SIMULATION ] - Worldly wobbles
Plus Online Maths Magazine: News Story
[ ASTRONOMY ] [ CHANDLER WOBBLE ] [ MATHEMATICAL MODELLING ] - Prawn crackers
Plus Online Maths Magazine: News Story
[ BERNOULLI EQUATION ] [ BUBBLE ] [ CAVITATION ] - The buzz on bumblebees
Plus Online Maths Magazine: News Story
[ BUMBLEBEE PARADOX ] [ REYNOLDS NUMBER ] [ VISCOSITY ] - Going with the flow
Fluid mechanics is the study of flows in both liquids and gases, and is therefore enormously important in understanding many natural phenomena, as well as in industrial applications. Geophysicist Herbert Huppert tells us what happens when two fluids of different densities meet, for example when volcanos erupt and hot ash-laden air is poured out into the atmosphere.
[ GRANULAR FLOW ] [ GRAVITY CURRENT ] [ PARTIAL DIFFERENTIAL EQUATION ] [ PARTICLE-LADEN GRAVITY CURRENT ] [ PYROCLASTIC FLOW ] [ TURBIDITY FLOW ] [ VOLCANIC ERUPTION ] - Core business
Plus Online Maths Magazine: News Story
[ DYNAMO EFFECT ] [ GEOMAGNETISM ] [ MAXWELL'S EQUATIONS OF ELECTROMAGNETISM ] - Hardboiled detectives
Plus Online Maths Magazine: News Story
[ CENTRE OF GRAVITY ] [ FRICTION ] [ GYROSCOPE ] [ KINETIC ENERGY ] [ POTENTIAL ENERGY ] - Just a little turbulence
Plus Online Maths Magazine: News Story
[ DAMPING ] [ NAVIER-STOKES EQUATIONS ] [ QUANTUM TURBULENCE ] [ REYNOLDS NUMBER ] [ SUPERFLUID ] [ TURBULENCE ] [ VISCOSITY ] [ VORTEX ] - Career interview: Fluid mechanics researcher
André Léger studies the fluid mechanics of food travelling through the intestines for consumer goods giant Unilever.
[ CHEMICAL ENGINEERING ] [ INDUSTRIAL MATHEMATICS ] [ MATHEMATICAL MODELLING ] - A current problem
Frances Elwell looks at the eddies and currents, from the pungent problem of sewage outflow to the search for bodies of people who have fallen into rivers, explaining that fluid mechanics lies behind it all.
[ CURRENT ] [ EDDIES ] [ SINE WAVE ] [ WAVE ] - Ripped off at the beach
Plus Online Maths Magazine: News Story
[ NAVIER-STOKES EQUATIONS ] [ OCEAN RIPS ] - And now, the weather...
Plus Online Maths Magazine: News Story
[ FLUID MECHANICS ] [ FORECASTING ] [ MATHEMATICAL MODELLING ] [ METEOROLOGY ] [ NAVIER-STOKES EQUATIONS ]
- Career interview: Audio software engineer
Skot McDonald talks to Plus about how he uses mathematics to understand music, and how he managed to combine his passions for music and computing to create a successful career.
[ DIGITAL SIGNAL PROCESSING ] [ FOURIER ANALYSIS ] [ FREQUENCY ] [ HARMONIC SERIES ] [ MATHEMATICS AND MUSIC ]
- Outer space: Superficiality
Plus Online Maths Magazine: Regular Item
[ FRACTAL ] [ SURFACE ] [ VOLUME ] - Unveiling the Mandelbrot set
Plus Online Maths Magazine: Feature Article
[ COMPLEX DYNAMICS ] [ COMPLEX NUMBER ] [ FRACTAL ] [ JULIA SET ] [ MANDELBROT SET ] - The artist's fractal fingerprint
Plus Online Maths Magazine: News Story
[ FRACTAL ]
- What mathematicians get up to
After 5,000 years, the game of Nine Men's Morris has succumbed to the power of modern computing, plus other recent mathematical discoveries in the world of games.
[ COMPUTER PROGRAMMING ] [ GAME OF NO CHANCE ] [ RECREATIONAL GAME ] - Game theory and the Cuban missile crisis
Steven J. Brams uses the Cuban missile crisis to illustrate the Theory of Moves, which is not just an abstract mathematical model but one that mirrors the real-life choices, and underlying thinking, of flesh-and-blood decision makers.
