1. Lecture 1: Jobs and Mathematics

2. Jobs in mathematics Q What type of jobs are there in mathematics?
Q Why are they interested in mathematicians?

3. Conclusion
Employers are interested in your mathematical skills which can be applied in a wide variety of situations.

4. Goal of this course
As you go through your university degree and learn mathematics, ask yourself constantly,
Q How can the maths I learnt help me understand the world?
Q How can the maths I learnt be applied to real-world problems?

5. Mathematical modelling
Mathematical modelling is about finding mathematical principles which can be used to describe and analyse real-world phenomena.
One of the goals of this course is practice this skill.

6. Simple example of modelling
Q: I borrow $ at 1% per month interest, and pay it back at $1500 per month. How long does it take to pay off?
Model: pn= amount owed after n months
p0=
pn+1= 1.01 pn
New mathematical Q: Solve for n such that pn=0.

7. Mathematical solution
p1= 1.01 p
p2= 1.01 p = 1.01( 1.01 p )
= 1.012p ( )
p3= 1.01 p = 1.013p ( )
……………..
pn = 1.01np (1.01n-1 + … )
= 1.01np (1.01n-1)/(1.01-1)

8. solution continued If pn=0 then 1.01n x 120 000= 150 000 (1.01n-1)
n log 1.01 = log 5
n =
It takes 162 months to repay the loan.

9. Modelling in this module
In this case, maths provides an exact model which gives a precise answer.
Though maths cannot always completely describe real-world phenomena, it is often still useful in understanding the world around us.
The main assessment task in this module involves a project where you should analyse mathematically some real-world phenomenon of this sort. This is an exercise in applying whatever mathematics you know.

10. On the project
Look at the course information sheet for details concerning the project, but here are some important deadlines:
Decide on your teams and a project topic in the next few weeks.
Give a 1 page plan and quick oral presentation in week 6.
Hand in your written report in week 11
Final oral presentations will be in weeks 9-13.