Undergraduate Programme and Module Handbook 2022-2023 (archived)

# Module MATH1597: Probability I

## Department: Mathematical Sciences

### MATH1597: Probability I

Type | Open | Level | 1 | Credits | 10 | Availability | Available in 2022/23 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.

#### Corequisites

- Calculus I (Maths Hons) (MATHNEW1) or Calculus I (MATH1061)

#### Excluded Combination of Modules

- Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.

#### Aims

- This module will give an introduction to the mathematics of probability.
- It will present a mathematical subject of key importance to the real-world ("applied") that is nevertheless based on rigorous mathematical foundations ("pure").
- It will present students with a wide range of mathematical ideas in preparation for more demanding and specialized material later.

#### Content

- A range of topics are treated each at an elementary level to give a foundation of basic concepts, results, and computational techniques.
- A rigorous approach is expected.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will:
- be able to solve a range of both routine and more challenging problems in probability theory.
- be familiar with the basic mathematical concepts of probability theory.
- have a broad knowledge of the subject area demonstrated by detailed familiarity with the following topics:
- set theoretic framework for sample spaces and events, including notions of countable and uncountable sets;
- event calculus, probability axioms, conditional probability, Bayes's formula, independence of events;
- discrete and continuous random variables and their distributions, including particular familiarity with the binomial, Poisson, normal and exponential distributions;
- joint distributions, conditional distributions, and independence of random variables;
- expected value of a random variable, variance, covariance, and moment generating functions;
- tail inequalities, the weak law of large numbers, and the central limit theorem.

Subject-specific Skills:

- Students will have basic mathematical skills in the following areas: modelling, abstract reasoning, numeracy

Key Skills:

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Tutorials provide active engagement and feedback to the learning process.
- Students are expected to develop their knowledge and skills with at least 50 hours of self-study.
- Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills. They are also an aid in developing students' awareness of standards required.
- Initial diagnostic testing and associated supplementary problems classes fill in gaps related to the wide variety of syllabuses available at Mathematics A-level.
- The examination provides a final assessment of the achievement of the student.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 27 | 3 pw in wks 1-3, 5, 7, 9; 2 pw in wks 4, 6, 8, 10; 1 revision in wk 21 | 1 Hour | 27 | |

Tutorials | 5 | 1 pw in wks 3, 5, 7, 9; 1 revision in wk 21 | 1 Hour | 5 | ■ |

Problems Classes | 4 | 1 pw in wks 4, 6, 8, 10 | 1 Hour | 4 | |

Support classes | 9 | 1 pw in wks 2-10 | 1 Hour | 9 | |

Preparation and Reading | 55 | ||||

Total | 100 |

#### Summative Assessment

Component: Continuous Assessment | Component Weighting: 10% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Fortnightly electronic or written assessments during the first 2 terms. Normally, each will consist of solving problems and will typically be one to two pages long. Students will have about one week to complete each assignment | 100% | ||

Component: Probability Examination | Component Weighting: 90% | ||

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 2 hours | 100% | Yes |

#### Formative Assessment:

Fortnightly written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students. Students will have about one week to complete each assignment. A 45-minute Collection paper at the beginning of Epiphany term.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University