# Offered by the Department of Mathematics

The BSc Honours (Research Orientation) degree programme in Mathematics intends to provide a deep and broad understanding of mathematics itself by focusing on understanding structures, patterns and conceptual relationships that lie in the core of mathematics. The core of the Mathematics honours degree programme consists of Algebra, Analysis and Topology/ Geometry which are traditionally considered as three main areas of Pure Mathematics. Mathematics is a challenging intellectual pursuit which provides an enormous excitement and satisfaction. The ideas develop in pure mathematics underpin patterns and structures that appear in modern science and technology and hence it plays a vital role in the development of science and technology.

The final year Pure Mathematics research project provides an opportunity for students to develop mathematical independence, experience open-ended inquiry and develop skills in speaking and writing about mathematics with high level sophistication. While the degree programme provides a solid preparation for further studies and research in both pure and applied mathematics, students have numerous opportunities of developing a range of skills such as critical thinking ability, creative problem solving ability and perseverance which are adaptable to diverse career options.

**Degree Aims**

At the end of the 04 years (SLQF Level 6) BSc Honours in Mathematics (Research Orientation) holders should be able to:

- demonstrate thorough and systematic understanding of advanced concepts in Mathematics.
- demonstrate effective mathematical thinking and problem solving skills, through the use of established techniques and development of new techniques.
- formulate problems carefully and precisely, deduce general principles from particular instances and reason logically to draw useful conclusions in the context of research and investigation.
- eloquently communicate & disseminate mathematical ideas clearly and coherently to audiences of varying mathematical sophistication.
- function independently as well as interdependently
- demonstrate leadership skills.
- express emotional and intellectual maturity in a global setting.
- learning and explore new mathematical knowledge independently.

### Entry Requirements

From Physical Science Intake:

To be eligible for this programme from physical science intake, a **minimum GPA of 3.30 for Level I and II AM core courses and AM 1012** taken together and a **GPA of 3.30 for Level I and II PM core courses** are required.

Selection will be based upon the total weighted marks obtained for **PM core courses.**

From Industrial Statistics and Mathematical Finance Intake:

To be eligible for this programme from IS and MF intake, a **minimum GPA of 3.70 for Level I and II PM core courses offered to IS and MF stream** and a **GPA of 3.30 for Level I and II FM core courses** are required.

Selection will be based upon the total weighted marks obtained for **PM core courses**.

### Course Modules

(L – No. of Lecture hours, P – No. of Practical hours, O – Optional, X – Compulsory)

#### Level 3

Course Code | Title | No. of Credits | No. of Hours | |
---|---|---|---|---|

PM 3031 | Linear Algebra | 3C | 45L | X |

PM 3032 | Group Theory | 4C | 60L | X |

PM 3033 | Real Analysis I | 3C | 45L | X |

PM 3034 | Real Analysis II | 3C | 45L | X |

PM 3035 | Complex Analysis | 4C | 60L | X |

PM 3036 | Topology I | 3C | 45L | X |

PM 3037 | Topology II | 3C | 45L | X |

PM 3038 | Analysis in Several Dimensions | 3C | 45L | O |

PM 3031 | Mathematical Methods I | 3C | 45L | O |

PM 3033 | Applied Dynamical Systems | 3C | 30L 30P | O |

PM 3035 | Discrete Applied Mathematics | 3C | 30L 30P | O |

PM 3036 | Applied Graph Theory | 3C | 30L 30P | O |

PM 3037 | Mathematical Methods II | 3C | 45L | O |

#### Level 4

Course Code | Title | No. of Credits | No. of Hours | |
---|---|---|---|---|

PM 4031 | Research Project | 8C | 240P | X |

PM 4032 | Commutative Algebra | 4C | 60L | X |

PM 4033 | Field Theory and Galois Theory | 4C | 60L | X |

PM 4034 | Measure Theory and Integration | 4C | 60L | X |

PM 4035 | Functional Analysis | 4C | 60L | X |

PM 4036 | Topological Spaces | 4C | 60L | O |

PM 4037 | Differential Geometry | 4C | 60L | O |

PM 4038 | Number Theory | 4C | 60L | O |

PM 4032 | Advanced Optimization | 3C | 45L | O |

AM 4033 | Non-Linear Programming | 3C | 45L | O |

AM 4038 | Stochastic Calculus | 3C | 30L 30P | O |