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Mathematics at University and beyond

Prof. James Hirschfeld

Department of Mathematics

University of Sussex

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Why study mathematics?

historysociology

english literatureart history

music

biologyfrench

sport science

geography

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Because...

you love it it's interesting it's easy it's a conversation stopper it's beautiful it's difficult

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Other good reasons...

5 years after graduating those with mathematics degrees earn more on average than any other graduates.

96% of 1996/97 mathematics graduates are now employed, higher than any other subject apart from medicine and dentistry.

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What type of jobs do mathematicians go into?

• Teaching• Actuary• Programmer• Accountant• Banker• Civil servant• Mathematical finance• Postgraduate study: MSc, PhD

Mathematics at University

What do you study? Calculus: differentiation/integration in higher dimensions Algebra/Geometry: vectors/matrices/lines/planes/conic sections Analysis: sequences/series/limits/convergence Computer programming: Matlab/Maple Many other interesting things

How do you learn?

Number of contact hours A typical term contains: 4 courses A typical week for each course consists of: 3 hours of lectures 1 hour exercise class Additional contact hours per week: 1 hour tutorial Office hours (2x1 hour)

Which University to choose?

Entry requirements Quality of teaching and support• National Student Survey

• Quality Assurance Agency

Location• The campus

• The city

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Interesting applications

of Mathematics• Special effects in films

• Pattern formation in nature

• Digital photography

• Medical imaging

Mathematics in the Movies Maths is used in creating many special effects

In order to create realistic animations of smoke, water and firecomplicated systems of equations (see next slide) need to be solved

Pirates of the Caribbean

Harry Potter and the Goblet of Fire

Finding Nemo

The Navier Stokes Equations

∂u + 1 ∆u + u · ∇u + ∇p = 0 in Ω x (0,T),

∇ · u = 0 in Ω x (0,T),

t

− ∂ Re−

Here u(x,y,z,t)=(u ,u ,u ) is a vector field

denoting the fluid’s velocity

p=p(x,y,z,t) is a scalar field denoting pressure

1 2 3

(a system of nonlinear partial differential equations)

∇ is the vector differential operator del or nabla

∆ = ∇ · is the scalar differential operator ∇ Laplacian

When Toy Story was made in 1999 simple,

hard, plastic toys were used in the

animations

Maths is used in the making of animated movies

By 2001 when Monsters Inc was

made advances in maths helpedenable the animation of more

visually rich human-like characters

Maths is used in animations to morph one shape into another

Mathematical Biology:

pattern formation

By solving relatively simple equations on complicated domains you can obtain many naturally occurring pattern formations

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Spots or stripes?Changing the domain but keeping the coefficients fixed gives rise to different patterns

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Slightly changing the coefficients in the equation but keeping the domain fixed also gives different patterns

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Image processing: maths is used in removing noise from digital

camera photos

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Similarly MRI scans include random noise which needs to be

smoothed out

Mathematical model of a human

heart

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.