Why Should I study Mathematics?

Robert BowlesAdmissions TutorMathematicsUCL

Mathematicians are interested in solving problems.

• Goldbach’s Conjecture• Josephus Problem

Goldbach Conjecture (1690 - 1764)Is every even number > 2 the sum of two primes?

6 = 3 + 3 8 = 3 + 5 10 = 5 + 5

12 = 7 + 5 14 = 7 + 7 16 = 11 + 5

True up to 1,000,000,000,000,000,000

1960’s Chen proved that every even number > 2 is the sum of a prime and a product of two primes

n = p + q.r, some primes p, q, r.

Josephus Flavius• Josephus, an ethnic Jew and priest fought the

Romans in the Jewish- Roman War of 66-73 as a military leader in Galilee. After the Jewish garrison of Yodfat fell, the Romans invaded, killing thousands; the survivors committed suicide.

• In circumstances that are somewhat unclear, Jospehus found himself trapped in a cave with forty of his companions. The Romans asked him to surrender, but his companions refused to allow this. He therefore suggested a method of collective suicide: kill each other, one by one, counting to every third person.

• http://www.cut-the-knot.org/recurrence/flavius.shtml

• Jospehus then went and joined the Roman army went to Rome and became a historian of the Roman-Jewish wars.

• http://en.wikipedia.org/wiki/Josephus

• How did Josephus know where to stand?

• Derivative Pricing, Islamic Banking and Finance• Mathematical models of the brain, blood circulation

and the liver. The immune system. Models of the bladder.

• Gravitation and Cosmology, Quantum Gravity. Relativity

• Geophysics, Medical imaging, Cosmology, Financial market

• Marine ecosystems analysis. Ecology. Fisheries recovery

• Modelling of cancer and embryonic development• Fluid flow. Transition to turbulent flow. Acoustics, jet

engine noise, traffic noise• Plastics, moulding. Plastic bag manufacture. Foams• Aircraft and helicopter performance in icy conditions• Free surface flows. The perfect teapot.• Climate Prediction. Weather Prediction. Current

Prediction.• Atmospheric chemistry and pollutants• Sand dune motion• Capsizing ships

Applications of Mathematics

• Explosives Storage. Shaped charges.• Crime prediction and prevention• Droplets and splashing. Meteorite Impacts• Food sorting. Egg incubation. Greenhouse

harvests.• Medical imaging. MRI data of the human brain • Guidance to brain surgeons• Formula 1 race car design• Measurement of surgeons’ and hospital

performance. Health service management. Admissions planning.

• Melting and Freezing. Statistical Mechanics.• Security and Codes

• Groups, Number Theory, Combinatorics, Analysis, Geometry, Probability.

Applications of Mathematics

Mathematics at University

Methods, Algebra, Analysis, Applications

for 1½ years.

Some choice in year 2.

Lots of choice in years 3 and 4.

Careers

• A mathematics degree is extremely vocational and is highly valued by prospective employers

• Transferable skills – logical thinking, analytical and critical minds, problem-solving skills

Careers

• Finance and Commerce• Statistics• Computing and Information

Technology• Scientific Establishments –

Meteorological Office• Industry• Teaching• Further Study• Almost anything else

University Study

• Take Mathematics and Further Mathematics at A-level.