Presentation – Year 13, Sam Harding

This week’s presentation was on the topic of infinity and the different types of it that occur throughout mathematics.

After a brief historical introduction, Sam showed us the famous tortoise and hare problem. That was followed by a discussion of improper integrals and fractals which provided an opportunity to introduce some of the Year 12s to calculus and the exponential function. The talk finished with a brief discussion of aleph-null and cardinality of different sets, followed by planning for our lecture trips in the coming weeks.

Speaker – Professor Arttu Rajantie, Imperial College, London

This week the TBSHS Maths and Physics Society were delighted to welcome Professor Arttu Rajantie from Imperial College. His lecture took place during enrichment on Wednesday 26th November and was attended by a large group of year 12 and 13s, as well as several gifted and talented students from lower down the school.

The Professor is an admissions tutor and also a member of Imperial’s Theoretical Physics research group, specialising in applications of quantum field theory in cosmology and particle physics. More relevantly to year 13 students, he has also worked at the Large Hadron Collider and is heavily involved in the MoEDAL experiment. This provided an excellent insight for the year 13s who will be visiting CERN in Geneva next February half term.

In addition to his work at Imperial College, Professor Rajantie is also a visiting professor at King’s College London and an external examiner for the University of Sussex. During the 5 years he spend in Cambridge he worked with Professor Ron Horgan, one of the society’s guests last year and husband to the school’s own languages teacher, Dr. Frances Horgan.

Professor Rajantie’s talk focused on the role of the Higgs field in particle physics and how the mechanism the gives elementary particles their mass actually works. With an analogy that involved rolling a cake tin with a magnet attached along a table, he convincingly demonstrated the symmetrical properties of the Higgs field and how oscillations give rise to mass. In his talk, Professor Rajantie also discussed the standard model of particle physics and the relative strengths of the fundamental forces of nature, explaining why massless force carriers give rise to forces acting over an infinite distance.

There was just enough time afterwards for several questions from the audience and for the presentation of a ‘thank you gift’ as a token of our appreciation. We would like to express our gratitude that Professor Rajantie took time out of his busy schedule to come and visit us and give a very interesting lecture.

Cambridge Physics Centre Lecture – Relativity

This week we took a trip to the Department of Physics at the University of Cambridge where Dr Julia Riley gave a lecture entitled ‘Relativity – understanding the connection between space and time’.

Meeting at Stortford station, we took a very crowded train to Cambridge where we then caught a taxi to the Bragg Building at the famous Cavendish laboratory – the site of discovery of the electron & neutron and where James Clark Maxwell formulated his laws of electromagnetism.

The hour-long lecture introduced us to the idea of inertial frames and Newtonian relativity before moving on to Einstein postulates and his more complicated theory of special relativity. Dr Riley showed how to derive the equation for the Lorentz factor and, through her excellent diagrams, explained the phenomena of length contraction and time dilation. The last few minutes of the lecture were occupied by a brief overview of general relativity and Einstein equivalency principle, as well as a short discussion of black holes.

The lectured was followed afterwards by a trip to Pizza Hut which I’m sure was enjoyed by everyone who attended! We would welcome any other students who wish to come to future lectures or to join the society on a Friday lunchtime.

Presentation – Year 13, Robin Franklin

This week’s presentation was given by Robin Franklin and was on the topic of mathematical proof.

After first looking at some basic proof by direct argument he quickly moved on to proof by contradiction, using the irrationality of square root of 2 and the base-3 logarithm of 2 as examples. The talk ended by showing the proof of Euler’s Identity using the Taylor expansions of sine, cosine and the natural exponent. Our thanks to Robin for his presentation.

Presentation – Year 13, Penny Hart

Our first student presentation of the academic year was by Year 13 student Penny Hart.

Despite the very large audience of almost 30 new Year 12s she gave a very convincing presentation on Fermat’s Last Theorem and modular clock arithmetic.  Afterwards we discussed our plans for the upcoming Festival of Ideas in Cambridge and Battle of Ideas in London, both of which we hope to attend in the future.