Unit name | 1AS Further Statistics |
---|---|

Unit code | MATH10001 |

Credit points | 20 |

Level of study | C/4 |

Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |

Unit director | Dr. Porter |

Open unit status | Open |

Pre-requisites |
Strictly Mathematics 1A20 (MATH11004)only. |

Co-requisites |
None. |

School/department | School of Mathematics |

Faculty | Faculty of Science |

**Unit aims**

To introduce and develop skill in the linear algebra and basic statistics needed to study the sciences at degree level.

The linear algebra section deals with vectors, matrices and eigenvalues (which are fundamental to atomic physics, molecular chemistry, computational graphics, and many other branches of science and engineering).

The last section of the unit provides a short introduction to the aspects of statistics of most interest and importance to scientists, covering the basics of probability, statistical distributions, hypothesis testing, regression etc. No previous statistical knowledge will be assumed.

**Syllabus**
The numbers of lectures (shown in brackets) are a rough guide only.

Linear algebra, 16 lectures 1.Matrices and vectors. Definition and motivation. What are they good for ? 2.Vectors. Addition and scaling, linear independence, bases. Dot product. Orthonormal sets. Cross product. Triple products. Lines and planes. 3.Matrices. Basic algebra, inverses. Determinants, geometrical interpretation, calculation of determinants. 4.Systems of linear equations. The geometry of solutions. 5.Eigenvalues, calculation for 2 x 2 and 3 x 3 case by the characteristic equation. Completeness of eigenvectors. Eigenvalues and eigenvectors of symmetric matrices. Applications.

Basic Statistics, 17 Lectures

Probability: The use of probability in everyday life and in scientific modelling. Exploratory methods: plotting data, structure exposed by suitable plots, log-log plots, outliers.

Probability models: Use of probability to model observed phenomena. Discrete variables: The Binomial distribution, the Poisson distribution Continuous variables: The Normal distribution: its uses and misuses.

Inference: Hypothesis testing and confidence intervals: What is a p-value? One- and two-sided tests. Standard errors. One and two sample t-tests, One-way Analysis of Variance.

Regression: Dependence and independence. Linear regression and correlation. Percentage of variability explained.

**Relation to Other Units**

The Linear algebra section is shared with the unit Mathematics 1AM. The statistics section is shared with the unit Mathematics 1ES. The unit carries on the teaching in Mathematics 1A20 (MATH11004).

After taking this unit, students should have: -a good understanding of single-variable calculus, as far as Taylor series, techniques for solving simple differential equations and working with Fourier series, -a basic familiarity with vectors and matrices, including eigenvalues and eigenvectors, -an insight into the value, use and interest of statistical methods in scientific work and thought, -the ability to apply simple statistical methods in their own scientific work and understand what they are doing, -an understanding of the statistical jargon used in scientific papers.

The Linear Algebra course is based on lectures supported by problems classes and tutorials on how to apply the techniques in solving problems.

The lecturer will distribute problem sheets based on the work done in lectures, and will set specific problems which you will be required to hand in to tutors for marking. From week 2 or 3 of the course, students will attend weekly tutorials in which homework questions and additional problems will be covered.

The Basic Statistics course is based on lectures and practical sessions in the Computing Laboratory on the ground floor of the School of Mathematics. You should tackle the worksheets in the practical sessions for the week in which the sheet is given out.

One examination worth 50%. 50% statistics coursework.

Recommended for the calculus and linear algebra parts of the unit, but not essential:

Jordan, D.W. & Smith, P. Mathematical Techniques: An introduction for the engineering, physical, and mathematical sciences (4th edition), Oxford University Press, Oxford, 2008.

Recommended for statistics, but not essential:

Gerald Keller, Applied Statistics with Microsoft Excel, published by Duxbury.