SujitsMathsTalks _ www.bit.ly/taiho123

Mathematics, Actuarial
Science and Statistics
University of Southampton
Dr Sujit Sahu
School of Mathematics


School of Mathematics
• Large student centred school
• Expertise across mathematical
physics, applied mathematics,
operational research, pure
mathematics and statistics
• Active links with business,
industry, science and technology
• A centre for interdisciplinary
research and teaching
• Large graduate school with three
thriving MSc programmes and
many research students
2


Mathematics students
• 550 MMath & BSc students
• 85 MSc students
• 48 PhD students

3

Teaching & Assessment
• Lectures
• Tutorials
• Supervisions
• Computing Labs
• Consolidation
Class

• Exams
• Coursework
• Projects
• Presentations
• In-class tests

• Private study
4


Course structure

Topology

Hyperbolic Geometry
Simulation and Queues

Mathematical Programming
Design and Analysis of Experiments

Algebra
Number Theory and Cryptography

Analysis
Relativity, Black Holes and Cosmology
Calculus
Differential Equations
Gravitational Waves
Geometry
Mathematical Modelling
Metric Spaces
Probability and Statistics

Applications of Mathematics in Biology

Mathematical Finance

Rings and Fields

Optimization

Differential Geometry and its Applications

Complex Function Theory

Groups and Symmetry

5


Programmes of Study
• Single Honours:

• Mathematics for Arts:

– BSc: Mathematics

– Mathematics with Music

– MMath: Mathematics

– Mathematics and French, German, Spanish

– BSc: Mathematical Studies

• Mathematics for Business:
– Mathematics with:

• Mathematics for Science:

– Actuarial Science, Economics, Finance – Mathematics with:
– Management Sciences, Statistics,

– Astronomy, Biology

– Operational Research, Computer Science– Physics, Computer Science
6


Some money making ideas with Mathematics
• Google search

• Linear Algebra

• Pricing financial options

• Differential Equations

• iPod and MP3

• Analysis

• “Green logistics”
• Formula 1 pit stop strategies
• Financial Portfolios
• Encryption of credit cards
• Airline pricing

• Operational Research
• Optimization
• Statistics
• Number Theory
• Linear Programming


Mathematics with Actuarial Science
• Our most popular programme!
• Lets learn a bit more about it!


Actuarial Science
Why choose Mathematics with Actuarial Science?
•

Actuarial Studies focus on the study of Mathematics and
Statistics integrated with:

•

Economics,

•

Finance,

•

Demography and

•

Actuarial Science

• For most people the excellent career prospects are the main
reason for choosing Mathematics + Actuarial Science


EXAMPLES OF ACTUARIAL SCIENCE
QUESTIONS
• Mr Patel is 65 and had a heart attack 3 years ago – how much
should his travel insurance to the USA for 2 weeks cost?
• How many children in India will require elementary
schooling in 2015?

• Could health insurance for my pet cat be included free as part
of my house insurance?
• How much will it cost if it rains at the Olympics in 2012?
• How much funding should the Indian Government put aside
for building new roads for the next 10 years?


TEST YOURSELVES……..
• Should health insurance be cheaper or more expensive for smokers?
MUCH CHEAPER
• How old do you have to be to have a 50% chance of dying in the next 6
months?
103
• If you are 80 what chance do you have of living until 81?
97%


How much do Actuaries earn?
• Lots!
• Typical Actuarial salaries start at about £60,000 (Rs 48 Lakh)
• Many Actuaries earn well over £150,000 (Rs 1.2 Crore!)
• The profession is very carefully regulated
• It also has a high professional profile
• And high professional standards
• -Actuaries are needed worldwide


Does India need more Actuaries?
• There are about 6000 professional actuaries for 6 crore
UK citizens.

• There are about 100 crore Indians. How many actuaries
are needed?
• See an article in rediff.com: For a 7-figure salary, be
an actuary
• Many banks such as HSBC will pay very highly to
Southampton graduates.
• Southampton is a brand name!


