EXAMPLE TOPICS, RESEARCH QUESTIONS & APPROACHES
MAINLY THEORETICAL ESSAYS
Topic: Cryptography
Research question: What is RSA (Rivest–Shamir–Adleman) encryption, and how does it help make the internet secure?
Outline of approach: Explain carefully how RSA works, making sure you show a full understanding of any mathematics used that is beyond the syllabus. Explain how this is used to make online transactions secure.
Topic: To infinity and beyond
Research question: How many infinities are there?
Outline of approach: Explore countably infinite sets, explaining concepts clearly and proving your ideas. Progress to the uncountable continuum and discuss how this might be extended further.
Topic: Fractal dimension
Research question: What are fractals, and what is fractal dimension? OR Length of a coastline
Outline of approach: Explain how fractals develop and explain their importance, perhaps exploring some limit problems such as finite area and infinite perimeter. From here, you could progress to the length of the coastline of a favourite island or to the idea of fractal dimension.
MAINLY PRACTICAL ESSAYS
Topic: The last rhinoceros
Research question: How long do the rhinos have left?
Outline of approach: Explore both the population size and the habitat of the rhinoceros. Can you come up with a realistic model for the population size or the habitat area? According to the model, which will reach zero first: population or habitat?
Topic: Getting to school by public transport
Research question: What is the quickest and/or cheapest route from your home to school?
Outline of approach: Consider the transport system in your area and compare different ways of getting to school. Estimate travel and walking times; consider an algorithm such as Dijkstra and decide on your preferred route.
Topic: Winning the English football Premier League
Research question: What is “home advantage”, and are Premier League football champions equally successful away from home?
Outline of approach: scrape raw data from the English Premier League football results to examine the distribution of goals scored at home and away. Is there a significant home advantage? Are the champions able to overcome this in their away games?
MAINLY THEORETICAL ESSAYS
Topic: Cryptography
Research question: What is RSA (Rivest–Shamir–Adleman) encryption, and how does it help make the internet secure?
Outline of approach: Explain carefully how RSA works, making sure you show a full understanding of any mathematics used that is beyond the syllabus. Explain how this is used to make online transactions secure.
Topic: To infinity and beyond
Research question: How many infinities are there?
Outline of approach: Explore countably infinite sets, explaining concepts clearly and proving your ideas. Progress to the uncountable continuum and discuss how this might be extended further.
Topic: Fractal dimension
Research question: What are fractals, and what is fractal dimension? OR Length of a coastline
Outline of approach: Explain how fractals develop and explain their importance, perhaps exploring some limit problems such as finite area and infinite perimeter. From here, you could progress to the length of the coastline of a favourite island or to the idea of fractal dimension.
MAINLY PRACTICAL ESSAYS
Topic: The last rhinoceros
Research question: How long do the rhinos have left?
Outline of approach: Explore both the population size and the habitat of the rhinoceros. Can you come up with a realistic model for the population size or the habitat area? According to the model, which will reach zero first: population or habitat?
Topic: Getting to school by public transport
Research question: What is the quickest and/or cheapest route from your home to school?
Outline of approach: Consider the transport system in your area and compare different ways of getting to school. Estimate travel and walking times; consider an algorithm such as Dijkstra and decide on your preferred route.
Topic: Winning the English football Premier League
Research question: What is “home advantage”, and are Premier League football champions equally successful away from home?
Outline of approach: scrape raw data from the English Premier League football results to examine the distribution of goals scored at home and away. Is there a significant home advantage? Are the champions able to overcome this in their away games?