Frontiers in Mathematics - MAT00125M

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Module summary

This module will give students an opportunity to learn about modern topics in mathematics, which are at the forefront of current research. Each student will choose 3 from a list of available topics and the topics running in a given year will be selected based on popularity. Each topic will run either as regular lectures or as directed learning (with one seminar and 3 drop-in sessions, one each week), depending on the number of students.

Related modules

Details about prerequisites for specific topics will be given here.

Pre-requisite modules

For all students: Pure or Applied Stream in year 2. There might be additional topic-specific prerequisites.

Co-requisite modules

Only for specific topics

Module will run

Occurrence	Teaching period
A	Semester 2 2025-26

Module aims

This module will give students an opportunity to learn about modern topics in mathematics, which are at the forefront of current research. Each student will choose 3 from a list of available topics and the topics running in a given year will be selected based on popularity. Each topic will run either as regular lectures or as directed learning (with one seminar and 3 drop-in sessions, one each week), depending on the number of students.

Module learning outcomes

By the end of the module, students will be able to:

1. Solve advanced problems involving modern mathematical tools in 3 different cutting edge research areas

2. Understand research papers in 3 different cutting edge research areas

3. Critically evaluate literature and formulate new ideas and conjectures in 3 different cutting edge research areas

Module content

This module will give students an opportunity to learn about modern topics in mathematics, which are at the forefront of current research. Each student will choose 3 from a list of available topics and the topics running in a given year will be selected based on popularity. Example topics are:

• Multi-valued functions and asymptotic analysis

• Laplace Integrals and differential equations

• Topics in Semigroup Theory

• Topics in Functional Analysis

• Introduction to conformal field theory

• Mathematical methods of biomechanics

• Statistical mechanics and biological matter

• Applications of tiling theory in virology

• Applications of group theory in virology

• Interacting QFT with path integrals

• QFT on curved spacetimes

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

This will depend on the choice of topics.