Hiya, there should be many opportunities for maths competitions, challenges, and work experience that you could consider. Here are a few suggestions:
UK Mathematics Trust: This organisation hosts a variety of competitions, including the Junior Mathematical Challenge, Intermediate Mathematical Challenge, and Senior Mathematical Challenge. These are national competitions that are open to students in the UK.
Scottish Mathematical Council: This organisation also hosts a variety of competitions, including the Scottish Mathematical Challenge, which is open to students in Scotland.
Mathematics Enrichment Club: This is a club for students in Scotland who are interested in mathematics. They host a variety of events and competitions throughout the year.
Scottish Universities Summer School in Physics and Astronomy (SUSSP): Although this program is focused on physics and astronomy, it may still be of interest to you as a maths student. SUSSP is a summer school that is held at the University of St Andrews and is designed for advanced undergraduate and graduate students.
Mathematics work experience: You may be able to find work experience opportunities in the field of mathematics through local universities, research institutions, or companies that use mathematics in their operations. You could also consider contacting local maths teachers or tutors to see if they have any suggestions.
Mathematics lectures: Many universities and institutions offer public lectures on mathematics topics. Check the websites of universities and organisations in your area to see if they have any upcoming events.
Remember that the most important thing is to demonstrate your passion for mathematics in your personal statement. Be sure to highlight any extracurricular activities, competitions, or work experience that you have participated in, and explain how these experiences have contributed to your interest in mathematics. Good luck with your application!