Douglas S. Bridges
Douglas S. Bridges

Sasso Lungo, Dolomites, Italy




Rotating Frames of Reference



Lagrange's equations are used to describe the motion of a particle relative to two rotating frames of reference. This leads to a derivation of Euler's equations for the rotation of a rigid body, and to a discussion of motion relative to the rotating earth. There is nothing original in the article, but the use of Lagrange's equations is interesting.





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.

                                                                                                                                                                                                                                      



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-Universit√§t, Munich, I was invited interviewed by M√ľnchnerUni. 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.