Maths Circle Lecture #2
Thanks to Dr Richard Lissaman for delivering the second lecture in our Maths Circle Lecture series.
Each year, Wilson’s hosts a series of Maths Circle Lectures on new and exciting developments in Mathematics delivered by experts in these fields. In the second lecture of the series, we were delighted to host Dr Richard Lissaman from the University of Warwick, who gave an exciting and perceptive talk on the Google Page Rank Algorithm and Machine Learning.
Dr Lissaman began by giving a brief introduction to matrix multiplication, then moving on to explain the use of such techniques in Google’s Page Rank Algorithm, which is one of the reasons for the company’s huge commercial success in the late 90s. The algorithm is based on ranking search results based on, their relevance to the initial search as well as the reputability of the source, something other search engines did not offer users at the time.
This provided a nice segue to introduce the concept of Markov chains, which I found extremely interesting and to be one of the highlights of the talk. In simple terms, Markov chains are mathematical models which are used to predict the probability of a sequence of events occurring based on the most recent event. The example Dr. Lissaman gave was determining the probability of whether it would be sunny or rainy tomorrow, based on the weather today.
The talk then shifted focus to machine learning, more specifically discussing the operation of neural networks, explaining their function through topics of linear regression and gradient descent. Finally, Dr. Lissaman showed us a demonstration of a neural network in action (you can try it out yourself: https://playground.tensorflow.org), with it being exceptionally fascinating to see the connections between different ‘neurons’ strengthen and fade in real time as the network repeated sought to solve a problem.
We at Wilson’s greatly appreciate the opportunities that are available to us in the form of competitions and lectures such as this, and hope that Dr. Lissaman will continue to visit and deliver such engaging talks.
Report written by Amey (Year 12)
Ever wondered how Google always gives you the top results you’ve been looking for? Richard Lissaman, a professor at the University of Warwick, gave us some interesting insight behind how the Google page rank algorithm works, using matrices and eigenvectors to keep track of the “scores” of each web page.
Beyond this, Dr Lissaman talked about the interesting world of machine learning, that so many companies have now utilised, and a “computer scientist” approach to finding a suitable model that fits a training set of data which can be used to make predictions with new, unseen data. Probably the highlight of the talk was at the end where Dr Lissaman got to show us how this worked in action through a visual example of a model trying to match a data set in real time, where we got to see how it could both succeed and struggle when faced with different data sets. In the end, we were left with some interesting visuals and some final thoughts on the process and how we could improve the model, but also, on some of the costs that we might need to consider when doing so.
Report written by Felix (Year 12)
