Undergraduate Programme and Module Handbook 2023-2024

# Module MATH3071: DECISION THEORY III

## Department: Mathematical Sciences

### MATH3071: DECISION THEORY III

Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2023/24 | Module Cap | Location | Durham |
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#### Prerequisites

- Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061), Probability I (MATH1597) and Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra I (MATH1071).

#### Corequisites

- None.

#### Excluded Combination of Modules

- None.

#### Aims

- To describe the basic ingredients of decision theory, for individuals and for groups, and to apply the theory to a variety of interesting and important problems.

#### Content

- Introduction to decision analysis: utility.
- Uncertainty.
- Statistical decision theory: Bayes decisions.
- Bargaining.
- Game theory.
- Influence diagrams, group decisions and social choice.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve novel and/or complex problems in Decision Theory.
- have a systematic and coherent understanding of theoretical mathematics in the field of Decision Theory.
- have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: Formulating decision problems and solving decision trees.
- Utility, value of money, multi-attribute utility.
- Use of data in decision making, statistical decision theory.
- Sequential decision making.
- Game theory, including two-person zero-sum games.
- Bargaining, including Nash' theory.
- Group decisions and social choice.

Subject-specific Skills:

- In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling.

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.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

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

Lectures | 42 | 2 per week for in Michaelmas and Epiphany; 2 in Easter | 1 Hour | 42 | |

Problems Classes | 8 | Fortnightly in each of terms 1 and 2 | 1 Hour | 8 | |

Preparation and Reading | 150 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

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

Written examination | 3 Hours | 100% |

#### Formative Assessment:

Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ 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