Diploma in Actuarial Science
Self-Study Guidance
This is based on information provided to new students by the UK Actuarial
Profession.
All students are expected to have the following mathematical skills and
knowledge before commencing the course. Although we may introduce some
brief revision of the material, none of this is taught and students who don’t have
the requisite probability and statistics background should not expect to be able
to complete every module.
Pre-calculus:
A
B
C
D
Permutations & combinations; expansion of (a+x)ⁿ
Using the sigma notation to express the sum of a series
Summing the terms of an arithmetic progression and a geometric progression
Interpolation and local approximation
Elementary calculus:
A
B
C
D
E
F
G
The idea of a limit
Differentiation of polynomial, exponential and logarithmic functions
Product, quotient and “function of a function” rules for differentiation
Definite and indefinite integration of polynomial and exponential functions
Area under a curve
Methods of numerical integration
Integration by substitution and by parts
More advanced calculus:
A
B
C
D
E
F
G
Higher order derivatives
Finding turning points of simple functions with polynomial and exponential terms,
curve sketching
Maximisation under constraints: method of Lagrange multipliers
Taylor’s theorem; power series expansion for exp(x)
Differentiation of definite integrals: Fundamental Theorem of the Calculus
Solving first order differential equations: exact, separable (including logistic),
linear
Second order differential equations with constant coefficients: complementary
function and particular integral
Calculus of two variables:
A
B
C
Partial derivatives of functions of two variables
Maxima and minima of functions of two variables
Double integrals and changing the order of double integrals
Algebra:
A
B
C
D
E
F
Matrix addition and multiplication
Determinant and inverse of a square matrix
Using matrices and vectors to represent linear equations
Solving simultaneous linear equations
Complex numbers
Linear difference equations with constant coefficients
Probability:
A
B
C
D
E
F
G
Sample spaces, events
The probability of an event
Basic rules of probability
Conditional probability
Independent events
Bayes Theorem
Tree diagrams
*we recommend that students who don’t know this material don’t register for the
Stochastic Modelling and Financial Economics 2 modules.
Statistics:
A
B
C
D
E
F
Diagrams and displays
Summary measures of level and variability (including standard deviation)
Random variables
Expectation
Binominal and Poisson distributions
Normal (Gaussian) distribution
Recommended Text Books for Revision/Self-Study
The “Schaum Outline” series from McGraw Hill is good for the fundamentals of
mathematics (ask in your bookshop or library – or visit the website www.schaums.com)
In particular:
Advanced Calculus by Wrede & Spiegel
Probability & Statistics by Spiegel, Schiller & Srinavasan.
Other recommended books include:
Elementary analysis: the theory of calculus: Ross: Springer
A concise introduction to pure mathematics: Leibeck: Chapman & Hall
Calculus with analytic geometry: Fraleigh: Addison Wesley
Fundamentals of university mathematics: McGregor et al: Albion
Miller & Miller: John E Freund’s Mathematical Statistics: Prentice Hall
Essential Statistics: Rees: Chapman & Hall.