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# Category Archives: teaching

## The future of universities

Film was one of the great inventions of the nineteenth century. For a century and a half, it was developed and improved, innovations such as colour and moving pictures were made, and photographers used it in artistic and creative ways. … Continue reading

## Mathematical Structures: coda

At the end of last term, my colleague Konstantin Ardakov took the final week of lectures in Mathematical Structures so I could go to Lisbon. This week, I am repaying the debt. The module is Introduction to Algebra; many of … Continue reading

## Mathematical Structures, 10

I will be in Portugal next week, and one of my colleagues has offered to take the lectures in the final week of term. But I managed to get to where I wanted to get; the last few lectures will … Continue reading

## History

Ten years ago, Queen Mary had a study programme in Discrete Mathematics. We were one of the first universities in Britain to do this, and I believe they invented a special UCAS code for the course. The study programme was … Continue reading

Posted in mathematics, teaching
Tagged codes, designs, discrete mathematics, finite geometry
1 Comment

## Mathematical Structures, 9

The last two weeks of the course are about proofs: how to construct them, how to read them, how to spot false proofs, and so on. In keeping with the spirit of the course, we have seen many proofs along … Continue reading

## Mathematical Structures, 8

Complex numbers this week bring us to the end of our journey through the number systems. I found this much easier going, and I hope the students did too. Complex numbers provided conceptual difficulties for mathematicians, who were reluctant to … Continue reading

Posted in exposition, teaching
Tagged complex numbers, De Moivre's Theorem, Euler's formula, solving the cubic
4 Comments

## Mathematical Structures, 7

This week, the test is over, and it’s back to work, on the real numbers. In keeping with the general theme of the course, real numbers are not defined as Dedekind cuts or Cauchy sequences, but as something much more … Continue reading

Posted in exposition, teaching
Tagged Achilles and the tortoise, Principle of the Supremum, real numbers, square roots
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## Mathematical Structures, 6.5

I wasn’t planning to post about the course this week, since it is revision week. But there are a few things to report: we had the test (more about that later); and I got back the summary of the student … Continue reading

## Mathematical Structures, 6

The main topic this week was integers, divisibility, and Euclid’s algorithm for greatest common divisor. How do you construct the integers from the natural numbers? There are two ways: You could say that Z = N∪{0}∪{−n:n∈N}. That is, an integer is either … Continue reading

## Mathematical structures, 5

When I commuted from Oxford, the worst part of the journey was the Hammersmith & City line from Paddington to Stepney Green, twelve stops. So I used to count off the twelve weeks of the semester as stops on that … Continue reading