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Pre-sessional Mathematics and Statistics course

A 5-day introductory intensive course in Mathematics and Statistics.  The objective of this course is to give you the opportunity to revise or update your knowledge of those quantitative skills essential for success in your chosen degree.  The course will involve three hours of formal lectures and three hours of workshops a day.

Although you may have covered this material in your first degree, we would encourage you to make every effort to attend this introductory week.  It will also be an opportunity to settle in Durham, meet students and staff and be better prepared for the beginning of your formal tuition.  There is no extra tuition fee for this course but you will need to pay for accommodation, which can usually be arranged in one of the Durham colleges. You will be invited to enrol on the pre-sessional course once you have been made an offer of a place. 

Mornings are devoted to lectures, and afternoons to workshops, in which students will go through exercises with a tutor.

MATHEMATICS

Day 1

  1. Introduction
  2. Sets
    (a) Special Sets
    (b) Set Relations
    (c) Set Operations
    (d) Venn Diagrams
  3. Financial Mathematics
  4. Differentiation and Integration
    (a) Differentiation and Integration Rules
    (b) Partial Derivatives
    (c) Maxima and Minima
    (d) Taylor Series
    (e) Differential equations
    (f) Stochastic calculus
  5. Optimal Control Theory

Day 2

  1. Matrix Algebra
    (a) Notations and Definitions
    (b) Matrix Operations
    (c) Rules on Matrix Algebra
    (d) Determinants
    (e) Rules on Determinants
    (f) Linear Equations
    (g) Linear Dependence, Singularity and Rank
    (h) Eigenvalues and Eigenvectors

STATISTICS

Day 3

  1. Introduction
  2. Probability and random variables
  3. Probability density functions
  4. Statistical independence
  5. Characteristics of probability distributions
    (a) Expected value
    (b) Variance
    (c) Covariance

Day 4

  1. The correlation coefficient
  2. The normal distribution
  3. Higher moments of probability distributions

Day 5

  1. Other important probability distributions:
    (a) The chi-square distribution
    (b) The t distribution
    (c) The F distribution
    (d) Lognormal distribution and its properties
  2. Statistical inference
    (a) Point estimation
    (b) Interval estimation

Extra material: Small sample properties of estimators

 

Suggested reading Appendix A of Gujarati (2003) Basic Econometrics (4th edition), McGraw-Hill, New York. [Note: this is also one of the main recommended texts for the FMBF and Econometrics modules].