Unit name | Probability 1 |
---|---|
Unit code | MATH11300 |
Credit points | 10 |
Level of study | C/4 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Professor. Balazs |
Open unit status | Not open |
Pre-requisites |
An A in A-level Mathematics or equivalent. |
Co-requisites |
Analysis 1 (MATH11006) and Calculus 1 (MATH11007), or equivalent. |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Unit aims
To introduce the basic ideas and methods of Probability, developing the concepts of random variables, expectations and variances. To look at some simple applications of these ideas and methods.
General Description of the Unit
Probability is an everyday concept of which most people have only a vague intuitive understanding. Study of games of chance, such as tossing dice and card games, resulted in early attempts to formalise the theory; but a satisfactory rigorous basis for the subject only came with the axiomatic theory of Kolmogorov in 1933. Today probability is a well established and actively researched area of mathematics with lively links to Analysis, Combinatorics, Functional Analysis, Game Theory, Geometry, Mathematical Physics, Statistics. It also serves as a very important basis which various disciplines build on (Biology, Computer Science, Economics, Engineering, Linguistics, Physics, Sociology, just to mention a few).
The unit starts with the idea of a probability space, which is how we model the outcome of a random experiment. Probability models are then introduced in terms of random variables (which are functions of the outcomes of a random experiment), and the simpler properties of standard discrete and continuous random variables are discussed. Motivation is given for studying the common quantities of interest (probabilities, expected values, variances and covariances). Finally techniques are developed for evaluating these quantities, including generating functions and conditional expectations.
Relation to Other Units
This unit provides the foundation for all probability and statistics units in later years.
Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html
When you have successfully completed this module you will be able to:
Transferable Skills
Model building. Especially the formal mathematical modelling of informal descriptions of events and processes.
Lectures supplemented (for first year students) by small group tutorials. Weekly problem sheets, with outline solutions handed out the following week.
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
Reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html