Maths and computer science · Ambitious · Dissertation

How search engines rank pages: a maths EPQ idea

Why it works as an EPQ

The random-surfer model turns ranking into a matrix problem you can solve for a small web you build.

Scope and difficulty

Ambitious. Ambitious. Further Maths matrices help a lot; keep the network small.

The maths

Builds on these A Level topics: Probability · Sequences and series.

You would learn:

• Matrices and matrix powers
• Markov chains and steady states
• Eigenvectors (informally)

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Build a small network of pages and its transition matrix.
2. Find the steady state by repeated multiplication.
3. Explain the damping factor and why it is needed.
4. Show how adding pages and links changes rankings, and judge defences.

Pitfalls

• Claiming to describe how any company ranks pages today.
• Matrix errors from inconsistent row and column conventions.

Where to start reading

• Search for: PageRank random surfer Markov chain example
• Search for: Markov chain steady state matrix power

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All maths and computer science ideas · all 93 ideas

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