[ CHICKEN ] [ MIXED STRATEGY ] [ NASH EQUILIBRIUM ] [ STABLE STRATEGY ] [ STRATEGY ] [ THEORY OF MOVES ] - Mathematical mysteries: Chomp
Plus Online Maths Magazine: Regular Item
[ STRATEGY ] - Mathematical mysteries: Survival of the nicest?
Plus Online Maths Magazine: Regular Item
[ ALTRUISM ] [ COOPERATION ] [ EVOLUTION ] [ ITERATED PRISONERS' DILEMMA ] [ PRISONERS' DILEMMA ] [ TIT FOR TAT ] [ TIT FOR TAT WITH FORGIVENESS ] - Games, Life and the Game of Life
When we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.
[ CELLULAR AUTOMATA ] [ GAME OF LIFE ] [ GO ] [ LOGIC ] [ LOGIC GATE ] [ SURREAL NUMBER ] - On the ball
If your team scores first in a football match, how likely is it to win? And when is it worth committing a professional foul? John Haigh shows us how to use probability to answer these and other questions, and explains the implications for the rules of the game.
[ FOOTBALL STRATEGY ] [ POISSON DISTRIBUTION ] [ PROBABILITY ] - Blast it like Beckham?
What tactics should a soccer player use when taking a penalty kick? And what can the goalkeeper do to foil his plans? John Haigh uses Game Theory to find the answers, and looks at his World Cup predictions from last issue.
[ DOMINATED STRATEGY ] [ FOOTBALL STRATEGY ] [ OPTIMAL STRATEGY ] [ PAYOFF MATRIX ] [ PENALTY TACTICS ] [ POISSON DISTRIBUTION ] - Love's a gamble
Plus Online Maths Magazine: News Story
[ EQUILIBRIUM ] [ GAME THEORY ] [ NASH EQUILIBRIUM ] [ PSYCHOLOGY ] - Game theory wins Nobel prize
Plus Online Maths Magazine: News Story
[ GAME THEORY ] [ NASH EQUILIBRIUM ] [ NOBEL PRIZE ]
- Mathematical mysteries: Kepler's conjecture
Plus Online Maths Magazine: Regular Item
[ HISTORY OF MATHEMATICS ] [ KEPLER'S CONJECTURE ] [ SPHERE PACKING PROBLEM ] [ THREE-DIMENSIONAL PACKING ] - The origins of fractals
The term fractal, introduced in the mid 1970's by Benoit Mandelbrot, is now commonly used to describe this family of non-differentiable functions that are infinite in length. Find out more about their origins and history.
[ CONTINUITY ] [ DIFFERENTIABILITY ] [ FRACTAL ] [ HILBERT SPACE-FILLING CURVE ] [ WEIERSTRASS' FUNCTION ] - Modelling nature with fractals
Computer games and cinema special effects owe much of their realism to the study of fractals. Martin Turner takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.
[ BROWNIAN MOTION ] [ FRACTAL ] [ FRACTAL FORGERY ] [ ITERATION ] [ MANDELBROT SURFACE ] [ VON KOCH CURVE ] - Time and motion
Whatever is so wonderful about point B that makes all the people at point A want to get there? Robert Hunt sits at point C, and muses on the problem.
[ GEODESIC ] [ GREAT CIRCLE ] [ LATITUDE ] [ LONGITUDE ] [ SCALAR (DOT) PRODUCT ] [ VECTOR ] - Mathematical Mysteries: Trisecting the Angle
Plus Online Maths Magazine: Regular Item
[ ANGLE TRISECTION ] [ CUBIC EQUATIONS ] [ PROOF ] [ TRIGONOMETRY ] [ WANTZEL'S LEMMA ] - Mathematical mysteries: How unilluminating!
Plus Online Maths Magazine: Regular Item
[ SNOOKER TABLE PROBLEM ] [ UNILLUMINABLE ROOM ] - Extracting beauty from chaos
Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
[ BIFURCATION ] [ CHAOS ] [ DYNAMICAL SYSTEM ] [ ERROR ] [ FRACTAL ] [ ITERATION ] [ LOGISTIC MAP ] [ LYAPUNOV EXPONENT ] [ MATHEMATICS AND ART ] [ ORBIT ] - 12:00 PMT?
