1. 1 Mathematics at University and beyond Prof. James Hirschfeld Department of Mathematics University of Sussex

2. 2 Why study mathematics? history sociology english literature art history music biology french sport science geography

3. 3 Because...  you love it  it's interesting  it's easy  it's a conversation stopper  it's beautiful  it's difficult

4. 4 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.

5. 5 What type of jobs do mathematicians go into? Teaching Actuary Programmer Accountant Banker Civil servant Mathematical finance Postgraduate study: MSc, PhD

6. Mathematics at University

7. 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

8. How do you learn?

9. 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)

10. Which University to choose?  Entry requirements  Quality of teaching and support National Student Survey Quality Assurance Agency  Location The campus The city

11. 11 Interesting applications of Mathematics Special effects in films Pattern formation in nature Digital photography Medical imaging

12. Mathematics in the Movies  Maths is used in creating many special effects In order to create realistic animations of smoke, water and fire complicated systems of equations (see next slide) need to be solved Pirates of the Caribbean Harry Potter and the Goblet of Fire Finding Nemo

13. 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 123 (a system of nonlinear partial differential equations) ∇ is the vector differential operator del or nabla ∆ = ∇ · ∇ is the scalar differential operator Laplacian

14. 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 helped enable the animation of more visually rich human-like characters

15.  Maths is used in animations to morph one shape into another

16. Mathematical Biology: pattern formation By solving relatively simple equations on complicated domains you can obtain many naturally occurring pattern formations

17. 17 Spots or stripes? Changing the domain but keeping the coefficients fixed gives rise to different patterns

18. 18 Slightly changing the coefficients in the equation but keeping the domain fixed also gives different patterns

19. 19 Image processing: maths is used in removing noise from digital camera photos

20. 20 Similarly MRI scans include random noise which needs to be smoothed out

21. Mathematical model of a human heart