Undergraduate Programme and Module Handbook 2024-2025

# Module MATH2617: Elementary Number Theory II

## Department: Mathematical Sciences

### MATH2617: Elementary Number Theory II

Type | Open | Level | 2 | Credits | 10 | Availability | Available in 2024/2025 | Module Cap | Location | Durham |
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#### Prerequisites

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

#### Corequisites

- None.

#### Excluded Combination of Modules

- None.

#### Aims

- To provide and introduction to the basics of number theory.

#### Content

- Review of basic features of integers.
- Congruences and modular arithmetic
- Quadratic reciprocity
- Diophantine equations

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Number Theory.
- have an awareness of the abstract concepts of theoretical mathematics in the field of Number Theory.
- have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: Fundamental theorem of arithmetic, modular arithmetic and chinese remainder theorem.
- Diophantine equations.

Subject-specific Skills:

- In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Abstract reasoning.

Key Skills:

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

- Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
- Weekly/Fortnightly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
- Tutorials provide active engagement and feedback to the learning process.
- 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 | 22 | 2 per week in Michaelmas and in first week of Easter | 1 Hour | 22 | |

Tutorials | 5 | Fortnightly in Michaelmas and one in Easter | 1 Hour | 5 | ■ |

Problems Classes | 4 | Fortnightly in Michaelmas | 1 Hour | 4 | |

Preparation and Reading | 69 | ||||

Total | 100 |

#### Summative Assessment

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

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

End of year written examination | 2 hours | 100% | Yes |

#### Formative Assessment:

Fortnightly or Weekly written assignments.

■ 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