Introductory description

FP014-30 Mathematics for Finance

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Pure Mathematics

• Equations and Inequalities
  (solving and applying linear, quadratic, and simultaneous equations/inequalities)
• Straight Line Graphs
  (relationship between an equation and its graph; gradients, parallel and perpendicular lines)
• Exponentials and Logarithms
  (laws of indices, surds and logarithms; solving exponential equations; e and ln)
• Functions and Sketches
  (domain and range; composite and inverse functions; graph sketching techniques)
• Vectors and Matrices
  (vector properties and arithmetic; dot product and perpendicular vectors; matrix operations; 2x2 determinants and inverse matrices; solving systems of equations)
• Differentiation
  (finding derivatives of polynomials, reciprocals, exponentials, logarithms and trigonometric functions; gradients of curves and stationary points; the chain, product and quotient rules)
• Integration
  (indefinite integration as a reverse of differentiation; evaluation of definite integrals)
• Numerical Methods
  (determining whether a solution exists in a given range; use methods such as interval bisection and Newton-Raphson to approximate solutions)
• Sequences and Series
  (making calculations involving arithmetic and geometric series, including sums to infinity)
• Expansions
  (using binomial, Maclaurin and Taylor series formulae to approximate functions)

Statistics and Probability

• Summarising Data
  (calculating/estimating measures of location (averages and quartiles) and deviation (spread) from data provided in a list or frequency table).
• Representing Data
  (drawing and interpreting box plots; using frequency density to interpret histograms; how to represent data appropriately, including when to use a particular type of graph or chart).
• Correlation and Regression
  (calculating and using the product moment correlation coefficient and least squares regression line for a set of bivariate data)
• Probability
  (simple theoretical and experimental probability including sample spaces; Venn diagrams; tree diagrams with independent or conditional events; and expected outcomes)
• Binomial and Poisson Distribution
  (identifying Binomial and Poisson situations, and using the formulae to calculate probabilities)
• The Normal Distribution
  (using given tables to find standard Z probabilities; converting to general normal distributions)
• Confidence Intervals
  (calculating confidence intervals for means and proportions, using various confidence levels)
• Hypothesis Testing
  (testing one-tailed and two-tailed hypotheses for population means and proportions; conducting a chi-squared test on some categorical data)

Learning outcomes

By the end of the module, students should be able to:

• Solve a variety of mathematical problems by selecting appropriate logical methods and implementing them precisely and rigorously to arrive at correct numerical or algebraic results.
• Undertake basic analyses of data by calculating summary statistics and representing data graphically, taking into account the suitability and limitations of different statistical measures and graph types.
• Use fundamental principles of probability to quantify uncertainty, and solve problems involving a selection of discrete and continuous probability distributions.
• Present written mathematical and statistical work clearly and logically.
• Apply mathematical and statistical knowledge to a variety of real-world contexts, selecting appropriate algebraic tools and statistical models where necessary.
• Interpret the meaning of calculated results within a given context, and use them to inform decision-making.
• Utilise technology such as a calculator or spreadsheet software to perform numerical calculation accurately.

Indicative reading list

Mathematics and Statistics for Business, Management and Finance (Swift, 1997)

Pure Mathematics:
Mathematics for economics and finance: methods and modelling (Anthony and Biggs, 1996)
Elements of Mathematics for Economics and Finance (Mavron and Phillips, 2010)

Statistics:
Probability and Statistics for Finance (Fabozzi et al, 2011)
Statistics for Economics, Accounting and Business Studies (Barrow, 2017)

View reading list on Talis Aspire

Subject specific skills

No subject specific skills defined for this module.

Transferable skills

No transferable skills defined for this module.