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Douglas S. Bridges

Sasso Lungo, Dolomites, Italy

## Differentiating rational power functions without limits

It is shown how to find the derivative of a rational power function by purely algebraic means, without the use of limits. The elementary but non-trivial proofs require the solution of second-order iteration schemes and the associated manipulation of binomial expressions.

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## James Dent's Diagram for Constructive Reverse Math

Extracted, with James's kind permission, from his 2013 PhD thesis, this diagram is an excellent resource for researchers in constructive reverse mathematics, as it shows clearly the interconnections between many principles (intuitionistic, omniscience, anti-Specker, ...) that play an important role in that area. It also has a substantial list of references in which details of the interconnections can be found.

## A Guest Professor Reflects

In January 2004, at the end of a sabbatical year at Ludwig-Maximilians-Universität, Munich, I was invited interviewed by MünchnerUni. Magazin to write down my thoughts about universities in Germany and New Zealand. This is the result of that invitation.

# A Constructive Theory of the Real Line

https://docs.zoho.com/file/5ce0zd6d2f0efc3804f9e92a8641a3004aa23

An axiomatic development of the constructive theory of the real numbers. In my experience, this is a good approach to the real for a course in which analysis, rather than foundational issues, is the main aim.

Notes on fluids and elasticity

These are notes typed, for my own edification, in 1970. They cover: basic continuum mechanics; the dynamics of fluids, including the Navier-Stokes equation; deformation of rods and beams.

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Very rudimentary foundations of mathematics

for advanced high-school students

This brief essay was the consequence of a discussion I had with the Head of Mathematics at Sherborne School in 1981. I had suggested that the School Maths Project might consider including a short discussion piece about the foundations of mathematics. The aim of the discussion piece was to stimulate good pupils in high school to do some reading on their own and to think about questions like `What is Mathematics?' that one does not normally come across even at university.