Top ten subjects studied by new entrants to the
Actuarial profession in 2004-7
Mathematics

350

Actuarial Science

198

Mathematics and other

89

Mathematics and Statistics

53

Economics

43

Statistics

29

Physics

31

Actuarial Maths and Statistics

30

Actuarial Science and Statistics 26
Mathematical Science

23


How does the system of exemptions work?
• One of the major attractions of a Mathematics with Actuarial
Science programme is the “exemptions”
• The professional examinations to become a fully-qualified
Actuary are long and difficult
• If a degree programme grants exemptions from some of
these then it may be possible to qualify as an Actuary much
quicker than normal
• A Southampton Maths with Actuarial Science graduate can
earn the maximum number of exemptions!

Exemptions from Actuarial Professional
Examinations
The new examination structure consists of:
• 8 exams at Core Technical stage (CT1 to CT8)
• 3 exams at Core Applications stage (CA1 to CA3)
• 2 exams at Specialist Technical stage (2 from ST1 to ST6)
• 1 exam at Specialist Application stage (1 from SA1 to SA6)
A total of 14 examinations must therefore be passed to qualify as an
Actuary.
Exemption from some of the Specialist exams by undertaking a course
of study or a research dissertation as an alternative is now possible.


Actuarial Professional Examinations: CT stage
CT1 Financial Mathematics
CT2 Finance and Financial Reporting
CT3 Probability and Mathematical Statistics
CT4 Models
CT5 Contingencies
CT6 Statistical Methods
CT7 Economics
CT8 Financial Economics


Agreement with the IoA
It has been agreed with the Institute of Actuaries that students achieving a
suitable performance in certain units will get an exemption from the
corresponding subject in the professional examinations.
A maximum of 8 exemptions out of the 8 CT stage units is possible

THE SOUTHAMPTON PROGRAMME OFFERS ALL 8
EXEMPTIONS
This means that after completing our programme you would be
over half way to qualifying as an actuary


What about Statistics?
“All knowledge is, in final analysis, history.
All sciences are, in the abstract, mathematics.
All judgements are in, in their rationale, statistics.”
Prof C. R. Rao


What is Statistics?
• Statistics is the scientific application of mathematical
principles to the collection, analysis, and presentation of
numerical data, and the interpretation of the results.
• Statisticians provide crucial guidance in determining what
information is reliable and which predictions can be trusted.
They often help search for clues to the solution of a scientific
mystery and sometimes keep investigators from being misled
by false impressions.
• Many economic, social, political, and military decisions
cannot be made without statistical techniques, such as the
design of experiments to gain government approval of a newly
manufactured drug.


What Do Statisticians Do?


Produce trustworthy data

 Analyse data to make their meaning clear
 Draw practical conclusions from data
Principles of 4-R’s: Reading, wRiting, aRithmetic and
 “Reasoning under Uncertainty”


Job Characteristics
• Use data to solve problems in a wide variety of fields
• Apply mathematical and statistical knowledge to social, economic, medical,
political, and ecological problems
• Work individually and/or as part of an interdisciplinary team
• Travel to consult with other professionals or attend conferences, seminars,
and continuing education activities
• Advance the frontiers of statistics, mathematics, and probability through
education and research
• If you enjoy any of these, a career in statistics may be right for you!


Examples of Statistics Careers
 Medicine
Search for improved medical treatments based on carefully designed
experiments.
 Environment
Produce data on the abundance and location of plants and animals, on
the spread of pollution from its sources, and on the possible effects of
changes in human activities.
 Industry

Maintain quality of goods and services and the efficiency with which
they are produced and delivered.
 Government Surveys
How many people are unemployed this month? What do we export to
China, and what do we import? Are rates of violent crime increasing or
decreasing?


What do I do as a Statistician?
• Sulfate pollution map of the Eastern US in 2001


Annual map for the North Atlantic Ocean