Plus Online Maths Magazine: News Story
[ LONGITUDE ] [ MERIDIAN ] [ TIME ] - Jackson's fractals
Plus Online Maths Magazine: News Story
[ DIMENSION ] [ FRACTAL ] [ LOGARITHM ] [ MATHEMATICS AND ART ] [ VON KOCH CURVE ] - Fractal expressionism
In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. Richard P. Taylor explains that Pollock's patterns are really fractals - the fingerprint of Nature.
[ CHAOS ] [ DIMENSION ] [ FRACTAL ] [ LEVY FLIGHT ] [ LOGARITHM ] [ MATHEMATICS AND ART ] [ SCALING ] - Analemmatic sundials: How to build one and why they work
We've all seen a traditional sundial, where a triangular wedge is used to cast a shadow onto a marked-out dial - but did you know that there is another kind? In this article, Chris Sangwin and Chris Budd tell us about a different kind of sundial, the analemmatic design, where you can use your own shadow to tell the time.
[ ANGULAR DISTANCE ] [ DECLINATION OF THE SUN ] [ ELLIPSE ] [ PROJECTION ] [ SUNDIAL ] [ TRIGONOMETRY ] - Mathematical mysteries: Right angle race
Plus Online Maths Magazine: Regular Item
[ RIGHT ANGLE CONSTRUCTION ] - Double bubble is no trouble
Plus Online Maths Magazine: News Story
[ MINIMAL SURFACE ] [ NON-STANDARD BUBBLE ] [ ROTATION ] [ STABILITY ] [ VOLUME ] - How big is the Milky Way?
A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Toby O'Neil describes how the mathematical theory of dimension gives us a way of approaching the question.
[ BOX DIMENSION ] [ CANTOR DUST ] [ DIMENSION ] [ FRACTAL ] [ PROJECTION ] [ SCALING ] - From quasicrystals to Kleenex
This pattern with kite-shaped tiles can be extended to cover any area, but however big we make it, the pattern never repeats itself. Alison Boyle investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures.
[ APERIODIC TILING ] [ ESCHER ] [ PENROSE TILING ] [ PERIODIC TILING ] [ QUASICRYSTAL ] [ QUASIPERIODICITY ] [ TESSELLATION ] - On the dissecting table
Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.
[ CONGRUENCE ] [ CUT-AND-SHIFT PROOF ] [ DISSECTION PROOF ] [ HENRY PERIGAL ] [ HISTORY OF MATHEMATICS ] [ LATTICE TILING ] [ PYTHAGORAS' THEOREM ] [ PYTHAGORAS TILING ] [ TESSELLATION ] - Measure for measure
Can you imagine objects that you can't measure? Not ones that don't exist, but real things that have no length or area or volume? It might sound weird, but they're out there. Andrew Davies gives us an introduction to Measure Theory.
[ BANACH-TARSKI PARADOX ] [ CANTOR DUST ] [ CANTOR SET ] [ FRACTAL ] [ LEBESGUE INTEGRATION ] [ MEASURABILITY ] [ MEASURE THEORY ] [ RIEMANN INTEGRATION ] [ SIERPINSKI'S CARPET ] - Mathematical mysteries: Strange Geometries
Plus Online Maths Magazine: Regular Item
[ CURVATURE ] [ CURVATURE OF SPACE ] [ ESCHER ] [ EUCLID'S ELEMENTS ] [ EUCLIDEAN GEOMETRY ] [ FLATNESS ] [ HYPERBOLIC GEOMETRY ] [ MERCATOR PROJECTION ] [ SPHERICAL GEOMETRY ] [ TRIGONOMETRY ] - New designs from Africa
Paulus Gerdes takes us on a tour of the mathematical properties of some beautiful designs inspired by the traditional art of Angolan tribespeople.
[ AFRICAN PICTOGRAM ] [ DIAGONAL SYMMETRY ] [ MAGIC SQUARE ] [ MATRIX ] - Reflecting on extinction
Plus Online Maths Magazine: News Story
[ ENDANGERED SPECIES ] [ SYMMETRY ] - Putting it in